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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 649848, 13 pages
http://dx.doi.org/10.1155/2012/649848
Research Article

On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions

1Institute of Mathematics, National University of Uzbekistan, Hodjaeva Street 29, Tashkent 100125, Uzbekistan
2Institute of Advanced Technology (ITMA), University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3Department of Civil Engineering, Faculty of Engineering, Geospatial, Information Science Center (GIS RC), University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Received 24 May 2012; Accepted 29 June 2012

Academic Editor: Allaberen Ashyralyev

Copyright © 2012 Ravshan Ashurov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the behavior of Fourier integrals summed by the symbols of elliptic operators and pointwise convergence of Fourier inversion. We consider generalized localization principle which in classical spaces was investigated by Sjölin (1983), Carbery and Soria (1988, 1997) and Alimov (1993). Proceeding these studies, in this paper, we establish sharp conditions for generalized localization in the class of finitely supported distributions.