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Seminars

Seminar
FIELD Math:Analysis
DATE January 11 (Mon), 2021
TIME 16:30-18:00
PLACE 8101
SPEAKER Lee, Sanghyuk
HOST Jeong, In-Jee
INSTITUTE 서울대학교
TITLE Almost everywhere convergence of Bochner-Riesz means for the Hermite expansion
ABSTRACT In this talk we consider almost everywhere convergence of the Bochner-Riesz means of the Hermite expansion and characterize the summability index for which the means converges almost everywhere. For $f\in L^p$ with $p\ge 2$ we show the Bochner-Riesz means converges almost everywhere if the summability index is bigger than $\alpha(p)=\max(n(1/4-1/2p)-1/4, 0)$ and the convergence generally fails if the index is smaller than $\alpha(p)$. This is in striking contrast with the classical Bochner-Riesz means of Fourier transform and Fourier series in that the required summability index is only half of the index for almost everywhere convergence of the classical Bochner-Riesz means of Fourier transform and Fourier series.
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