Summability of Hermite expansions. I

1989/01/01 by S. Thangavelu, Sundaram Thangavelu · 2 citations
Mathematics · #Mathematical functions and polynomials #Mathematical Analysis and Transform Methods #Approximation Theory and Sequence Spaces

paper · doi:10.1090/s0002-9947-1989-99923-2

Abstract

We study the summability of one-dimensional Hermite expansions. We prove that the critical index for the Riesz summability is <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1 slash 6"> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">1/6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . We also prove analogues of the Fejér-Lebesgue theorem and Riemann’s localisation principle.

Citations

• Mean Convergence of Expansions in Laguerre and Hermite Series

Cited by

• Convergence of Hermite expansions in modulation spaces
• Almost everywhere convergence of Bochner-Riesz means for the Hermite type Laguerre expansions

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