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Generalizations of two-index two-variable Hermite matrix polynomials. (English) Zbl 1186.15019

The authors provide some answers to the problems arising in the study of the development of matrix functions in series of Hermite matrix polynomials. They obtain an explicit representation and an expansion of the matrix exponential in a series of these matrix polynomials. They also prove that the generalized Hermite matrix polynomials satisfy a matrix differential equation.

MSC:

15A54 Matrices over function rings in one or more variables
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
15A16 Matrix exponential and similar functions of matrices
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