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

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 classicalLpspaces 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.

The approximation of the solution of wave problems by spectral expansions connected with elliptic differential operators

“…We refer the readers to the research by Ahmedov et al, [11] for the results on the convergence of the eigenfunction expansions of the distributions on the unit sphere. The problems on the generalized localization of the spectral expansions of the distributions are considered in the papers by Alimov [12] and Ashurov et al, [13]. A survey of all the techniques related to contrast enhancement of images is given in [14], which also contains all the advantages and disadvantages of these techniques.…”