##### Department of Mathematics,

University of California San Diego

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### Analysis Seminar

## Victor Lie

#### Purdue

## The pointwise convergence of Fourier Series near $L^1$. Historical evolution, main questions, recent developments, implications.

##### Abstract:

In our talk we will discuss the old and celebrated question regarding the pointwise behavior of Fourier Series near $L^1$. This presentation will include \begin{itemize} \item the resolution of Konyagin's conjecture (ICM, Madrid 2006) on the pointwise convergence of Fourier Series along lacunary subsequences; \item the $L^1$-strong convergence of Fourier Series along lacunary subsequences. \item recent progress on the $L^1$-strong convergence of (the full) Fourier Series. \end{itemize} We end with several considerations on the relevance/impact of the above items on the subject of the pointwise convergence of Fourier Series.

Ioan Bejenaru

### June 6, 2017

### 10:00 AM

### AP&M 7321

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