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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Summability of Hermite expansions. I


Author: S. Thangavelu
Journal: Trans. Amer. Math. Soc. 314 (1989), 119-142
MSC: Primary 42C10; Secondary 42A24
DOI: https://doi.org/10.1090/S0002-9947-1989-99923-2
Part II: Trans. Amer. Math. Soc. (1) (1989), 143-170
MathSciNet review: 958904
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Abstract: We study the summability of one-dimensional Hermite expansions. We prove that the critical index for the Riesz summability is $ 1/6$. We also prove analogues of the Fejér-Lebesgue theorem and Riemann's localisation principle.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1989-99923-2
Keywords: Hermite expansion, summability, Riesz means, oscillatory integrals
Article copyright: © Copyright 1989 American Mathematical Society