Complex path integral representation for semiclassical linear functionals

DOI10.1006/jath.1998.3190zbMath0920.42016OpenAlexW2009253718MaRDI QIDQ1270288

I. A. Rocha, Francisco Marcellán

Publication date: 31 August 1999

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.1998.3190

zbMATH Keywords

linear functionalssemiclassical orthogonal polynomialsdistributional equation

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (15)

Bilinear semiclassical moment functionals and their integral representation ⋮ On semiclassical linear functionals of classs=2: classification and integral representations ⋮ Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials ⋮ Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions ⋮ Biorthogonal polynomials for two-matrix models with semiclassical potentials ⋮ Strong Asymptotics of the Orthogonal Polynomials with Respect to a Measure Supported on the Plane ⋮ Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials ⋮ The dependence on the monodromy data of the isomonodromic tau function ⋮ Enveloping Superalgebra U(osp(1|2)) and Orthogonal Polynomials in Discrete Indeterminate ⋮ Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights ⋮ Semi-classical linear functionals and integral representation II ⋮ Boutroux curves with external field: equilibrium measures without a variational problem ⋮ Semi-Classical Linear Functionals and Integral Representation ⋮ Discrete Painlevé equations for recurrence coefficients of Laguerre–Hahn orthogonal polynomials of class one ⋮ Multiple orthogonal polynomials

Cites Work

• Orthogonal polynomials and their derivatives. I
• Sur la suite de polynômes orthogonaux associée à la forme \(u=\delta_ c+\lambda (x-c)^{-1}L\). (On the sequence of orthogonal polynomials associated with the form \(u=\delta_ c+\lambda (x-c)^{- 1}L)\)
• A Padé-type approach to non-classical orthogonal polynomials
• Prolégomènes à l'étude des polynômes orthogonaux semi- classiques. (Preliminary remarks for the study of semi-classical orthogonal polynomials)
• Laguerre-Freud's equations for the recurrence coefficients of semi- classical orthogonal polynomials
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• On semiclassical linear functionals: Integral representations
• Orthogonal Polynomials and Their Derivatives, II
• Complex Weight Functions for Classical Orthogonal Polynomials
• Distributional Weight Functions for Orthogonal Polynomials
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