This article is cited in 3 papers

On Multiple Integrals of Special Form

R. N. Miroshin

Saint-Petersburg State University

Abstract: Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples.

Keywords: multiple integral, integral operator, iterated kernel, Markov process, Fourier integral transform, Hankel integral transform, Bessel function.

UDC: 518.2

Received: 17.05.2006
Revised: 13.02.2007

DOI: 10.4213/mzm3849

 English version: Mathematical Notes, 2007, 82:3, 357–365

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