Displaying similar documents to “On uniform convergence of Hermite series”

Hermite Series with Polar Singularities

Boychev, Georgi S. (2012)

Mathematica Balkanica New Series

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MSC 2010: 33C45, 40G05 Series in Hermite polynomials with poles on the boundaries of their regions of convergence are considered.

An analogue of Gutzmer's formula for Hermite expansions

S. Thangavelu (2008)

Studia Mathematica

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We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of L²(ℝⁿ) under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.

Triebel-Lizorkin spaces for Hermite expansions

Jay Epperson (1995)

Studia Mathematica

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This paper develops some Littlewood-Paley theory for Hermite expansions. The main result is that certain analogues of Triebel-Lizorkin spaces are well-defined in the context of Hermite expansions.

Some relations satisfied by Hermite-Hermite matrix polynomials

Ayman Shehata, Lalit Mohan Upadhyaya (2017)

Mathematica Bohemica

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The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the...

Hermite pseudospectral method for nonlinear partial differential equations

Ben-yu Guo, Cheng-long Xu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Hermite polynomial interpolation is investigated. Some approximation results are obtained. As an example, the Burgers equation on the whole line is considered. The stability and the convergence of proposed Hermite pseudospectral scheme are proved strictly. Numerical results are presented.