Characterizations of the Friedrichs Extensions of Singular Sturm–Liouville Expressions

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Previous article Next article Characterizations of the Friedrichs Extensions of Singular Sturm–Liouville ExpressionsHans G. Kaper, Man Kam Kwong, and Anton ZettlHans G. Kaper, Man Kam Kwong, and Anton Zettlhttps://doi.org/10.1137/0517056PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractA method is presented to characterize selfadjoint realizations of a singular Sturm–Liouville differential expression on a finite interval, where the singularities are of limit-circle type.[1] M. A. Naimark, Linear differential operators. Part I: Elementary theory of linear differential operators, Frederick Ungar Publishing Co., New York, 1967xiii+144 35:6885 M. A. Naimark, Linear differential operators. Part II: Linear differential operators in Hilbert space, With additional material by the author, and a supplement by V. È. Ljance. Translated from the Russian by E. R. Dawson. English translation edited by W. N. Everitt, Frederick Ungar Publishing Co., New York, 1968xv+352 41:7485 Google Scholar[2] N. I. Akhiezer and , I. M. Glazman, Theory of linear operators in Hilbert space. Vol. I, Translated from the Russian by Merlynd Nestell, Frederick Ungar Publishing Co., New York, 1961xi+147 41:9015a N. I. Akhiezer and , I. M. Glazman, Theory of linear operators in Hilbert space. Vol. II, Translated from the Russian by Merlynd Nestell, Frederick Ungar Publishing Co., New York, 1963v+218 41:9015b Google Scholar[3] H. Weyl, Üher gewöhnliche Differentialgleichungen mit Singulärituten and die zugehörigen Entwicklungen willkürlicher Funktionen, Math. Ann, 68 (1910), 220–269 CrossrefGoogle Scholar[4] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Vol. 2, Oxford Univ. Press, Cambridge, 1962 CrossrefGoogle ScholarKeywordsSturm–Liouville differential operatorssingularities of limit-circle typeselfadjoint realizationsFriedrichs extension Previous article Next article FiguresRelatedReferencesCited ByDetails Friedrichs extensions of a class of singular Hamiltonian systemsJournal of Differential Equations, Vol. 293 | 1 Aug 2021 Cross Ref On self-adjoint boundary conditions for singular Sturm–Liouville operators bounded from belowJournal of Differential Equations, Vol. 269, No. 9 | 1 Oct 2020 Cross Ref Friedrichs extensions for singular Hamiltonian operators with intermediate deficiency indicesJournal of Mathematical Analysis and Applications, Vol. 461, No. 2 | 1 May 2018 Cross Ref On Properties of the Legendre Differential ExpressionResults in Mathematics, Vol. 42, No. 1-2 | 16 May 2013 Cross Ref The Friedrichs Extension of Singular Differential OperatorsJournal of Differential Equations, Vol. 160, No. 2 | 1 Jan 2000 Cross Ref Density, spectral theory and homoclinics for singular Sturm-Liouville systemsJournal of Computational and Applied Mathematics, Vol. 52, No. 1-3 | 1 Jul 1994 Cross Ref Singular Second-Order Operators: The Maximal and Minimal Operators, and Selfadjoint Operators in BetweenMojdeh Hajmirzaahmad and Allan M. KrallSIAM Review, Vol. 34, No. 4 | 2 August 2006AbstractPDF (1871 KB)Eigenvalue and eigenfunction computations for Sturm-Liouville problemsACM Transactions on Mathematical Software, Vol. 17, No. 4 | 1 Dec 1991 Cross Ref Volume 17, Issue 4| 1986SIAM Journal on Mathematical Analysis761-1035 History Submitted:17 August 1984Published online:17 July 2006 InformationCopyright © 1986 Society for Industrial and Applied MathematicsKeywordsSturm–Liouville differential operatorssingularities of limit-circle typeselfadjoint realizationsFriedrichs extensionMSC codes34B2547E05PDF Download Article & Publication DataArticle DOI:10.1137/0517056Article page range:pp. 772-777ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics