The convergence of Fourier series in eigenfunctions of the Schrödinger operator with Kato potential. (English. Russian original) Zbl 1128.35314

Serov, V. S.

Math. Notes 67, No. 5, 639-645 (2000); translation from Mat. Zametki 67, No. 5, 755-763 (2000).

Summary: We obtain sharp conditions for the absolute uniform convergence of Fourier series in the eigenfunctions of the Schrödinger operator with Kato potential in a bounded domain for functions lying in the domains of generalized fractional powers of the original Schrödinger operator or in generalized Besov classes with a sharp exponent.

MSC:

35J10	Schrödinger operator, Schrödinger equation
35C10	Series solutions to PDEs
35P10	Completeness of eigenfunctions and eigenfunction expansions in context of PDEs

Keywords:

Schrödinger operator; eigenfunction expansion; generalized Fourier series; convergence

References:

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