In this article, we investigate some important theoretical aspects of the deformed wavelet transform, which is a novel variant of the wavelet transform based on generalized translation and dilation operators governed ...
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In this article, we investigate some important theoretical aspects of the deformed wavelet transform, which is a novel variant of the wavelet transform based on generalized translation and dilation operators governed by the well-known Dunkl transform. Besides studying all the fundamental properties, we establish the Calder & oacute;n's and inversion formulae associated with the newly proposed transform. Most importantly, we formulate a new class of localization operators associated with the deformed wavelet transform and examine the Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>p$$\end{document}-boundedness and compactness properties of such operators in detail.
The Dunkl-Bessel wavelet transform (DBWT) is a novel addition to the class of wavelet transforms. Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful...
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The Dunkl-Bessel wavelet transform (DBWT) is a novel addition to the class of wavelet transforms. Knowing the fact that the study of the time-frequency analysis is both theoretically interesting and practically useful, the first aim of this article is to explore the main theorems of harmonic analysis of this novel transformation. The second aim is to study some quantitative uncertainty principles associated with the proposed transformation. Our third endeavour is to study the Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>{p}$$\end{document} boundedness and compactness of localization operators associated with the DBWT. Further, we study their trace class properties and we prove that they are in the Schatten-von Neumann.
We prove that localization operators associated to ridgelet transforms with L-p symbols are bounded linear operators on L-2(R-n). operators closely related to these localization operators are shown to be in the trace ...
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We prove that localization operators associated to ridgelet transforms with L-p symbols are bounded linear operators on L-2(R-n). operators closely related to these localization operators are shown to be in the trace class and a trace formula for them is given.
Based on the resolution of the identity formulas for curvelet transforms, localization operators are initiated and their trace class properties are studied.
Based on the resolution of the identity formulas for curvelet transforms, localization operators are initiated and their trace class properties are studied.
In this paper, we study a class of pseudo-differential operators known as time-frequency localization operators on Zn, which depend on a symbol. and twowindows functions g(1) and g(2). We define the short-time Fourier...
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In this paper, we study a class of pseudo-differential operators known as time-frequency localization operators on Zn, which depend on a symbol. and twowindows functions g(1) and g(2). We define the short-time Fourier transform on Z(n) xT(n) and modulation spaces on Z(n), and present some basic properties. Then, we use modulation spaces on Z(n) x T-n as appropriate classes for symbols, and study the boundedness and compactness of the localization operators on modulation spaces on Z(n). Then, we show that these operators are in the Schatten-von Neumann class. Also, we obtain the relation between the Landau-Pollak-Slepian type operator and the localization operator on Z(n). Finally, under suitable conditions on the symbols, we prove that the localization operators are paracommutators, paraproducts and Fourier multipliers.
localization operators have a relatively recent development in pure and applied mathematics. Motivated by Wong's approach, we will study in this paper the time-frequency analysis associated with the hypergeometric...
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localization operators have a relatively recent development in pure and applied mathematics. Motivated by Wong's approach, we will study in this paper the time-frequency analysis associated with the hypergeometric Wigner transform related to the Cherednik operators in the case of the root system BCd.
We study the short-time Fourier transformation, modulation spaces, Gabor representations and time-frequency localization operators, for functions and tempered distributions that have as range space a Banach or a Hilbe...
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We study the short-time Fourier transformation, modulation spaces, Gabor representations and time-frequency localization operators, for functions and tempered distributions that have as range space a Banach or a Hilbert space. In the Banach space case the theory of modulation spaces contains some modifications of the scalar-valued theory, depending on the Banach space. In the Hilbert space case the modulation spaces have properties similar to the scalar-valued case and the Gabor frame theory essentially works. For localization operators in this context symbols are operator-valued. We generalize two results from the scalar-valued theory on continuity on certain modulation spaces when the symbol belongs to an L(p,q) space and M(infinity), respectively. The first result is true for any Banach space as range space, and the second result is true for any Hilbert space as range space.
In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on a symbol. and two windows functions g(1) and g(2). We first present some basic properties...
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In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on a symbol. and two windows functions g(1) and g(2). We first present some basic properties of the windowed Opdam-Cherednik transform. Then, we use modulation spaces associated with the Opdam-Cherednik transform as appropriate classes for symbols and windows and study the boundedness and compactness of the localization operators associated with the windowed Opdam-Cherednik transform on modulation spaces. Finally, we show that these operators are in the Schatten-von Neumann class.
The notion of a polar wavelet transform is introduced. The underlying non-unimodular Lie group, the associated square-integrable representations and admissible wavelets are studied. The resolution of the identity form...
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The notion of a polar wavelet transform is introduced. The underlying non-unimodular Lie group, the associated square-integrable representations and admissible wavelets are studied. The resolution of the identity formula for the polar wavelet transform is then formulated and proved. localization operators corresponding to the polar wavelet transforms are then defined. It is proved that under suitable conditions on the symbols, the localization operators are, in descending order of complexity, paracommutators, paraproducts and Fourier multipliers.
localization operators have a relatively recent development in pure and applied mathematics. Motivated by Wong’s approach, we will study in this paper the time–frequency analysis associated with the generalized Wign...
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