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Exact estimate for the spectral function of the singular Schrödinger operator. (English) Zbl 0633.35056

The author studies the spectral function of the singular Schrödinger operators with a countably set of complex eigenvalues, defined on bounded three dimensional domains. In the main result of the paper it is proved that the spectral function can be expressed as a sum of two functions: one of them is explicitly defined and for the another it is given an estimate. From this it is deduced a sufficient condition of summability for the eigenfunction expansions.
Reviewer: D.Ştefănescu

MSC:

35P05 General topics in linear spectral theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
35C10 Series solutions to PDEs
40A30 Convergence and divergence of series and sequences of functions
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