Geodesic
On Multiple Integrals of Special Form
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 401-410.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2007_82_3_a8,
     author = {R. N. Miroshin},
     title = {On {Multiple} {Integrals} of {Special} {Form}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {401--410},
     publisher = {mathdoc},
     volume = {82},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a8/}
}
TY  - JOUR
AU  - R. N. Miroshin
TI  - On Multiple Integrals of Special Form
JO  - Matematičeskie zametki
PY  - 2007
SP  - 401
EP  - 410
VL  - 82
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a8/
LA  - ru
ID  - MZM_2007_82_3_a8
ER  - 
%0 Journal Article
%A R. N. Miroshin
%T On Multiple Integrals of Special Form
%J Matematičeskie zametki
%D 2007
%P 401-410
%V 82
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a8/
%G ru
%F MZM_2007_82_3_a8
R. N. Miroshin. On Multiple Integrals of Special Form. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 401-410. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a8/

[1] R. N. Miroshin, “Ob odnom klasse mnogokratnykh integralov”, Matem. zametki, 73:3 (2003), 390–401 | MR | Zbl

[2] R. N. Miroshin, “Skhodimost ryadov Raisa i Longe–Khigginsa dlya statsionarnykh gaussovskikh markovskikh protsessov pervogo poryadka”, Teoriya veroyatn. i ee primen., 26:1 (1981), 101–120 | MR | Zbl

[3] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971 | MR | Zbl

[4] V. A. Ditkin, A. P. Prudnikov, Integralnye preobrazovaniya i operatsionnoe ischislenie, Nauka, M., 1974 | MR | Zbl

[5] G. Beitmen, A. Erdeii, Tablitsy integralnykh preobrazovanii, t. 1, Nauka, M., 1969 ; т. 2, Наука, М., 1970 | MR | Zbl | MR | Zbl