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Spectral analysis of a nonselfadjoint differential operator arising in the one-dimensional problem of scattering by a Brownian particle. (English. Russian original) Zbl 0618.35085
Math. USSR, Sb. 57, 371-390 (1987); translation from Mat. Sb., Nov. Ser. 129(171), No. 3, 358-377 (1986).
The author investigates the spectral properties of the linear nonselfadjoint differential operator of the type \(- \partial_{xx}+i\kappa \partial_{yy}+q(x-y)\). Here \(\kappa\in {\mathbb{R}}\), Im \(q\leq 0\), \(| q(z)| \leq C(1+| z|)^{-3- \alpha}\); C, \(\alpha >0\). The main result is the theorem on expansion in eigenfunctions of this operator.
Reviewer: A.Venkov
MSC:
35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
35P25 Scattering theory for PDEs
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