On properties of the Legendre differential expression

DOI10.1007/BF03323553zbMath1058.33008MaRDI QIDQ1411428

W. Norrie Everitt, Vojislav Marić, Lance L. Littlejohn

Publication date: 29 October 2003

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceHilbert spaceself-adjoint operatorLegendre polynomialsleft-definite spacecomplete orthogonal setleft definite operator

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) Positive linear operators and order-bounded operators (47B65) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (6)

Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression ⋮ On the spectra of left-definite operators ⋮ Properties and decompositions of domains for powers of the Jacobi differential operator ⋮ Glazman-Krein-Naimark theory, left-definite theory and the square of the Legendre polynomials differential operator ⋮ Spectral analysis of the sixth-order Krall differential expression ⋮ Left-definite theory with applications to orthogonal polynomials

Cites Work

• An integral operator inequality with applications
• Properties of the operator domains of the fourth-order Legendre-type differential expressions
• A general left-definite theory for certain self-adjoint operators with applications to differential equations
• A left-definite study of Legendre's differential equation and the fourth-order Legendre type differential equation
• No Continuum in E 2 Has the TMP. I. Arcs and Spheres
• Characterizations of the Friedrichs Extensions of Singular Sturm–Liouville Expressions
• On the boundary condition for the Legendre polynomials
• A generalisation of Niessen's limit-circle criterion
• THE LEGENDRE POLYNOMIALS UNDER A LEFT DEFINITE ENERGY NORM
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