A left-definite study of Legendre's differential equation and the fourth-order Legendre type differential equation

DOI10.1007/BF03322519zbMath0967.34015WikidataQ115390781 ScholiaQ115390781MaRDI QIDQ1977518

Rolf Vonhoff

Publication date: 30 August 2001

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

zbMATH Keywords

maximal operatorfourth-order Legendre-type differential equationleft-definite deficiency indicesLegendre's differential equationlocally uniformly convergent expansions

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Weyl theory and its generalizations for ordinary differential equations (34B20) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10)

Related Items (10)

A general left-definite theory for certain self-adjoint operators with applications to differential equations ⋮ Singular left-definite Sturm--Liouville problems ⋮ Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression ⋮ On the spectra of left-definite operators ⋮ On properties of the Legendre differential expression ⋮ A left-definite study of Legendre's differential equation and the fourth-order Legendre type differential equation ⋮ Glazman-Krein-Naimark theory, left-definite theory and the square of the Legendre polynomials differential operator ⋮ Left-definite problems of regular self-adjoint differential equations of even order ⋮ Left-definite theory with applications to orthogonal polynomials ⋮ Counting and computing eigenvalues of left-definite Sturm--Liouville problems

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