Journal ArticleDOI
The Bargmann transform on modulation and Gelfand–Shilov spaces, with applications to Toeplitz and pseudo-differential operators
Reads0
Chats0
TLDR
In this article, the authors investigated mapping properties for the Bargmann transform on an extended family of modulation spaces whose weights and their reciprocals are allowed to grow faster than exponentials and proved that this transform is isometric and bijective from modulation spaces to convenient Lebesgue spaces of analytic functions.Abstract:
We investigate mapping properties for the Bargmann transform on an extended family of modulation spaces whose weights and their reciprocals are allowed to grow faster than exponentials. We prove that this transform is isometric and bijective from modulation spaces to convenient Lebesgue spaces of analytic functions. We use this to prove that such modulation spaces fulfill most of the continuity properties which are valid for modulation spaces with moderate weights. Finally we use the results to establish continuity properties of Toeplitz and pseudo-differential operators on these modulation spaces, and on Gelfand–Shilov spaces.read more
Citations
More filters
Journal ArticleDOI
Images of function and distribution spaces under the bargmann transform
TL;DR: In this paper, a broad family of test function spaces and their dual (distribution) spaces is considered, including Gelfand-Shilov spaces and a family of Test Function Spaces introduced by Pilipovic.
Journal ArticleDOI
Every Matrix is a Product of Toeplitz Matrices
Ke Ye,Lek-Heng Lim +1 more
TL;DR: In this article, it was shown that toeplitz and Hankel matrices do not have a subspace of size at most 2n+5, and that such subspaces do not exist even if the factors are symmetric Toplitz or persymmetric Hankel.
Journal ArticleDOI
Pseudo-differential operators in a Gelfand-Shilov setting
Marco Cappiello,Joachim Toft +1 more
TL;DR: In this article, the authors introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and prove mapping properties for these operators on Gelfand-Shilov sp...
Journal ArticleDOI
Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces
TL;DR: In this article, the authors give global characterisations of Gevrey-Roumieu spaces of ultradifferentiable functions on compact Lie groups in terms of the representation theory of the group and the spectrum of the Laplace-Beltrami operator.
Journal ArticleDOI
Gabor Representations of evolution operators
TL;DR: In this paper, a time-frequency analysis of Fourier multipliers and pseudodierential operators with symbols of Gevrey, analytic and ultra- analytic type, is performed.
References
More filters
Book
Interpolation Spaces: An Introduction
Jöran Bergh,Jörgen Löfström +1 more
TL;DR: In this paper, the authors define the Riesz-Thorin Theorem as a necessary and sufficient condition for interpolation spaces, and apply it to approximate spaces in the context of vector spaces.
Book
Foundations of Time-Frequency Analysis
TL;DR: The topics range from the elemen- tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita- tive methods in time-frequency analysis and the theory of pseudodifferential operators.
Book
Harmonic analysis in phase space
TL;DR: The authors provides a coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts.