Feichtinger, HG and Gumber, A (2021) Completeness of shifted dilates in invariant Banach spaces of tempered distributions. In: Proceedings of the American Mathematical Society, 149 (12). pp. 5195-5210.
Full text not available from this repository.Abstract
We show that well-established methods from the theory of Banach modules and time-frequency analysis allow to derive completeness results for the collection of shifted and dilated version of a given (test) function in a quite general setting. While the basic ideas show strong similarity to the arguments used in a recent paper by V. Katsnelson we extend his results in several directions, both relaxing the assumptions and widening the range of applications. There is no need for the Banach spaces considered to be embedded into (L2(ℝ), || · ||2), nor is the Hilbert space structure relevant. We choose to present the results in the setting of the Euclidean spaces, because then the Schwartz space S'(ℝd) (d ≥ 1) of tempered distributions provides a well-established environment for mathematical analysis. We also establish connections to modulation spaces and Shubin classes (Qs(ℝd), || · ||Qs), showing that they are special cases of Katsnelson’s setting (only) for s ≥ 0. ©2021 American Mathematical Society
| Item Type: | Journal Article |
|---|---|
| Publication: | Proceedings of the American Mathematical Society |
| Publisher: | American Mathematical Society |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Approximation by translations; Banach modules; Banach spaces of tempered distributions; Beurling algebra; Compactness; Modulation spaces; Shubin spaces |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 06 Jun 2023 10:17 |
| Last Modified: | 06 Jun 2023 10:17 |
| URI: | https://eprints.iisc.ac.in/id/eprint/81823 |
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