Summability of Hermite expansions. II
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- by S. Thangavelu PDF
- Trans. Amer. Math. Soc. 314 (1989), 143-170 Request permission
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
- Andrzej Hulanicki and Joe W. Jenkins, Almost everywhere summability on nilmanifolds, Trans. Amer. Math. Soc. 278 (1983), no. 2, 703–715. MR 701519, DOI 10.1090/S0002-9947-1983-0701519-0
- Benjamin Muckenhoupt, Mean convergence of Hermite and Laguerre series. I, II, Trans. Amer. Math. Soc. 147 (1970), 419-431; ibid. 147 (1970), 433–460. MR 0256051, DOI 10.1090/S0002-9947-1970-0256051-9
- S. Thangavelu, Summability of Hermite expansions. I, II, Trans. Amer. Math. Soc. 314 (1989), no. 1, 119–142, 143–170. MR 958904, DOI 10.1090/S0002-9947-1989-99923-2
Additional Information
- © Copyright 1989 American Mathematical Society
- 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
- MathSciNet review: 958904