Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016
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Bull. Korean Math. Soc. 2009; 46(1): 87-97

Printed January 1, 2009

Copyright © The Korean Mathematical Society.

The stability of the sine and cosine functional equations in Schwartz distributions

Jeongwook Chang and Jaeyoung Chung

Kunsan National University

Abstract

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We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Sch\-war\-tz distributions, Fourier hyperfunctions, and Gelfand generalized functions.

Keywords: Hyers-Ulam stability, trigonometric functional equation, distributions, Fourier hyperfunctions, Gelfand generalized functions, heat kernel

MSC numbers: 39B82, 46F12

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