Geodesic
On the eigenfunctions of the Beltrami–Laplace operator on homogeneous symmetric spaces of rank 1
Sbornik. Mathematics, Tome 33 (1977) no. 2, pp. 261-280 
V. K. Rogov. On the eigenfunctions of the Beltrami–Laplace operator on homogeneous symmetric spaces of rank 1. Sbornik. Mathematics, Tome 33 (1977) no. 2, pp. 261-280. http://geodesic.mathdoc.fr/item/SM_1977_33_2_a5/
@article{SM_1977_33_2_a5,
     author = {V. K. Rogov},
     title = {On the eigenfunctions of the {Beltrami{\textendash}Laplace} operator on homogeneous symmetric spaces of rank~1},
     journal = {Sbornik. Mathematics},
     pages = {261--280},
     year = {1977},
     volume = {33},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_33_2_a5/}
}
TY  - JOUR
AU  - V. K. Rogov
TI  - On the eigenfunctions of the Beltrami–Laplace operator on homogeneous symmetric spaces of rank 1
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 261
EP  - 280
VL  - 33
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1977_33_2_a5/
LA  - en
ID  - SM_1977_33_2_a5
ER  - 
%0 Journal Article
%A V. K. Rogov
%T On the eigenfunctions of the Beltrami–Laplace operator on homogeneous symmetric spaces of rank 1
%J Sbornik. Mathematics
%D 1977
%P 261-280
%V 33
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1977_33_2_a5/
%G en
%F SM_1977_33_2_a5

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

This paper concerns itself with a differential equation which arises in the determination of the eigenfunctions of the Beltrami–Laplace operator on homogeneous symmetric spaces of rank 1. It is related to the Whittaker equation, and its coefficients are quadratic forms which do not depend on the variable of differentiation. All of the solutions of this equation in a space of generalized functions with restricted growth are described. Bibliography: 7 titles.

[1] I. M. Gelfand, G. E. Shilov, Prostranstva osnovnykh i obobschennykh funktsii, Obobschennye funktsii, vyp. 2, Fizmatgiz, M., 1958 | MR

[2] G. E. Shilov, Matematicheskii analiz, vtoroi spetsialnyi kurs, Nauka, M., 1965 | MR

[3] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, t. I, gipergeometricheskaya funktsiya, funktsii Lezhandra, Nauka, M., 1965

[4] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, t. II, funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny, Nauka, M., 1966 | MR

[5] I. M. Gelfand, G. E. Shilov, Nekotorye voprosy teorii differentsialnykh uravnenii, Obobschennye funktsii, vyp. 3, Fizmatgiz, M., 1958 | MR

[6] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenie, Fizmatgiz, M., 1963 | MR

[7] V.-B. K. Rogov, “Sobstvennye funktsii operatora Beltrami–Laplasa na giperboloidakh”, Trudy MIITa, no. 413, 1972, 143–164 | MR