A spectral study of the second-order exceptional \(X_1\)-Jacobi differential expression and a related non-classical Jacobi differential expression

DOI10.1016/j.jmaa.2014.08.016zbMath1303.33012arXiv1404.1882OpenAlexW2012014452MaRDI QIDQ458316

Jessica Stewart, Lance L. Littlejohn, Constanze Liaw, Quinn Wicks

Publication date: 7 October 2014

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

Full work available at URL: https://arxiv.org/abs/1404.1882

zbMATH Keywords

orthogonal polynomialsspectral theory\(X_{1}\)-Jacobi polynomialsGlazman-Krein-Naimark theoryleft-definite theory

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Linear ordinary differential equations and systems (34A30)

Related Items (6)

A Bochner type characterization theorem for exceptional orthogonal polynomials ⋮ The spectrum of self-adjoint extensions associated with exceptional Laguerre differential expressions ⋮ General solution of the exceptional Hermite differential equation and its minimal surface representation ⋮ Exceptional Jacobi polynomials ⋮ Singular left-definite Hamiltonian systems in the Sobolev space ⋮ Moment representations of exceptional \(X_{1}\) orthogonal polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A conjecture on exceptional orthogonal polynomials
• The Sobolev orthogonality and spectral analysis of the Laguerre polynomials \(\{L_{n}^{-k}\}\) for positive integers \(k\)
• Two-step Darboux transformations and exceptional Laguerre polynomials
• Über Polynomsysteme, die Sturm-Liouvilleschen Differenzengleichungen genügen
• An extension of Bochner's problem: exceptional invariant subspaces
• Structure theorems for linear and nonlinear differential operators admitting invariant polynomial subspaces
• Classification of linear differential operators with an invariant subspace of monomials
• Sobolev orthogonal polynomials and second-order differential equations
• An integral operator inequality with applications
• A general left-definite theory for certain self-adjoint operators with applications to differential equations
• The Jacobi-Stirling numbers
• Asymptotic and interlacing properties of zeros of exceptional Jacobi and Laguerre polynomials
• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression
• On orthogonal polynomials spanning a non-standard flag
• Exceptional orthogonal polynomials and the Darboux transformation
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

This page was built for publication: A spectral study of the second-order exceptional \(X_1\)-Jacobi differential expression and a related non-classical Jacobi differential expression