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Sur le développement spectral de l’opérateur de Schrödinger. (On the spectral expansion of the Schrödinger operator). (French) Zbl 0711.47027

We prove the local uniform convergence of spectral expansions of the Laplace operator with discrete spectrum lying in the complex plane. For the selfadjoint Schrödinger operator with arbitrary spectrum we obtain convergence in Liouville classes. We get an estimate of the Green function.

MSC:

47F05 General theory of partial differential operators
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J10 Schrödinger operator, Schrödinger equation
47A10 Spectrum, resolvent
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