Geodesic
Representation of a Multiple Integral of Special Form by a Series
Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 96-103

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

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. 
@article{MZM_2013_93_1_a8,
     author = {R. N. Miroshin},
     title = {Representation of a {Multiple} {Integral} of {Special} {Form} by a {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {96--103},
     publisher = {mathdoc},
     volume = {93},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a8/}
}
TY  - JOUR
AU  - R. N. Miroshin
TI  - Representation of a Multiple Integral of Special Form by a Series
JO  - Matematičeskie zametki
PY  - 2013
SP  - 96
EP  - 103
VL  - 93
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a8/
LA  - ru
ID  - MZM_2013_93_1_a8
ER  - 
%0 Journal Article
%A R. N. Miroshin
%T Representation of a Multiple Integral of Special Form by a Series
%J Matematičeskie zametki
%D 2013
%P 96-103
%V 93
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a8/
%G ru
%F MZM_2013_93_1_a8
R. N. Miroshin. Representation of a Multiple Integral of Special Form by a Series. Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 96-103. http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a8/