2-variable generalized Hermite matrix polynomials and Lie algebra representation

DOI10.1016/S0034-4877(10)00024-8zbMath1229.33018OpenAlexW1995201278WikidataQ115339927 ScholiaQ115339927MaRDI QIDQ540801

Nusrat Raza, Subuhi Khan

Publication date: 3 June 2011

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(10)00024-8

zbMATH Keywords

Lie groupsLie algebrarepresentation theorymatrix polynomialsgenerating relationMultivariate Hermite polynomials

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (13)

Some properties of Hermite based Appell matrix polynomials ⋮ Models of Lie algebra \(sl(2, \mathbb{C})\) and special matrix functions by means of a matrix integral transformation ⋮ Certain properties of Konhauser matrix polynomials via Lie algebra techniques ⋮ Certain properties of generalized Hermite-type matrix polynomials using Weisner's group theoretic techniques ⋮ On \(q\)-special matrix functions using quantum algebraic techniques ⋮ Matrix-valued hypergeometric Appell-type polynomials ⋮ Lie algebras of matrix difference differential operators and special matrix functions ⋮ Certain generating matrix relations of generalized Bessel matrix polynomials from the view point of Lie algebra method ⋮ Multi-variable Hermite matrix polynomials: properties and applications ⋮ Analytical properties of the two-variables Jacobi matrix polynomials with applications ⋮ Finding hybrid families of special matrix polynomials associated with Sheffer sequences ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Generalized Hermite polynomials and supergaussian forms
• Some applications of the Hermite matrix polynomials series expansions
• Generalized Bessel functions and generalized Hermite polynomials
• Laguerre matrix polynomials and systems of second-order differential equations
• Orthogonal matrix polynomials and higher-order recurrence relations
• Orthogonal matrix polynomials and applications
• Lie theory and special functions
• Partial differential equations for hypergeometric functions of two argument matrices
• Markov's Theorem for Orthogonal Matrix Polynomials
• 2-variable Laguerre matrix polynomials and Lie-algebraic techniques
• Special Functions for the Symmetric Space of Positive Matrices
• On generalized Hermite matrix polynomials
• Operational versus Lie-algebraic methods and the theory of multi-variable Hermite polynomials
• Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument
• The growth of Laguerre matrix polynomials on bounded intervals.
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