Mark Krein's Method of Directing Functionals and Singular Potentials

2011/10/31 by Charles Fulton, Fulton, Charles, Heinz Langer +3
Mathematics · #34B24 #34B30 #34L05 #47B25 #47E05 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:34B24 #msc:34B30 #msc:34L05 #msc:47B25 #msc:47E05

paper · pdf · doi:10.48550/arxiv.1110.6709

8 pages

arxiv created 2011/10/31 · arxiv updated 2011/11/01

Abstract

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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