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L-p-Integrability, Dimensions of Supports of Fourier Transforms and Applications

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
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
Depositing User: Id for Latest eprints
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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