October 17, 2018
4:30PM - 5:30PM
Math Building 105
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2018-10-17 16:30:00
2018-10-17 17:30:00
Several Complex Variables Seminar - Jue Xiong
Title: Norm convergence of partial sums of $H^1$ functions
Speaker: Jue Xiong (Ohio State University)
Abstract: A classical observation of Riesz says that truncations of a general $\sum_{n=0}^{\infty}a_nz^n$ in the Hardy space $H^1$ do not converge in $H^1$. A substitute positive result is proved: these partial sums always converge in the Bergman norm $A^1$. The result is extended to complete Reinhardt domains in $\mathbb{C}^n$. A new proof of the failure of $H^1$ convergence is also given.
Math Building 105
OSU ASC Drupal 8
ascwebservices@osu.edu
America/New_York
public
Date Range
Add to Calendar
2018-10-17 16:30:00
2018-10-17 17:30:00
Several Complex Variables Seminar - Jue Xiong
Title: Norm convergence of partial sums of $H^1$ functions
Speaker: Jue Xiong (Ohio State University)
Abstract: A classical observation of Riesz says that truncations of a general $\sum_{n=0}^{\infty}a_nz^n$ in the Hardy space $H^1$ do not converge in $H^1$. A substitute positive result is proved: these partial sums always converge in the Bergman norm $A^1$. The result is extended to complete Reinhardt domains in $\mathbb{C}^n$. A new proof of the failure of $H^1$ convergence is also given.
Math Building 105
Department of Mathematics
math@osu.edu
America/New_York
public
Title: Norm convergence of partial sums of $H^1$ functions
Speaker: Jue Xiong (Ohio State University)
Abstract: A classical observation of Riesz says that truncations of a general $\sum_{n=0}^{\infty}a_nz^n$ in the Hardy space $H^1$ do not converge in $H^1$. A substitute positive result is proved: these partial sums always converge in the Bergman norm $A^1$. The result is extended to complete Reinhardt domains in $\mathbb{C}^n$. A new proof of the failure of $H^1$ convergence is also given.
