Topic
Modulation space
About: Modulation space is a research topic. Over the lifetime, 520 publications have been published within this topic receiving 11327 citations.
Papers published on a yearly basis
Papers
1 Jan 2003
TL;DR: A literal reproduction of the 1983 report by Feichtinger, with only the obvious typos being corrected, one additional section and minor extra footnotes, is given in this paper.
Abstract: This is a literal reproduction of the 1983 report [55] by Hans G. Feichtinger, with only the obvious typos being corrected, one additional section and minor extra footnotes. Only few symbols have been changed to more standard ones, e.g. for the translation operator (which was L y , following Hans Reiter) has been replaced by T y , and instead of K(G) we write C c (G) now. We hope that by adding comments about recent papers on modulation spaces and publications which have appeared in the meantime , as well as updates to the bibliography the reader will find this " new edition " interesting. Of course the page numbers differ slightly from those in the original report (it was 52 pages long), but the numbering system of theorems and remarks has been preserved in the present version (so that one may refer to the results of this paper, which is now better accessible, in the same way as to the original report.)
687 citations
TL;DR: In this paper, continuity for weighted modulation spaces is discussed, and it is shown that many such spaces can be obtained in a canonical way from the corresponding standard modulation spaces, and the trace operator a↦a(0, ·) acting on modulationspaces.
425 citations
TL;DR: In this article, a new Segal algebraS0(G) of continuous functions on an arbitrary locally compact abelian groupG is defined by means of a certain kind of "atomic" representation.
Abstract: By means of a certain kind of ‘atomic’ representation a new Segal algebraS0(G) of continuous functions on an arbitrary locally compact abelian groupG is defined. From various characterizations ofS0(G), e. g. as smallest element within the family of all strongly character invariant Segal algebras, functorial properties of the symbolS0 are derived, which are similar to those of the spacel (G) of Schwartz-Bruhat functions, e. g. invariance under the Fourier transform, or compatibility with restrictions to closed subgroups. The corresponding properties of its Banach dualS'0(G) as well as some of their applications are to be given in a subsequent paper.
391 citations
TL;DR: In this paper, the authors studied several non-commutative generalizations of Wiener's Lemma and their application to Gabor theory and solved a conjecture of Janssen, Feichtinger and one of us.
Abstract: As a consequence, Ca is invertible and bounded on all ?p(Zd) for 1 < p < oo simultaneously. In this article we study several non-commutative generalizations of Wiener's Lemma and their application to Gabor theory. The paper is divided into two parts: the first part (Sections 2 and 3) is devoted to abstract harmonic analysis and extends Wiener's Lemma to twisted convolution. The second part (Section 4) is devoted to the theory of Gabor frames, specifically to the design of dual windows with good time-frequency localization. In particular, we solve a conjecture of Janssen, Feichtinger and one of us [17], [18], [9]. These two topics appear to be completely disjoint, but they are not. The solution of the conjectures about Gabor frames is an unexpected application of methods from non-commutative harmonic analysis to application-oriented mathematics. It turns out that the connection between twisted convolution and the Heisenberg group and the theory of symmetric group algebras are precisely the tools needed to treat the problem motivated by signal analysis. To be more concrete, we formulate some of our main results first and will deal with the details and the technical background later.
296 citations
1 May 2006
TL;DR: In this paper, the authors provide historical perspectives and background on the motivations which led to the invention of the modulation spaces by the author almost 25 years ago, as well as comments about their role for ongoing research eorts within time-frequency analysis.
Abstract: This note provides historical perspectives and background on the motivations which led to the invention of the modulation spaces by the author almost 25 years ago, as well as comments about their role for ongoing research eorts within time-frequency analysis. We will also describe the role of modulation spaces within the more general coorbit theory developed
265 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 8 |
| 2024 | 20 |
| 2023 | 14 |
| 2022 | 63 |
| 2021 | 38 |
| 2020 | 40 |