Raani, Senthil KS (2014) L-p-Integrability, Dimensions of Supports of Fourier Transforms and Applications. In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 20 (4). pp. 801-815.
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Official URL: http://dx.doi.org/ 10.1007/s00041-014-9334-5
Abstract
It is proved that there does not exist any non zero function in with if its Fourier transform is supported by a set of finite packing -measure where . It is shown that the assertion fails for . The result is applied to prove L-p Wiener Tauberian theorems for R-n and M(2).
| Item Type: | Journal Article |
|---|---|
| Publication: | JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS |
| Publisher: | SPRINGER BIRKHAUSER |
| Additional Information: | Copy right for this article belongs to the SPRINGER BIRKHAUSER, 233 SPRING STREET, 6TH FLOOR, NEW YORK, NY 10013 USA |
| Keywords: | Supports of Fourier Transform; Hausdorff dimension; Packing measure; Salem sets; Ahlfors-David regular sets; Wiener Tauberian theorems |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 03 Sep 2014 07:53 |
| Last Modified: | 03 Sep 2014 07:53 |
| URI: | http://eprints.iisc.ac.in/id/eprint/49721 |
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