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734 results on '"Feichtinger H"'

1. Modulation spaces, multipliers associated with the special affine Fourier transform

Author

Biswas, M. H. A., Feichtinger, H. G., and Ramakrishnan, R.

Subjects
Mathematics - Functional Analysis, 42A38, 42B25, 42B35
Abstract

We study some fundamental properties of the special affine Fourier transform (SAFT) in connection with the Fourier analysis and time-frequency analysis. We introduce the modulation space $\boldsymbol {M}^{r,s}_A$ in connection with SAFT and prove that if a bounded linear operator between new modulation spaces commutes with $A$-translation, then it is a $A$-convolution operator. We also establish H\"{o}rmander multiplier theorem and Littlewood-Paley theorem associated with the SAFT., Comment: 26 pages

Published
2022

2. Navier-Stokes Equation in Super-Critical Spaces $E^s_{p,q}$

Author

Feichtinger, H., Gröchenig, K., Li, Kuijie, and Wang, Baoxiang

Subjects
Mathematics - Analysis of PDEs, 35Q55, 42B35, 42B37
Abstract

In this paper we develop a new way to study the global existence and uniqueness for the Navier-Stokes equation (NS) and consider the initial data in a class of modulation spaces $E^s_{p,q}$ with exponentially decaying weights $(s<0, \ 1

Published
2019

3. Asymptotic boundary forms for tight Gabor frames and lattice localization domains

Author

Feichtinger, H. G., Nowak, K., and Pap, M.

Subjects
Mathematics - Classical Analysis and ODEs, 47B35, 42C15, 81Q20
Abstract

We consider Gabor localization operators $G_{\phi,\Omega}$ defined by two parameters, the generating function $\phi$ of a tight Gabor frame $\{\phi_\lambda\}_{\lambda \in \Lambda}$, parametrized by the elements of a given lattice $\Lambda \subset \Bbb{R}^2$, i.e. a discrete cocompact subgroup of $\Bbb{R}^2$, and a lattice localization domain $\Omega \subset \Bbb{R}^2$ with its boundary consisting of line segments connecting points of $\Lambda$. We find an explicit formula for the boundary form $BF(\phi,\Omega)=\text{A}_\Lambda \lim_{R\rightarrow \infty}\frac{PF(G_{\phi,R\Omega})}{R}$, the normalized limit of the projection functional $PF(G_{\phi,\Omega})=\sum_{i=0}^{\infty}\lambda_i(G_{\phi,\Omega})(1-\lambda_i(G_{\phi,\Omega}))$, where $\lambda_i(G_{\phi,\Omega})$ are the eigenvalues of the localization operators $G_{\phi,\Omega}$ applied to dilated domains $R\Omega$, $R$ is an integer and $\text{A}_\Lambda$ is the area of the fundamental domain of the lattice $\Lambda$., Comment: 35 pages

Published
2015

4. Gabor analysis over finite Abelian groups

Author

Feichtinger, H. G., Kozek, W., and Luef, F.

Subjects
Mathematics - Group Theory
Abstract

The topic of this paper are (multi-window) Gabor frames for signals over finite Abelian groups, generated by an arbitrary lattice within the finite time-frequency plane. Our generic approach covers simultaneously multi-dimensional signals as well as non-separable lattices. The main results reduce to well-known fundamental facts about Gabor expansions of finite signals for the case of product lattices, as they have been given by Qiu, Wexler-Raz or Tolimieri-Orr, Bastiaans and Van-Leest, among others. In our presentation a central role is given to spreading function of linear operators between finite-dimensional Hilbert spaces. Another relevant tool is a symplectic version of Poisson's summation formula over the finite time-frequency plane. It provides the Fundamental Identity of Gabor Analysis.In addition we highlight projective representations of the time-frequency plane and its subgroups and explain the natural connection to twisted group algebras. In the finite-dimensional setting these twisted group algebras are just matrix algebras and their structure provides the algebraic framework for the study of the deeper properties of finite-dimensional Gabor frames., Comment: Revised version: two new sections added, many typos fixed

Published
2007

5. Wiener Amalgam Spaces for the Fundmental Identity of Gabor Analysis

Author

Feichtinger, H. G. and Luef, F.

Subjects
Mathematics - Functional Analysis
Abstract

In the last decade it has become clear that one of the central themes within Gabor analysis (with respect to general time-frequency lattices) is a duality theory for Gabor frames, including the Wexler-Raz biorthogonality condition, the Ron-Shen's duality principle or Janssen's representation of a Gabor frame operator. All these results are closely connected with the so-called {\it Fundamental Identity of Gabor Analysis}, which we derive from an application of Poisson's summation formula for the symplectic Fourier transform. The new aspect of this presentation is the description of range of the validity of this Fundamental Identity of Gabor Analysis using Wiener amalgam spaces and Feichtinger's algebra $S_0(\R^d)$. Our approach is inspired by Rieffel's use of the Fundamental Identity of Gabor Analysis in the study of operator algebras generated by time-frequency shifts along a lattice, which was later independently rediscovered by Tolmieri/Orr, Janssen, and Daubechies et al., and Feichtinger/Kozek at various levels of generality, in the context of Gabor analysis., Comment: Some typos are fixed

Published
2005

9. Banach Gelfand Triples for Gabor Analysis

Author

Feichtinger, H., Luef, F., Cordero, E., Morel, J. -M., editor, Takens, F., editor, Teissier, B., editor, Feichtinger, Hans G., Helffer, Bernard, Lamoureux, Michael P., Lerner, Nicolas, Toft, Joachim, Rodino, Luigi, editor, and Wong, M. W., editor

Published
2008
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10. Niere und ableitende Harnwege

Author

Ulrich, W., Ratschek, M., Susani, M., Feichtinger, H., Kain, R., Asboth, F., Österreichischen Gesellschaft für Pathologie, Asboth, F., editor, Beham, A., editor, Beer, F., editor, Böhm, G., editor, Breitenecker, G., editor, Budka, H., editor, Chott, A., editor, Denk, H., editor, Dietze, O., editor, Dinges, H. P., editor, Drlicek, M., editor, Faschinger, Ch., editor, Feichtinger, H., editor, Feigl, W., editor, Fellinger-Augustin, I., editor, Hanak, H., editor, Höfler, H., editor, Hönigsmann, H., editor, Hofstädter, F., editor, Holzner, J. H., editor, Kain, R., editor, Kerl, H., editor, Kleinert, R., editor, Klimpfinger, M., editor, Lax, S., editor, Leibl, W., editor, Mikuz, G., editor, Neuhold, N., editor, Öhlinger, W., editor, Popper, H. H., editor, Radaszkiewicz, Th., editor, Ratschek, M., editor, Reiner, A., editor, Salzer-Kuntschik, M., editor, Schmalzer, E., editor, Schmid, Ch., editor, Schmid, K. W., editor, Susani, M., editor, Syre, G., editor, Ullrich, R., editor, Ulrich, W., editor, Weger, R. A., editor, Wüstinger, Ch., editor, and Wuketich, St., editor

Published
1994
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14. Schilddrüsenkarzinom

Author

Niederle, B., Zimmermann, G., Ladurner, D., Behmel, A., Dam, K., Depisch, D., Dudzczak, R., Feichtinger, H., Fink, M., Flores, J., Fridrich, L., Fritzsche, H., Galvan, G., Haas, O. A., Kaserer, K., Kletter, K., Kroiss, A., Langsteger, W., Lax, S. F., Lind, P., Manzl, M., Markt, B., Maschek, W., Neuhold, N., Ogris, E., Pfragner, R., Pimpl, W., Prohaska, R., Riccabona, G., Roka, R., Schmid, K. W., Sedlmayer, F., Stockhammer, M., Wolf, G., Vierhapper, H., and Smola, M. G., editor

Published
1999
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30. Buchbesprechungen

Author

Rindler, H., Sigmund, K., Cap, A., Kowol, G., Schmitt, K., Auinger, K., Mitsch, H., Telec, P., Krattenthaler, C., Baxa, Ch., Schoissengeier, J., Schmidt, K., Muthsam, H., Hofbauer, F., Haslinger, F., Hörmann, G., Hoffmann-Ostenhof, M., Feichtinger, H. G., Huyer, W., Cenker, Ch., Bürger, R., Michor, P., and Cenker, Ch.

Published
1998
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31. Buchbesprechungen

Author

Schmitt, P., Mitsch, H., Telec, P., Feichtinger, H. G., Schoissengeier, J., Neumaier, A., Kowol, G., Neuwirther, M., Michor, P., Rindler, H., Bürger, R., and Muthsam, H.

Published
1998
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32. Buchbesprechungen

Author

Muthsam, H., Schmitt, P., Rindler, H., Mitsch, H., Auinger, K., Schoissengeier, J., Feichtinger, H. G., Grosser, M., Strohmer, T., Haslinger, F., Bürger, R., Kowol, G., Reichel, H. -C., Michor, P., Losert, V., Futschik, A., Sigmund, K., Baxa, Ch., Götz, S., Neuwirther, M., Grossmann, W., and Hörmann, G.

Published
1998
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35. Buchbesprechungen

Author

Hoffmann-Ostenhof, M., Kowol, G., Cap, A., Sigmund, K., Teleĉ, P., Schoissengeier, J., Mitsch, H., Baxa, C., Haslinger, F., Bürger, R., Hofbauer, J., Feichtinger, H. G., Muthsam, H., Hörmann, G., Raith, P., Futschik, A., Cenker, C., and Müller, W.

Published
1997
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36. Buchbesprechungen

Author

Cap, A., Ulovec, A., Michor, P., Schmitt, P., Bürger, R., Krattenthaler, C., Teleĉ, P., Neuwirther, M., Hofbauer, J., Kowol, G., Volkov, M. V., Kriegl, A., Hoffmann-Ostenhof, M., Kunzinger, M., Feichtinger, H. G., Zimmermann, G., Grosser, M., Schichl, H., and Muthsam, H.

Published
1997
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39. Buchbesprechungen

Author

Hoffmann-Ostenhof, M., Kowol, G., Muthsam, H., Schmitt, P., Reichel, H. -C., Rindler, H., Schwabl, H. D., Mitsch, H., Slovák, J., Neuwirther, M., Michor, P., Schichl, H., Cap, A., Krattenthaler, C., Feichtinger, H. G., Hofbauer, J., Hörmann, G., Kriegl, A., and Baxa, CH.

Published
1995
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42. Buchbesprechungen

Author

Muthsam, H., Rindler, H., Krattenthaler, C., Mitsch, H., Schoissengeier, J., Neuwirther, M., Haslinger, F., Hofbauer, J., Sigmund, K., Feichtinger, H. G., Reichel, H. C., Hofbauer, F., Futschik, A., and Hoffmann-Ostenhof, M.

Published
1994
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44. Buchbesprechungen

Author

Hoffmann-Ostenhof, M., Kowol, G., Mitsch, H., Schmitt, P., Rindler, H., Krattenthaler, C., Baxa, Ch., Schoissengeier, J., Neuwirther, M., Michor, P., Feichtinger, H. G., Hofbauer, J., Schichl, H., Hofbauer, F., Bürger, R., Schachermayer, W., Cap, A., Hörmann, G., Kriegl, A., and Sigmund, K.

Published
1994
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45. Buchbesprechungen

Author

Mitsch, H., Rindler, H., Michor, P., Kowol, G., Krätzel, E., Sigmund, K., Zöchling, J., Hoffmann-Ostenhof, M., Muthsam, H., Feichtinger, H. G., Hofbauer, F., Baxa, Ch., and Bürger, R.

Published
1994
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48. Buchbesprechungen

Author

Kowol, G., Krattenthaler, C., Mitsch, H., Rindler, H., Schoissengeier, J., Kriegl, A., Haslinger, F., Bürger, R., Muthsam, H., Feichtinger, H. G., Hofbauer, F., Bomze, I., Hoffmann-Ostenhof, M., and Losert, V.

Published
1992
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49. Buchbesprechungen

Author

Reiter, H., Rindler, H., Michor, P., Krattenthaler, C., Bürger, R., Ruppert, W. A. F., Haslinger, F., Hofbauer, J., Feichtinger, H. G., Kowol, G., Reichel, H. -C., and Muthsam, H.

Published
1992
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50. Buchbesprechungen

Author

Krattenthaler, C., Muthsam, H., Reiter, H., Schmitt, P., Schoissengeier, J., Michor, P., Ruppert, W. A. F., Haslinger, F., Hofbauer, J., Sigmund, K., Bürger, R., Grosser, M., Mattes, J., Reichel, H. -C., Kriegl, A., and Feichtinger, H. G.

Published
1991
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