Glazman-Krein-Naimark theory, left-definite theory and the square of the Legendre polynomials differential operator

DOI10.1016/J.JMAA.2016.06.010zbMath1353.47084arXiv1510.07337OpenAlexW2964311518MaRDI QIDQ530300

Lance L. Littlejohn, Quinn Wicks

Publication date: 29 July 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.07337

zbMATH Keywords

boundary conditionsself-adjoint operatorLegendre polynomialsGlazman-Krein-Naimark theoryleft-definite theory

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Weyl theory and its generalizations for ordinary differential equations (34B20) General theory of ordinary differential operators (47E05)

Related Items (5)

Properties and decompositions of domains for powers of the Jacobi differential operator ⋮ Boundary conditions associated with the general left-definite theory for differential operators ⋮ Singular left-definite Hamiltonian systems in the Sobolev space ⋮ Perspectives on general left-definite theory ⋮ Boundary triples and Weyl \(m\)-functions for powers of the Jacobi differential operator

Cites Work

• Legendre-Stirling permutations
• An integral operator inequality with applications
• On properties of the Legendre differential expression
• A general left-definite theory for certain self-adjoint operators with applications to differential equations
• The Jacobi-Stirling numbers
• Floquet theory for left-definite Sturm-Liouville problems
• Legendre polynomials, Legendre--Stirling numbers, and the left-definite spectral analysis of the Legendre differential expression
• A left-definite study of Legendre's differential equation and the fourth-order Legendre type differential equation
• The Legendre-Stirling numbers
• On the asymptotic normality of the Legendre-Stirling numbers of the second kind
• On the boundary condition for the Legendre polynomials
• THE LEGENDRE POLYNOMIALS UNDER A LEFT DEFINITE ENERGY NORM
• A combinatorial interpretation of the Legendre-Stirling numbers
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