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Your search keyword '"Struppa, Daniele C."' showing total 90 results
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90 results on '"Struppa, Daniele C."'

1. Reconstructing Superoscillations Buried Deeply in Noise

Author

White, Derek D., Zhang, Shunxing, Soda, Barbara, Kempf, Achim, Struppa, Daniele C., Jordan, Andrew N., and Howell, John C.

Subjects
Physics - Optics
Abstract

We utilize a method using frequency combs to construct waves that feature superoscillations - local regions of the wave that exhibit a change in phase that the bandlimits of the wave should not otherwise allow. This method has been shown to create superoscillating regions that mimic any analytic function - even ones well outside the bandlimits - to an arbitrary degree of accuracy. We experimentally demonstrate that these waves are extremely robust against noise, allowing for accurate reconstruction of a superoscillating target function thoroughly buried in noise. We additionally show that such a construction can be easily used to range-resolve a signal well below the commonly accepted fundamental limit.

Published
2024

2. Short-time Fourier transform and superoscillations

Author

Alpay, Daniel, De Martino, Antonino, Diki, Kamal, and Struppa, Daniele C.

Subjects
Mathematics - Functional Analysis
Abstract

In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time Fourier transform acts on superoscillation sequences. We then apply the supershift property to prove that the short-time Fourier transform preserves the superoscillatory behavior by taking the limit. It turns out that these computations lead to interesting connections with various features of time-frequency analysis such as Gabor spaces, Gabor kernels, Gabor frames, 2D-complex Hermite polynomials, and polyanalytic functions. We treat different cases depending on the choice of the window function moving from the general case to more specific cases involving the Gaussian and the Hermite windows. We consider also an evolution problem with an initial datum given by superoscillation multiplied by the time-frequency shifts of a generic window function. Finally, we compute the action of STFT on the approximating sequences with a given Hermite window., Comment: to appear in Applied and Computational Harmonic Analysis

Published
2024

10. Superoscillations and Fock spaces

Author

Alpay, Daniel, Colombo, Fabrizio, Diki, Kamal, Sabadini, Irene, and Struppa, Daniele C.

Subjects
Mathematical Physics
Abstract

In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences with normalized Hermite functions. It turns out that these special wave functions can be constructed also by computing the approximating sequence of the normalized Hermite functions. First, we start by treating the case when a superoscillating sequence is multiplied by the Gaussian function. Then, we extend these calculations to the case of normalized Hermite functions leading to interesting relations with Weyl operators. In particular, we show that the Segal-Bargmann transform maps superoscillating sequences onto a superposition of coherent states. Following this approach, the computations lead to a specific linear combination of the normalized reproducing kernels (coherent states) of the Fock space. As a consequence, we obtain two new integral Bargmann-type representations of superoscillating sequences. We also investigate some results relating superoscillation functions with Weyl operators and Fourier transform.

Published
2023

11. Integral representation of superoscillations via complex Borel measures and their convergence

Author

Behrndt, Jussi, Colombo, Fabrizio, Schlosser, Peter, and Struppa, Daniele C.

Subjects
Mathematical Physics
Abstract

In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some convergence to a plane wave is the standard characterizing feature of a superoscillating function in mathematics and quantum mechanics. Also there exists a certain discrepancy between the representation of superoscillations either as generalized Fourier series, as certain integrals or via special functions. The aim of this work is to close these gaps and give a general definition of superoscillations, covering the well-known examples in the existing literature. Superoscillations will be defined as sequences of holomorphic functions, which admit integral representations with respect to complex Borel measures and converge to a plane wave in the space $\mathcal{A}_1(\mathbb{C})$ of exponentially bounded entire functions.

Published
2023

12. The Mathematics of Painting: the Birth of Projective Geometry in the Italian Renaissance

Author

Gentili, Graziano, Simonutti, Luisa, and Struppa, Daniele C.

Subjects
Mathematics - History and Overview, 00A66, 00A09
Abstract

We show how the birth of perspective painting in the Italian Renaissance led to a new way of interpreting space that resulted in the creation of projective geometry. Unlike other works on this subject, we explicitly show how the craft of the painters implied the introduction of new points and lines (points and lines at infinity) and their projective coordinates to complete the Euclidean space to what is now called projective space. We demonstrate this idea by looking at original paintings from the Renaissance, and by carrying out the explicit analytic calculations that underpin those masterpieces.

Published
2022
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13. A H\'ormander-Fock space

Author

Alpay, Daniel, Colombo, Fabrizio, Diki, Kamal, Sabadini, Irene, and Struppa, Daniele C.

Subjects
Mathematics - Complex Variables
Abstract

In a recent paper we used a basic decomposition property of polyanalytic functions of order $2$ in one complex variable to characterize solutions of the classical $\overline{\partial}$-problem for given analytic and polyanalytic data. Our approach suggested the study of a special reproducing kernel Hilbert space that we call the H\"ormander-Fock space that will be further investigated in this paper. The main properties of this space are encoded in a specific moment sequence denoted by $\eta=(\eta_n)_{n\geq 0}$ leading to a special entire function $\mathsf{E}(z)$ that is used to express the kernel function of the H\"ormander-Fock space. We present also an example of a special function belonging to the class ML introduced recently by Alpay et al. and apply a Bochner-Minlos type theorem to this function, thus motivating further connections with the theory of stochastic processes.

Published
2022

14. H\'ormander's $L^2$-method, $\bar{\partial}$-problem and polyanalytic function theory in one complex variable

Author

Alpay, Daniel, Colombo, Fabrizio, Diki, Kamal, Sabadini, Irene, and Struppa, Daniele C.

Subjects
Mathematics - Complex Variables
Abstract

In this paper we consider the classical $\bar{\partial}$-problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of polyanalytic functions in order to construct particular solutions of this problem and obtain new H\"ormander type estimates using suitable powers of the Cauchy-Riemann operator. We also compute particular solutions of the $\bar{\partial}$-problem for specific polyanalytic data such as the It\^o complex Hermite polynomials and polyanalytic Fock kernels.

Published
2022

15. Super-phenomena in arbitrary quantum observables

Author

Jordan, Andrew N., Aharonov, Yakir, Struppa, Daniele C., Colombo, Fabrizio, Sabadini, Irene, Shushi, Tomer, Tollaksen, Jeff, Howell, John C., and Vamivakas, A. Nick

Subjects
Quantum Physics, Mathematical Physics
Abstract

Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechanical operators as a weak value, where the preselected state is a superposition of eigenstates of the operator with eigenvalues bounded to a range, and the postselection state is a local position. Superbehavior of this operator occurs whenever the operator's weak value exceeds its eigenvalue bound. We give illustrative examples of this effect for total angular momentum and energy. In the later case, we demonstrate a sequence of harmonic oscillator potentials where a finite energy state converges everywhere on the real line, using only bounded superpositions of states whose asymptotic energy vanishes - "energy out of nothing". This limit requires postselecting the particle in a region whose size diverges in the considered limit. We further show that superenergy behavior implies that the state superoscillates in time with a rate given by the superenergy divided by the reduced Planck's constant. This example demonstrates the possibility of mimicking a high-energy state with coherent superpositions of nearly zero-energy states for as wide a spatial region as desired. We provide numerical evidence of these features to further bolster and elucidate our claims., Comment: 9 pages, 5 figures, expanded treatment of time

Published
2022

18. Infinite Order Differential Operators with a Glimpse to Applications to Superoscillations

Author

Aoki, Takashi, Okada, Yasunori, Sabadini, Irene, Struppa, Daniele C., Gohberg, Israel, Founding Editor, Ball, Joseph A., Series Editor, Böttcher, Albrecht, Series Editor, Dym, Harry, Series Editor, Langer, Heinz, Series Editor, Tretter, Christiane, Series Editor, Alpay, Daniel, editor, Behrndt, Jussi, editor, Colombo, Fabrizio, editor, Sabadini, Irene, editor, and Struppa, Daniele C., editor

Published
2023
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19. Spherical Series and Differential

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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20. Integral Representations

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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21. Fractional Transformations and the Unit Ball

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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22. Singularities

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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23. Infinite Products

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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24. Zeros

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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25. Definitions and Basic Results

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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26. Regular Power Series

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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27. Maximum Modulus Theorem and Applications

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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28. Generalizations

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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29. Applications

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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30. Function Theory Over Non-symmetric Slice Domains

Author

Gentili, Graziano, Stoppato, Caterina, Struppa, Daniele C., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Gentili, Graziano, Stoppato, Caterina, and Struppa, Daniele C.

Published
2022
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31. Assessment of Vegetation Changes in Saudi Arabia Using Harmonic Analysis and ENSO Indices

Author

Li, Wenzhao, El-Askary, Hesham, Qurban, Mohamed, Manikandan, K. P., Ashri, Mohammad H. Makkawi, Piechota, Thomas, Struppa, Daniele C., Pisello, Anna Laura, Editorial Board Member, Hawkes, Dean, Editorial Board Member, Bougdah, Hocine, Editorial Board Member, Rosso, Federica, Editorial Board Member, Abdalla, Hassan, Editorial Board Member, Boemi, Sofia-Natalia, Editorial Board Member, Mohareb, Nabil, Editorial Board Member, Mesbah Elkaffas, Saleh, Editorial Board Member, Bozonnet, Emmanuel, Editorial Board Member, Pignatta, Gloria, Editorial Board Member, Mahgoub, Yasser, Editorial Board Member, De Bonis, Luciano, Editorial Board Member, Kostopoulou, Stella, Editorial Board Member, Pradhan, Biswajeet, Editorial Board Member, Abdul Mannan, Md., Editorial Board Member, Alalouch, Chaham, Editorial Board Member, O. Gawad, Iman, Editorial Board Member, Nayyar, Anand, Editorial Board Member, Amer, Mourad, Series Editor, El-Askary, Hesham, editor, Erguler, Zeynal Abiddin, editor, Karakus, Murat, editor, and Chaminé, Helder I., editor

Published
2022
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37. A Hörmander–Fock space.

Author

Alpay, Daniel, Colombo, Fabrizio, Diki, Kamal, Sabadini, Irene, and Struppa, Daniele C.

Abstract

In a recent paper, we used a basic decomposition property of polyanalytic functions of order 2 in one complex variable to characterize solutions of the classical $ \bar {\partial } $ ∂ ¯ -problem for given analytic and polyanalytic data. Our approach suggested the study of a special reproducing kernel Hilbert space that we call the Hörmander–Fock space that will be further investigated in this paper. The main properties of this space are encoded in a specific moment sequence denoted by $ \eta =(\eta _n)_{n\geq ~0} $ η = (η n) n ≥ 0 leading to a special entire function $ \mathsf {E}(z) $ E (z) that is used to express the kernel function of the Hörmander–Fock space. We present also an example of a special function belonging to the class Mittag-Leffler (ML) introduced recently by Alpay et al. and apply a Bochner–Minlos type theorem to this function, thus motivating further connections with the theory of stochastic processes. [ABSTRACT FROM AUTHOR]

Published
2024
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40. Monotonicity of certain left and right Riemann sums

Author

Alpay, Daniel, Behrndt, Jussi, Colombo, Fabrizio, Sabadini, Irene, Struppa, Daniele C., Bouthat, Ludovick, Mashreghi, Javad, Morneau-Guérin, Frédéric, Alpay, Daniel, Behrndt, Jussi, Colombo, Fabrizio, Sabadini, Irene, Struppa, Daniele C., Bouthat, Ludovick, Mashreghi, Javad, and Morneau-Guérin, Frédéric

Abstract

In an otherwise instructive 2012 article, Szilard provided a flawed argument purportedly establishing that the left (resp. right) Riemann sum of f(x) = 1/1+x^2 with respect to the uniform partition of [0,1] into n equal intervals is monotonically decreasing (resp. increasing) relative to n. A few years later, D. Borwein, J. M. Borwein and B. Sims developed a symmetrization technique that allowed them to provide a rectified proof that the right Riemann sum of f(x) = 1/1+x^2 really is monotonically increasing relative to n. They also provided numerical evidence suggesting that the left Riemann sum is decreasing but they did not succeed in proving it. In the first part of this paper, we exploit the symmetrization technique to provide a proof that the left Riemann sum is indeed decreasing with respect to n. Subsequently, we show, using elementary calculus techniques, some trigonometry computations as well as calculations involving generalized binomial coefficients, that the left and right Riemann sums with respect to the uniform partition of [0,1] of the family of functions of the form sin^p(pi x) are monotonically increasing relative to n, regardless of the value of p in (0,2). In so doing, we answer a problem that came up in the context of foundational research on questions situated at the intersection of matrix theory and metric geometry

Published
2023

41. The Merchant and the Mathematician: Commerce and Accounting

Author

Gentili, Graziano, Simonutti, Luisa, Struppa, Daniele C, Gentili, Graziano, Simonutti, Luisa, and Struppa, Daniele C

Abstract

In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved.

Published
2023

42. Musica

Author

Gentili, Graziano, Simonutti, Luisa, and Struppa, Daniele C.

Abstract

La musica si sviluppa e appare quando permettiamo ai numeri di acquisire un aspetto dinamico e di creare, attraverso la loro crescita, le varie chiavi che permettono la ricchezza della tessitura musicale. Questa idea era semplicemente accennata nell'opera di Platone, ma la sua importanza per la visione filosofica del mondo non può essere sottovalutata. In questo articolo iniziamo a discutere quella che probabilmente è la prima testimonianza scritta di un tentativo di creare un buon temperamento e poi seguiamo l'approccio dei pitagorici, i cui problemi hanno costretto i musicisti, nei secoli successivi fino al Rinascimento e all'inizio dell'epoca moderna, a proporre molte varianti diverse., RESEARCH TRENDS IN HUMANITIES Education & Philosophy, Vol 10 (2023): RTH - Education & Philosophy

Published
2023
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43. Hörmander’s L2-Method, ∂¯-Problem and Polyanalytic Function Theory in One Complex Variable.

Author

Alpay, Daniel, Colombo, Fabrizio, Diki, Kamal, Sabadini, Irene, and Struppa, Daniele C.

Abstract

In this paper we consider the classical ∂ ¯ -problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of polyanalytic functions in order to construct particular solutions of this problem and obtain new Hörmander type estimates using suitable powers of the Cauchy-Riemann operator. We also compute particular solutions of the ∂ ¯ -problem for specific polyanalytic data such as the Itô complex Hermite polynomials and polyanalytic Fock kernels. [ABSTRACT FROM AUTHOR]

Published
2023
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47. Arithmetic and Analysis of the Series , Part II

Author

Sebbar, Ahmed, Gohberg, Israel, Founding Editor, Ball, Joseph A., Series Editor, Böttcher, Albrecht, Series Editor, Dym, Harry, Series Editor, Langer, Heinz, Series Editor, Tretter, Christiane, Series Editor, Alpay, Daniel, editor, Behrndt, Jussi, editor, Colombo, Fabrizio, editor, Sabadini, Irene, editor, and Struppa, Daniele C., editor

Published
2023
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48. Lipschitz-Type Bounds for Functions of Operators with Noncompact Perturbations

Author

Skripka, Anna, Gohberg, Israel, Founding Editor, Ball, Joseph A., Series Editor, Böttcher, Albrecht, Series Editor, Dym, Harry, Series Editor, Langer, Heinz, Series Editor, Tretter, Christiane, Series Editor, Alpay, Daniel, editor, Behrndt, Jussi, editor, Colombo, Fabrizio, editor, Sabadini, Irene, editor, and Struppa, Daniele C., editor

Published
2023
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49. Automorphisms of Hyper-Reinhardt Free Spectrahedra

Author

McCullough, Scott, Gohberg, Israel, Founding Editor, Ball, Joseph A., Series Editor, Böttcher, Albrecht, Series Editor, Dym, Harry, Series Editor, Langer, Heinz, Series Editor, Tretter, Christiane, Series Editor, Alpay, Daniel, editor, Behrndt, Jussi, editor, Colombo, Fabrizio, editor, Sabadini, Irene, editor, and Struppa, Daniele C., editor

Published
2023
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50. Fluid–Plate Interaction with Kelvin-Voigt Damping and Bending Moment at the Interface: Well-posedness, Spectral Analysis, Uniform Stability

Author

Mahawattege, Rasika, Triggiani, Roberto, Gohberg, Israel, Founding Editor, Ball, Joseph A., Series Editor, Böttcher, Albrecht, Series Editor, Dym, Harry, Series Editor, Langer, Heinz, Series Editor, Tretter, Christiane, Series Editor, Alpay, Daniel, editor, Behrndt, Jussi, editor, Colombo, Fabrizio, editor, Sabadini, Irene, editor, and Struppa, Daniele C., editor

Published
2023
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