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Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2011; 48(2): 387-396

Printed March 1, 2011

https://doi.org/10.4134/BKMS.2011.48.2.387

Copyright © The Korean Mathematical Society.

On the initial values of solutions of a general functional equation

Jae-Young Chung and Dohan Kim

Kunsan National University, Seoul National University

Abstract

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We consider a general functional equation with time variable which arises when we investigate regularity problems of some general functional equations. As a result we prove the regularity of the initial values of the solutions. Also as an application we prove the regularity of solutions of some classical functional equations and their distributional versions.

Keywords: functional equation, convolution, generalized function, heat kernel

MSC numbers: 39B82, 46F10

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