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Transactions of the American Mathematical Society

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

 
 

 

Summability of Hermite expansions. II


Author: S. Thangavelu
Journal: Trans. Amer. Math. Soc. 314 (1989), 143-170
MSC: Primary 42C10; Secondary 42A24
DOI: https://doi.org/10.1090/S0002-9947-1989-0958904-7
Part I: Trans. Amer. Math. Soc. (1) (1989), 119-142
MathSciNet review: 958904
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Abstract: We study the summability of $ n$-dimensional Hermite expansions where $ n > 1$. We prove that the critical index for the Riesz summability is $ (n - 1)/2$. We also prove analogues of the Fejér-Lebesgue theorem and Riemann's localisation principle when the index $ \alpha $ of the Riesz means is $ > (3n - 2)/6$ .


References [Enhancements On Off] (What's this?)

  • [1] A. Hulanicki and J. W. Jenkins, Almost everywhere summability on nilmanifolds, Trans. Amer. Math. Soc. 278 (1983), 703-715. MR 701519 (85f:22011)
  • [2] B. Muckenhoupt, Mean convergence of Hermite and Laguerre series. I, Trans. Amer. Math. Soc. 147 (1970), 419-431. MR 0256051 (41:711)
  • [3] S. Thangavelu, Summability of Hermite expansions. I, Trans. Amer. Math. Soc. 314 (1989), 119-142. MR 958904 (91b:42048)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1989-0958904-7
Keywords: Hermite expansion, summability, Riesz means, oscillatory integrals
Article copyright: © Copyright 1989 American Mathematical Society

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