Motivated by the recent paper of Boggiatto-Garello (J Pseudo-Differ Oper Appl 11:93-117, 2020) where a Gabor operator is regarded as pseudodifferential operator with symbol p(x, ?) periodic on both the variables, we s...
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Motivated by the recent paper of Boggiatto-Garello (J Pseudo-Differ Oper Appl 11:93-117, 2020) where a Gabor operator is regarded as pseudodifferential operator with symbol p(x, ?) periodic on both the variables, we study the continuity and invertibility, on general time frequency invariant spaces, of pseudodifferential operators with completely periodic symbol and general t quantization.
In this paper, we are concerned about the local well-posedness of Vlasov-Poisson-Fokker-Planck (VPFP) in modulation-Lebesgue space for large initial data. To accomplish this goal, we establish convolution inequalities...
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In this paper, we are concerned about the local well-posedness of Vlasov-Poisson-Fokker-Planck (VPFP) in modulation-Lebesgue space for large initial data. To accomplish this goal, we establish convolution inequalities associated with the fundamental solution to Fokker-Planck equation. The product formula and off-diagonal estimates involving the electronic term are established as well. & COPY;2023 Elsevier Inc. All rights reserved.
We introduce and study continuity properties of the Gabor product g and relate it to the well-known product formula for the short-time Fourier transform (STFT). We derive a phase space representation of the cubic nonl...
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We introduce and study continuity properties of the Gabor product g and relate it to the well-known product formula for the short-time Fourier transform (STFT). We derive a phase space representation of the cubic nonlinear Schrodinger equation in terms of the Gabor product, and discuss how the Gabor product can be used in the study of nonlinear dynamics of mixed quantum states.
The full characterization of the class of Fresnel integrable functions is an open problem in functional analysis, with significant applications to mathematical physics (Feynman path integrals) and the analysis of the ...
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The full characterization of the class of Fresnel integrable functions is an open problem in functional analysis, with significant applications to mathematical physics (Feynman path integrals) and the analysis of the Schr & ouml;dinger equation. In finite dimension, we prove the Fresnel integrability of functions in the Sj & ouml;strand class M infinity,1 - a family of continuous and bounded functions, locally enjoying the mild regularity of the Fourier transform of an integrable function. This result broadly extends the current knowledge on the Fresnel integrability of Fourier transforms of finite complex measures, and relies upon ideas and techniques of Gabor wave packet analysis. We also discuss infinite-dimensional extensions of this result. In this connection, we extend and make more concrete the general framework of projective functional extensions introduced by Albeverio and Mazzucchi. In particular, we obtain a concrete example of a continuous linear functional on an infinite-dimensional space beyond the class of Fresnel integrable functions. As an interesting byproduct, we obtain a sharp M infinity,1 -> L infinity operator norm bound for the free Schr & ouml;dinger evolution operator. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
We deduce factorization properties for Wiener amalgam spaces WLp,q, an extended family of modulation spaces M(omega, B), and for Schatten symbols s(p)(w) in pseudo-differential calculus under e. g. convolutions, twist...
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We deduce factorization properties for Wiener amalgam spaces WLp,q, an extended family of modulation spaces M(omega, B), and for Schatten symbols s(p)(w) in pseudo-differential calculus under e. g. convolutions, twisted convolutions and symbolic products. Here M(omega, B) can be any quasi-Banach Orlicz modulation space. For example we show that WL1,r * WLp,q = WLp,q and WL1,r#s(p)(w) = s(p)(w) when r is an element of (0, 1], r <= p, q < infinity. In particular we improve Rudin's identity L-1 * L-1 = L-1. (c) 2024 The Author(s). Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG). This is an open access article under the CC BY license (http://***/licenses/by/4.0/).
This article pays homage to the life and work of Hans Georg Feichtinger. It focusses on his major mathematical achievements and important professional aspects.
This article pays homage to the life and work of Hans Georg Feichtinger. It focusses on his major mathematical achievements and important professional aspects.
We introduce and study a new class of translation-modulation invariant Banach spaces of ultradistributions. These spaces show stability under Fourier transform and tensor products;furthermore, they have a natural Bana...
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We introduce and study a new class of translation-modulation invariant Banach spaces of ultradistributions. These spaces show stability under Fourier transform and tensor products;furthermore, they have a natural Banach convolution module structure over a certain associated Beurling algebra, as well as a Banach multiplication module structure over an associated Wiener-Beurling algebra. We also investigate a new class of modulation spaces, the Banach spaces of ultradistributions M-F on R-d, associated to translation-modulation invariant Banach spaces of ultradistributions F on R-2d.
We perform Wigner analysis of linear operators. Namely, the standard time frequency representation Short-time Fourier Transform (STFT) is replaced by the A-Wigner distribution defined by W-A(f) = mu(A)(f circle times ...
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We perform Wigner analysis of linear operators. Namely, the standard time frequency representation Short-time Fourier Transform (STFT) is replaced by the A-Wigner distribution defined by W-A(f) = mu(A)(f circle times f), where A is a 4d x 4d symplectic matrix and mu(A) is an associate metaplectic operator. Basic examples are given by the so-called tau-Wigner distributions. Such representations provide a new characterization for modulation spaces when tau is an element of (0, 1). Furthermore, they can be efficiently employed in the study of the off-diagonal decay for pseudodifferential operators with symbols in the Sjostrand class (in particular, in the Hormander class S-0,0(0)). The novelty relies on defining time-frequency representations via metaplectic operators, developing a conceptual framework and paving the way for a new understanding of quantization procedures. We deduce micro-local properties for pseudodifferential operators in terms of the Wigner wave front set. Finally, we compare the Wigner with the global Hormander wave front set and identify the possible presence of a ghost region in the Wigner wave front. In the second part of the paper applications to Fourier integral operators and Schrodinger equations will be given (c) 2022 Elsevier Inc. All rights reserved.
In this paper, we study the Cauchy problem for Hartree type equation iu(t) + u(xx) = [K * vertical bar u vertical bar(2)] with Cauchy data in modulation spaces Mp,q(R). We establish global well-posedness results in Mp...
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In this paper, we study the Cauchy problem for Hartree type equation iu(t) + u(xx) = [K * vertical bar u vertical bar(2)] with Cauchy data in modulation spaces Mp,q(R). We establish global well-posedness results in Mp,p' (R) when K(x) = lambda/vertical bar x vertical bar(gamma), (lambda is an element of R, 0 < gamma < 1) with no smallness condition on initial data, where p' is the Holder conjugate of p. Our proof uses a splitting method inspired by the work of Vargas-Vega, Hyakuna-Tsutsumi, Grunrock and Chaichenets et al. to the modulation space setting and exploits polynomial growth of the Schrodinger propagator on modulation spaces. (c) 2022 Elsevier Inc. All rights reserved.
作者：
Cordero, ElenaGiacchi, GianlucaUniv Torino
Dipartimento Matemat Via Carlo Alberto 10 I-10123 Turin Italy Univ Bologna
Dipartimento Matemat Piazza Porta San Donato 5 I-40126 Bologna Italy HES SO Valais Wallis
Inst Syst Engn Sch Engn Rue Ind 23 CH-1950 Sion Switzerland Lausanne Univ Hosp
Rue Bugnon 46 CH-1011 Lausanne Switzerland Univ Lausanne
Lausanne Univ Hosp Rue Bugnon 46 CH-1011 Lausanne Switzerland Univ Lausanne
Dept Diagnost & Intervent Radiol Rue Bugnon 46 CH-1011 Lausanne Switzerland Sense Innovat & Res Ctr
Ave Provence 82 CH-1007 Lausanne Switzerland
We introduce new frames, called metaplectic Gabor frames, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions, cf. [7,8,5,17,27,28]. Namely, we develop the theory of metaple...
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We introduce new frames, called metaplectic Gabor frames, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions, cf. [7,8,5,17,27,28]. Namely, we develop the theory of metaplectic atoms in a full-general setting and prove an inversion formula for metaplectic Wigner distributions on Rd. Its discretization provides metaplectic Gabor ***, we deepen the understanding of the so-called shift-invertible metaplectic Wigner distributions, showing that they can be represented, up to chirps, as rescaled short-time Fourier transforms. As an application, we derive a new characterization of modulation and Wiener amalgam spaces. Thus, these metaplectic distributions (and related frames) provide meaningful definitions of local frequencies and can be used to measure effectively the local frequency content of signals.(c) 2023 Elsevier Inc. All rights reserved.
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