Real Paley-Wiener theorems in spaces of ultradifferentiable functions

被引：20
|
作者：
Boiti, Chiara [1 ]
Jornet, David [2 ]
Oliaro, Alessandro [3 ]
机构：
[1] Univ Ferrara, Dipartimento Matemat & Informat, Via Machiavelli 30, I-44121 Ferrara, Italy
[2] Univ Politecn Valencia, IUMPA, Camino Vera S-N, E-46071 Valencia, Spain
[3] Univ Turin, Dipartimento Matemat, Via Carlo Alberto 10, I-10123 Turin, Italy
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 278卷 / 04期
关键词：
Real Paley-Wiener theorems; Weighted Schwartz classes; Short-time Fourier transform; Wigner transform; PARTIAL-DIFFERENTIAL OPERATORS;
D O I：
10.1016/j.jfa.2019.108348
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop real Paley-Wiener theorems for classes S-omega of ultradifferentiable functions and related L-p-spaces in the spirit of Bang and Andersen for the Schwartz class. We introduce results of this type for the so-called Gabor transform and give a full characterization in terms of Fourier and Wigner transforms for several variables of a Paley-Wiener theorem in this general setting, which is new in the literature. We also analyze this type of results when the support of the function is not compact using polynomials. Some examples are given. (C) 2019 Elsevier Inc. All rights reserved.
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页数：45
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