Two definitions of a determinant and proof of the Szegö–Kac theorem
Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 3, pp. 475-480
Citer cet article
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
[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.