On the zeros of eigenfunctions of polynomial differential operators

DOI10.1063/1.526743zbMath0585.47037OpenAlexW2001744533WikidataQ58363733 ScholiaQ58363733MaRDI QIDQ3711088

E. Buendía, M. A. Sanchez-Buendia, Jesús S. Dehesera

Publication date: 1985

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.526743

zbMATH Keywords

momentsorthogonal polynomialsoperatorasymptotic valuesdensity of nodes around the meanpolynomial eigenfunctions of an ordinary polynomial differentialpolynomial eigenfunctions of an ordinary polynomial differential operator

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General theory of ordinary differential operators (47E05) Dilations, extensions, compressions of linear operators (47A20) Linear differential equations in abstract spaces (34G10)

Related Items (7)

Sum rules for zeros of polynomials and generalized Lucas polynomials ⋮ Computing the moments of the density of zeros for orthogonal polynomials ⋮ The moments of the density of zeros for the relativistic Hermite and Laguerre polynomials ⋮ Algebraic and spectral properties of some quasiorthogonal polynomials encountered in quantum radiation ⋮ A representation formula of sum rules for zeros of polynomials ⋮ On the calculation of moments of the zero density of classical and semiclassical orthogonal polynomials ⋮ Distributions of zeros of discrete and continuous polynomials from their recurrence relation

Cites Work

• On the polynomial solutions of ordinary differential equations of the fourth order
• Orthogonal polynomials satisfying fourth order differential equations
• Sum rules for zeros of polynomials. I
• Theorem Relating the Eigenvalue Density for Random Matrices to the Zeros of the Classical Polynomials
• Nonuniqueness of solutions in quantum field theory
• An Inequality for Kurtosis

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