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Matematicheskie Zametki, 2013, Volume 93, Issue 1, Pages 96–103
DOI: https://doi.org/10.4213/mzm8895 (Mi mzm8895) 		 
Representation of a Multiple Integral of Special Form by a Series

R. N. Miroshin

Saint-Petersburg State University
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DOI: https://doi.org/10.4213/mzm8895
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.
Received: 27.05.2010
Revised: 10.01.2012
English version:
Mathematical Notes, 2013, Volume 93, Issue 1, Pages 137–142
DOI: https://doi.org/10.1134/S0001434613010124
Bibliographic databases:
Document Type: Article
UDC: 518.2+519.21
Language: Russian
Citation: R. N. Miroshin, “Representation of a Multiple Integral of Special Form by a Series”, Mat. Zametki, 93:1 (2013), 96–103; Math. Notes, 93:1 (2013), 137–142
Citation in format AMSBIB
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