This article is cited in 8 papers

On eigenfunctions of an operator corresponding to the poles of the analytic continuation of the resolvent through the continuous spectrum

B. R. Vainberg


Abstract: It is well known that the kernel of the resolvent of the operator $-\Delta+q(x)$ ($q(x)$ finite) over the whole space, or over the exterior of a bounded domain with homogeneity conditions on the boundary, can be meromorphically continued through the continuous spectrum onto the second sheet of a two-sheeted Riemann surface. The poles of this continuation lying in the second sheet correspond to generalized eigen and associated functions exponentially increasing at infinity. In this paper we study the problem of orthogonality of these functions. In addition the problem of which generalized eigenfunctions are the usual eigenfunctions is mentioned.
Bibliography: 8 titles.

UDC: 517.43

MSC: Primary 35P05; Secondary 47F05

Received: 05.01.1971

 English version: Mathematics of the USSR-Sbornik, 1972, 16:2, 307–322

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