Geodesic
Two definitions of a determinant and proof of the Szegö–Kac theorem
Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 3, pp. 475-480 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A new proof of the Szegö–Kac theorem is given. It is based on a reformulation of the problem in terms of infinite bounded matrices and the connection between the two natural definitions of the determinant for such matrices. 
@article{TMF_1983_55_3_a12,
     author = {B. N. Valuev},
     title = {Two definitions of a~determinant and proof of the {Szeg\"o{\textendash}Kac} theorem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {475--480},
     year = {1983},
     volume = {55},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_55_3_a12/}
}
TY  - JOUR
AU  - B. N. Valuev
TI  - Two definitions of a determinant and proof of the Szegö–Kac theorem
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1983
SP  - 475
EP  - 480
VL  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1983_55_3_a12/
LA  - ru
ID  - TMF_1983_55_3_a12
ER  - 
%0 Journal Article
%A B. N. Valuev
%T Two definitions of a determinant and proof of the Szegö–Kac theorem
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1983
%P 475-480
%V 55
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1983_55_3_a12/
%G ru
%F TMF_1983_55_3_a12
B. N. Valuev. Two definitions of a determinant and proof of the Szegö–Kac theorem. Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 3, pp. 475-480. http://geodesic.mathdoc.fr/item/TMF_1983_55_3_a12/

[1] Szegö G., Commun. du Seminaire mathem. de L'universite de Lund, tome supplimentaire dedie a Marcel Riesz, 1952, 228–238 | MR | Zbl

[2] Kac M., Duke Math. J., 21 (1954), 501–509 | DOI | MR | Zbl

[3] Grenander U., Sege G., Teplitsevy formy i ikh prilozheniya, IL, M., 1961, 101 pp. | MR

[4] Kats M., Veroyatnost i smezhnye voprosy v fizike, Mir, M., 1965, 73 pp. | Zbl

[5] Montroll E. W., Potts R., Ward J., J. Math. Phys., 4:2 (1963), 308–322 | DOI | MR

[6] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972, 196 pp. | MR | Zbl

[7] Dirak P., Spinory v gilbertovom prostranstve, Mir, M., 1978, 77 pp.