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Mark Krein's method of directing functionals and singular potentials
Author(s) -
Fulton Charles,
Langer Heinz,
Luger Annemarie
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100301
Subject(s) - mathematics , eigenvalues and eigenvectors , singular solution , square integrable function , scalar (mathematics) , integrable system , mathematical analysis , singular point of a curve , measure (data warehouse) , spectral measure , pure mathematics , quantum mechanics , geometry , physics , database , computer science
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.