On almost everywhere and mean convergence of Hermite and Laguerre expansions

S. Thangavelu

Displaying similar documents to “On almost everywhere and mean convergence of Hermite and Laguerre expansions”

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S. Lewandowska, J. Mikusiński (1974)

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Triebel-Lizorkin spaces for Hermite expansions

Jay Epperson (1995)

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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.

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S. Thangavelu (2008)

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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.

Hermite Series with Polar Singularities

Boychev, Georgi S. (2012)

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

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Almost everywhere summability of Laguerre series

Krzysztof Stempak (1991)

Studia Mathematica

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We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions $ℓ_{n}^{a} (x) = {(n! / Γ (n + a + 1))}^{1 / 2} e^{- x / 2} L_{n}^{a} (x)$ , n = 0,1,2,..., in $L^{2} (ℝ_{+}, x^{a} d x)$ , a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function $f \in L^{p} (x^{a} d x)$ , 1 ≤ p ≤ ∞, converge to f a.e. The main tool we use is a Hardy-Littlewood type maximal operator associated with a generalized Euclidean convolution.

Some properties of generalized Hermite polynomials

A. Pain (1971)

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Detlef Müller (1989)

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Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

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The aim of this paper is to extend the study of Riesz transforms associated to Dunkl Ornstein-Uhlenbeck operator considered by A. Nowak, L. Roncal and K. Stempak to higher order.

Some relations satisfied by Hermite-Hermite matrix polynomials

Ayman Shehata, Lalit Mohan Upadhyaya (2017)

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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...

A simple proof of the $L^{p}$ continuity of the higher order Riesz transforms with respect to the gaussian measure $γ_{d}$

Liliana Forzani, Roberto Scotto, Wilfredo Urbina (2001)

Séminaire de probabilités de Strasbourg

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