This article is cited in 12 papers

The spectral shift function for a dissipative and a selfadjoint operator, and trace formulas for resonances

A. V. Rybkin


Abstract: A trace formula is given for an abstract pair consisting of a dissipative operator and a selfadjoint operator, and a connection is established between the spectral shift function of this pair and the corresponding scattering matrix. As a consequence, trace formulas are obtained for a specific dissipative operator arising in the problem of resonance scattering of plane waves on a one-dimensional semi-infinite crystal.
Bibliography: 8 titles.

UDC: 517.98

MSC: Primary 47A40, 47B10, 47B25, 47B44; Secondary 34B25, 47A10, 47A55

Received: 19.07.1983

 English version: Mathematics of the USSR-Sbornik, 1986, 53:2, 421–431

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