The left-definite spectral theory for the classical Hermite differential equation.

DOI10.1016/S0377-0427(00)00335-6zbMath1091.47506WikidataQ115339026 ScholiaQ115339026MaRDI QIDQ1587408

Richard Wellman, Lance L. Littlejohn, W. Norrie Everitt

Publication date: 2000

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hermite polynomialsStirling numbers of the second kindspectral theoremLagrangian symmetricleft-definite self-adjoint operatorleft-definite Sobolev space

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General spectral theory of ordinary differential operators (34L05) General theory of ordinary differential operators (47E05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items

The left-definite spectral theory for the Dunkl--Hermite differential-difference equation, Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression, Asymptotics of Stirling and Chebyshev-Stirling Numbers of the Second Kind, A combinatorial interpretation of the Legendre-Stirling numbers, On the spectra of left-definite operators, New family of Jacobi-Stirling numbers, The Legendre-Stirling numbers, q-differential equations for q-classical polynomials and q-Jacobi-Stirling numbers, Left-definite problems of regular self-adjoint differential equations of even order, Left-definite theory with applications to orthogonal polynomials, Legendre polynomials, Legendre--Stirling numbers, and the left-definite spectral analysis of the Legendre differential expression, On the asymptotic normality of the Legendre-Stirling numbers of the second kind

Cites Work

• A general left-definite theory for certain self-adjoint operators with applications to differential equations
• S-hermitesche Rand-Eigenwertprobleme. I
• Generating Functions for Bessel and Related Polynomials
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