Geodesic
On the probabilistic representation of the resolvent of the two-dimensional Laplacian
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 189-200 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper we consider a family of random linear operators that arises in the construction of a probabilistic representation of the resolvent of the two-dimensional Laplacian. It is shown that with probability $1$ the operators of this family are integral operators in $L_2(\mathbb{R}^2)$. The properties of the kernels of the corresponding operators are also investigated. 
@article{ZNSL_2022_510_a10,
     author = {A. K. Nikolaev},
     title = {On the probabilistic representation of the resolvent of the two-dimensional {Laplacian}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {189--200},
     year = {2022},
     volume = {510},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a10/}
}
TY  - JOUR
AU  - A. K. Nikolaev
TI  - On the probabilistic representation of the resolvent of the two-dimensional Laplacian
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 189
EP  - 200
VL  - 510
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a10/
LA  - ru
ID  - ZNSL_2022_510_a10
ER  - 
%0 Journal Article
%A A. K. Nikolaev
%T On the probabilistic representation of the resolvent of the two-dimensional Laplacian
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 189-200
%V 510
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a10/
%G ru
%F ZNSL_2022_510_a10
A. K. Nikolaev. On the probabilistic representation of the resolvent of the two-dimensional Laplacian. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 189-200. http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a10/

[1] D. K. Faddeev, B. Z. Vulikh, N. N. Uraltseva, Izbrannye glavy analiza i vysshei algebry, Izd–vo Leningr. un-ta, L., 1981

[2] M. Sh. Birman, M. Z. Solomyak, Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, Izd–vo Leningr. un-ta, L., 1980

[3] G. Beitmen, A. Erdeii, Funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny. Vysshie transtsendentnye funktsii, v. 2, 2-e izd., Nauka, M., 1974 | MR

[4] G. Vatson, Teoriya besselevykh funktsii, IL, M., 1949

[5] J. Ponce de Leon, “Revisiting the ortogonality of Bessel functions of the first kind on an infinite interval”, European J. Phys., 36:1 (2014), 015016