Mark Krein's Method of Directing Functionals and Singular Potentials

Details Mark Krein's Method of Directing Functionals and Singular Potentials Mark Krein's Method of Directing Functionals and Singular Potentials

2011-10-31

arxiv.org/abs/1110.6709v1

Mathematics

Spectral Theory

8 pages

Scientific paper

It is shown that M. Krein's method of directing functionals can be used to
prove the existence of a scalar spectral measure for certain Sturm-Liouville
equations with two singular endpoints. The essential assumption is the
existence of a solution of the equation that is square integrable at one
singular endpoint and depends analytically on the eigenvalue parameter.

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