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International Journal of Mathematics and Mathematical Sciences
Volume 12, Issue 4, Pages 685-692
http://dx.doi.org/10.1155/S0161171289000840

Periodic Boehmians

Department of Mathematics, California State University, Stanislaus 801 W. Monte Vista Avenue, Turlock, CA 95380, USA

Received 23 January 1988; Revised 14 November 1988

Copyright © 1989 Hindawi Publishing Corporation. 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

A class of generalized functions, called periodic Boehmians, on the unit circle, is studied. It is shown that the class of Boehmians contain all Beurling distributions. An example of a hyperfunctlon that is not a Boehmian is given. Some growth conditions on the Fourier coefficients of a Boehmian are given. It is shown that the Boehmians, with a given complete metric topological vector space topology, is not locally bounded.