Geodesic
The Generalized D'Alembert Operator on Compactified Pseudo-Euclidean Space
Matematičeskie zametki, Tome 85 (2009) no. 5, pp. 652-660.

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

It is proved that the D'Alembert operator in $\mathbb R^n$ with multidimensional time, bordered by operators of multiplication by some function, and subject to an acceptance condition at infinity is a self-adjoint operator with discrete spectrum. The spectrum and eigenfunctions are explicitly described.
Keywords: D'Alembert differential operator, self-adjoint operator, pseudo-Euclidean space, Kelvin transformation, Laplace operator, spherical function.
Mots-clés : conformal transformation group 
@article{MZM_2009_85_5_a1,
     author = {A. S. Blagoveshchenskii},
     title = {The {Generalized} {D'Alembert} {Operator} on {Compactified} {Pseudo-Euclidean} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {652--660},
     publisher = {mathdoc},
     volume = {85},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_5_a1/}
}
TY  - JOUR
AU  - A. S. Blagoveshchenskii
TI  - The Generalized D'Alembert Operator on Compactified Pseudo-Euclidean Space
JO  - Matematičeskie zametki
PY  - 2009
SP  - 652
EP  - 660
VL  - 85
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_85_5_a1/
LA  - ru
ID  - MZM_2009_85_5_a1
ER  - 
%0 Journal Article
%A A. S. Blagoveshchenskii
%T The Generalized D'Alembert Operator on Compactified Pseudo-Euclidean Space
%J Matematičeskie zametki
%D 2009
%P 652-660
%V 85
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_85_5_a1/
%G ru
%F MZM_2009_85_5_a1
A. S. Blagoveshchenskii. The Generalized D'Alembert Operator on Compactified Pseudo-Euclidean Space. Matematičeskie zametki, Tome 85 (2009) no. 5, pp. 652-660. http://geodesic.mathdoc.fr/item/MZM_2009_85_5_a1/

[1] A. S. Blagoveschenskii, “O nekotorykh novykh zadachakh dlya volnovogo uravneniya”, Trudy V Vsesoyuznogo simpoziuma po difraktsii i rasprostraneniyu voln (Leningrad, 13–17 iyunya 1970 g.), Nauka, L., 1971, 29–36

[2] A. S. Blagoveschenskii, A. N. Vasilev, “Nekotorye novye korrektnye zadachi dlya ultragiperbolicheskogo uravneniya”, Vestn. LGU. Ser. matem., mekh., astron., 1976, no. 19, 152–153 | MR | Zbl

[3] R. Penrouz, V. Rindler, Spinory i prostranstvo-vremya. Spinornye i tvistornye metody v geometrii prostranstva-vremeni, Mir, M., 1988 | MR | Zbl

[4] V. A. Dubrovin, S. P. Novikov, A. G. Fomenko, Sovremennaya geometriya. Metody i prilozheniya, Nauka, M., 1986 | MR | Zbl

[5] Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, eds. M. Abramovits, I. Stigan, Nauka, M., 1979 | MR | Zbl

[6] A. S. Blagoveschenskii, “O kharakteristicheskoi zadache dlya ultragiperbolicheskogo uravneniya”, Matem. sb., 63:1 (1964), 137–168 | MR | Zbl

[7] I. V. Volovich, V. V. Kozlov, “O summiruemykh s kvadratom resheniyakh uravneniya Kleina–Gordona na mnogoobraziyakh”, Dokl. RAN, 408:3 (2006), 317–320 | MR | Zbl

[8] V. V. Kozlov, I. V. Volovich, “Finite action Klein–Gordon solutions on Lorentzian manifolds”, Int. J. Geom. Methods Mod. Phys., 3:7 (2006), 1349–1357 | DOI | MR | Zbl