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Your search keyword '"PEIRONE, ROBERTO"' showing total 7 results
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7 results on '"PEIRONE, ROBERTO"'

2. Self-similar Energies on Fractals with Connected Interior

Author

Peirone, Roberto and Peirone, Roberto

Subjects
Eigenfunctions, Dirichlet forms, Fractals, Mathematics::Number Theory, [MATH.MATH-SP] Mathematics [math]/Spectral Theory [math.SP], [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

In this paper, I prove the existence of a regular eigenform for suitable weights, on fractals with the only assumptions that the boundary cells are separated and the union of the interior cells is connected. This result improves previous results, and works for many of the usually considered finitely ramified fractals.

Published
2009

3. EIGENFORMS ON FRACTALS WITH CONNECTED INTERIOR AND THREE VERTICES.

Author

ELIA, MATTEO and PEIRONE, ROBERTO

Subjects
*GEOMETRIC vertices, *FRACTALS, *COEFFICIENTS (Statistics), *MATHEMATICS, *FINITE geometries
Abstract

An important problem in analysis on fractals is the existence and the determination of an eigenform on a given finitely ramified fractal. It is known that on every fractal either with three vertices or with connected interior, an eigenform exists for suitable weights on the cells. In this paper, we prove that if the fractal has three vertices and connected interior, the form having all coefficients equal to 1 is an eigenform for suitable weights on the cells. [ABSTRACT FROM AUTHOR]

Published
2018
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4. Scaling distances on finitely ramified fractals.

Author

Peirone, Roberto

Subjects
*FRACTAL analysis, *MEASUREMENT of distances, *FRACTALS, *MATRICES (Mathematics), *DISTANCES, *LIPSCHITZ spaces
Abstract

In this article we study two problems about the existence of a distance d on a given fractal having certain properties. In the first problem, we require that the maps ψi defining the fractal be Lipschitz of prescribed constants less than 1 with respect to the distance d, and in the second one, we require that arbitrary compositions of the maps ψi be uniformly bi-Lipschitz of related constants. Both problems have been investigated previously by other authors. In this article, on a large class of finitely ramified fractals,we prove that these two problems are equivalent and give a necessary and sufficient condition for the existence of such a distance. Such a condition is expressed in terms of asymptotic behavior of the product of certain matrices associated to the fractal. [ABSTRACT FROM AUTHOR]

Published
2017
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5. Uniqueness of eigenforms on fractals - II.

Author

Peirone, Roberto

Subjects
*FRACTAL analysis, *GEOMETRIC analysis, *DIRICHLET forms, *MATHEMATICAL forms, *CHARACTERS sums (Mathematics)
Abstract

I give an explicitly verifiable necessary and sufficient condition for the uniqueness of the eigenform on finitely ramified fractals, once an eigenform is known. This improves the results of my previous paper [16], where I gave some necessary and some sufficient conditions, and with a relatively mild additional requirement on the known eigenform. The result of this paper can be interpreted as a uniqueness result for self-similar energies on finitely ramified fractals. [ABSTRACT FROM AUTHOR]

Published
2015
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6. Uniqueness of eigenforms on fractals.

Author

Peirone, Roberto

Subjects
*FRACTALS, *DIRICHLET forms, *EUCLIDEAN algorithm, *GASKETS, *EIGENFUNCTIONS, *INVARIANT subspaces
Abstract

I give some rather general criteria for the uniqueness of the eigenform on finitely ramified fractals. In particular, I characterize the uniqueness in the case of four vertices with some additional condition, and give some examples of non-tree symmetric fractals where the eigenform is not unique. [ABSTRACT FROM AUTHOR]

Published
2014
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7. Existence of Self-similar Energies on Finitely Ramified Fractals

Author

Roberto Peirone and Peirone, Roberto

Subjects
Discrete mathematics, Eigenforms, Partial differential equation, General Mathematics, Mathematics::Number Theory, Structure (category theory), [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Energies, Operator (computer programming), Fractal, Fractals, Settore MAT/05 - Analisi Matematica, Eigenform, Analysis, Eigenvalues and eigenvectors, Mathematics, Boundary cell
Abstract

A self-similar energy on finitely ramified fractals can be constructed starting from an eigenform, i.e., an eigenvector of a special operator defined on the fractal. In this paper, we prove two existence results for regular eigenforms that consequently are existence results for self-similar energies on finitely ramified fractals. The first result proves the existence of a regular eigenform for suitable weights on fractals, assuming only that the boundary cells are separated and the union of the interior cells is connected. This result improves previous results and applies to many finitely ramified fractals usually considered. The second result proves the existence of a regular eigenform in the general case of finitely ramified fractals in a setting similar to that of P.C.F. self-similar sets considered, for example, by R. Strichartz in [11]. In this general case, however, the eigenform is not necessarily on the given structure, but is rather on only a suitable power of it. Nevertheless, as the fractal generated is the same as the original fractal, the result provides a regular self-similar energy on the given fractal.

Published
2011

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