Atlas: Hulls and kernels of function classes and behavior of the Fourier transform by Archil Gulisashvili

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15th Southeastern Analysis Meeting and Shanks Lecture
May 20-23, 1999
Vanderbilt University
Nashville, TN, USA

Organizers
Daoxing Xia, Dechao Zheng, Eric Schechter

Hulls and kernels of function classes and behavior of the Fourier transform
by
Archil Gulisashvili
Department of Mathematics, Ohio University, Athens, OH 45701

We find the rearrangement-invariant, equimodular, and solid hulls and kernels of some function classes on n-dimensional Euclidean space Rⁿ. These classes consist of all functions for which the Fourier transform belongs to a given space A of tempered distributions. We consider the cases where A is the space L^p, the space L^p_loc, or the space M of compex Borel measures of locally bounded variation. We also introduce and study new function classes which arise as the hulls of some of the classes under consideration.

Date received: April 2, 1999