Representation of a Multiple Integral of Special Form by a Series

R. N. Miroshin

Saint-Petersburg State University

Abstract: Multiple integrals generalizing the iterated kernels of linear integral equations are expressed by a series each of whose terms is proportional to the product of two orthogonal functions in the case of a similar representation of the kernel. Besides integral equations, these integrals have applications in the theory of Markov processes. The results obtained are illustrated by several examples.

Keywords: multiple integral, linear integral equation, iterated kernel, Markov process, Kolmogorov–Chapman equation, orthogonal function.

UDC: 518.2+519.21

Received: 27.05.2010
Revised: 10.01.2012

DOI: 10.4213/mzm8895

 English version: Mathematical Notes, 2013, 93:1, 137–142

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