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Sturm–Liouville problems with singular non‐selfadjoint boundary conditions
Author(s) -
Eberhard Walter,
Freiling Gerhard,
Zettl Anton
Publication year - 2005
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.200310318
Subject(s) - mathematics , eigenvalues and eigenvectors , class (philosophy) , sturm–liouville theory , boundary value problem , singular solution , boundary (topology) , mathematical analysis , pure mathematics , physics , quantum mechanics , artificial intelligence , computer science
Singular boundary conditions are formulated for non‐selfadjoint Sturm–Liouville problems which are limitcircle in a very general sense. The characteristic determinant is constructed and it is shown that it can be used to extend the Birkhoff theory for so called “Birkhoff regular boundary conditions” to the singular case. This is illustrated for a class of singular Birkhoff‐regular problems; in particular we prove for this class an asymptotic formula for the eigenvalues and an expansion theorem. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)