Geodesic
Spectrum of a self-adjoint operator in $L_2(K)$, where $K$ is a local field; analog of the Feynman–Kac formula
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 18-24 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider operators in $L_2(K)$, where $K$ is a local field that is a sum of the operator of convolution with a generalized function and multiplication by a function. A criterion of self-adjointness is given, and some results on the discrete spectrum are obtained. An analog of the Feynman–Kac formula is derived. 
@article{TMF_1991_89_1_a2,
     author = {R. S. Ismagilov},
     title = {Spectrum of a~self-adjoint operator in $L_2(K)$, where~$K$ is a local field; analog of the {Feynman{\textendash}Kac} formula},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {18--24},
     year = {1991},
     volume = {89},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a2/}
}
TY  - JOUR
AU  - R. S. Ismagilov
TI  - Spectrum of a self-adjoint operator in $L_2(K)$, where $K$ is a local field; analog of the Feynman–Kac formula
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1991
SP  - 18
EP  - 24
VL  - 89
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a2/
LA  - ru
ID  - TMF_1991_89_1_a2
ER  - 
%0 Journal Article
%A R. S. Ismagilov
%T Spectrum of a self-adjoint operator in $L_2(K)$, where $K$ is a local field; analog of the Feynman–Kac formula
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1991
%P 18-24
%V 89
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a2/
%G ru
%F TMF_1991_89_1_a2
R. S. Ismagilov. Spectrum of a self-adjoint operator in $L_2(K)$, where $K$ is a local field; analog of the Feynman–Kac formula. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 18-24. http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a2/

[1] Gelfand I. M., Graev M. I., Pyatetskii-Shapiro I. I., Teoriya predstavlenii i avtomorfnye funktsii, Nauka, M., 1966 | MR

[2] Saloff-Coste Laurent, “Pseudodifferential operators on local fields”, C. R. Academie de Sc. Paris, Serie 1, 2 (1983), 171–174 | MR

[3] Titchmarsh E. Ch., Razlozheniya po sobstvennym funktsiyam, T. 2, IL, M., 1966 | MR

[4] Vladimirov V. S., UMN, 43:5 (263) (1988), 17–53 | MR | Zbl

[5] Gelfand I. M., Vilenkin N. Ya., Nekotorye primeneniya garmonicheskogo analiza, Fizmatgiz, M., 1961 | MR

[6] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 2, Mir, M., 1978 | MR

[7] Ismagilov R. S., Izv. AN SSSR. Ser. matem., 31:2 (1967), 361–390 | MR | Zbl

[8] Ismagilov R. S., Izv. AN SSSR. Ser. matem., 33:6 (1969), 1296–1323 | MR | Zbl

[9] Vladimirov V. S., Volovitch I. V., Lett. Math. Phys., 18:2 (1989), 43–53 | DOI | MR | Zbl

[10] Vladimirov V. S., Volovich I. V., Zelenov E. I., Izv. AN SSSR. Ser. matem., 54:2 (1990), 275–302 | MR | Zbl