Regularized spectral shift function for one-dimensional Schrödinger operator with slowly decreasing potential. (English) Zbl 0623.47060

Koplienko, L. S.

Sib. Math. J. 26, 365-369 (1985).

Translation from Sib. Mat. Zh. 26, No.3(151), 72-77 (Russian) (1985; Zbl 0581.47034).

MSC:

47F05	General theory of partial differential operators
47A10	Spectrum, resolvent

Keywords:

one-dimensional Schrödinger operator with slowly decreasing potential; shift

Citations:

Zbl 0581.47034

References:

[1]	M. G. Krein, ?On perturbation determinants and the trace formula,? Dokl. Akad. Nauk SSSR,144, No. 2, 268-273 (1962).
[2]	M. G. Krein, ?On some new studies in perturbation theory,? First Summer Mathematical School, Kanev (1963), pp. 104-183.
[3]	I. M. Lifshits, ?On a problem of perturbation theory,? Usp. Mat. Nauk,7, No. 1, 171-180 (1952). · Zbl 0046.21203
[4]	V. S. Buslaev and L. D. Faddeev, ?On trace formulas for the differential singular Sturm-Liouville operator,? Dokl. Akad. Nauk SSSR,132, No. 1, 13-16 (1960). · Zbl 0129.06501
[5]	V. A. Yavryan, ?On the spectral shift function for Sturm-Liouville operators,? Dokl. Akad. Nauk Arm. SSR,38, No. 3, 193-198 (1964). · Zbl 0198.18801
[6]	M. Sh. Birman and M. G. Krein, ?On theory of wave operators and scattering operators,? Dokl. Akad. Nauk SSSR,144, No. 3, 475-480 (1962).
[7]	L. S. Koplienko, ?On trace formula for disturbances of nonkernel type,? Sib. Mat. Zh.,25, No. 5, 62-71 (1984).
[8]	I. C. Gohberg and M. G. Krein, Introduction to Theory of Linear Nonselfadjoint Operators, Amer. Math. Soc. (1969). · Zbl 0181.13504
[9]	V. B. Matveev and M. M. Skriganov, ?Scattering problem for radial Schrödinger equation with slowly decreasing potential,? Teor. Mat. Fiz.,10, No. 2, 238-248 (1972). · Zbl 0254.47018
[10]	E. C. Titchmarsh, Eigenfunction Expansions, Oxford Univ. Press (1962). · Zbl 0099.05201
[11]	V. S. Buslaev and V. B. Matveev, ?Wave operators for Schrödinger equation with slowly decreasing potential,? Teor. Mat. Fiz.,2, No. 3, 367-376 (1970).