Uncertainty principles as embeddings of modulation spaces

被引：15

作者：

Galperin, YV

Gröchenig, K

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Sacred Heart Univ, Dept Math, Fairfield, CT USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2002年 / 274卷 / 01期

关键词：

uncertainty principle; modulation space; short-time Fourier transform; Gabor expansion; embedding of function spaces;

D O I：

10.1016/S0022-247X(02)00279-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A class of new uncertainty principles is derived in the form of embeddings of Fourier-Lebesgue spaces into modulation spaces. These embeddings provide practical, sufficient conditions for a function to belong to a modulation space. Counterexamples based on the properties of Gabor expansions demonstrate that the embeddings are optimal. (C) 2002 Elsevier Science (USA). All rights reserved.

引用

页码：181 / 202

页数：22

共 50 条

[1] Uncertainty principles for the Opdam-Cherednik transform on modulation spaces
Poria, Anirudha
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2021, 32 (03) : 191 - 206
[2] Convolutions and embeddings for weighted modulation spaces
Toft, J
ADVANCES IN PSEUDO-DIFFERENTIAL OPERATORS, 2004, 155 : 165 - 186
[3] Embeddings of some classical Banach spaces into modulation spaces
Okoudjou, KA
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (06) : 1639 - 1647
[4] QUALITATIVE UNCERTAINTY PRINCIPLES FOR THE WINDOWED OPDAM–CHEREDNIK TRANSFORM ON WEIGHTED MODULATION SPACES
Mondal, Shyam Swarup
Poria, Anirudha
arXiv, 2021,
[5] Uncertainty principles in Hilbert spaces
Goh S.S.
Micchelli C.A.
Journal of Fourier Analysis and Applications, 2002, 8 (4) : 335 - 373
[6] Uncertainty principles in Hilbert spaces
Goh, SS
Micchelli, CA
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2002, 8 (04) : 335 - 373
[7] On Compactness of Embeddings of Fourier-Lebesgue Spaces into Modulation Spaces
Galperin, Yevgeniy V.
INTERNATIONAL JOURNAL OF ANALYSIS, 2013,
[8] Qualitative uncertainty principles for the windowed Opdam-Cherednik transform on weighted modulation spaces
Mondal, Shyam Swarup
Poria, Anirudha
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (16) : 10424 - 10439
[9] On the degree of compactness of embeddings between weighted modulation spaces
Hinrichs, Aicke
Piotrowska, Iwona
Piotrowski, Mariusz
JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2008, 6 (03): : 303 - 317
[10] Uncertainty principles in Banach spaces and signal recovery
Goh, Say Song
Goodman, Tim N. T.
JOURNAL OF APPROXIMATION THEORY, 2006, 143 (01) : 26 - 35

← 1 2 3 4 5 →