A general left-definite theory for certain self-adjoint operators with applications to differential equations

DOI10.1006/jdeq.2001.4078zbMath1008.47029OpenAlexW1973729530MaRDI QIDQ1614727

Lance L. Littlejohn, Richard Wellman

Publication date: 8 September 2002

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4078

zbMATH Keywords

spectrumleft-definite Hilbert spacesleft-definite operators

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Linear symmetric and selfadjoint operators (unbounded) (47B25)

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Cites Work

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• The Sobolev orthogonality and spectral analysis of the Laguerre polynomials \(\{L_{n}^{-k}\}\) for positive integers \(k\)
• Differential operators and the Legendre type polynomials
• The left-definite Legendre type boundary problem
• Sobolev orthogonal polynomials and second-order differential equations
• Semi-boundedness of ordinary differential operators
• Symmetrizability of differential equations having orthogonal polynomial solutions
• Left definite theory for second order differential operators with mixed boundary conditions
• The Laguerre type operator in a left definite Hilbert space
• A left-definite study of Legendre's differential equation and the fourth-order Legendre type differential equation
• S-hermitesche Rand-Eigenwertprobleme. I
• Certain differential equations for Tchebycheff polynomials
• ON SOME PROPERTIES OF THE LEGENDRE TYPE DIFFERENTIAL EXPRESSION
• REGULAR LEFT DEFINITE BOUNDARY VALUE PROBLEMS OF EVEN ORDER
• Differential Operators and the Laguerre Type Polynomials
• On the m -Coefficient of Weyl for a Differential Equation with an Indefinite Weight Function
• On the boundary condition for the Legendre polynomials
• PRODUCTS OF DIFFERENTIAL EXPRESSIONS WITHOUT SMOOTHNESS ASSUMPTIONS
• THE LEGENDRE POLYNOMIALS UNDER A LEFT DEFINITE ENERGY NORM
• Linksdefinite singuläre kanonische Eigenwertprobleme. II.
• Left‐Definite Regular Hamiltonian Systems
• SELF-ADJOINTNESS FOR THE WEYL PROBLEM UNDER AN ENERGY NORM
• Generating Functions for Bessel and Related Polynomials
• Left-definite Sturm-Liouville problems

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