Winding numbers and Fourier series

Details Winding numbers and Fourier series Winding numbers and Fourier series

2010-03-30

arxiv.org/abs/1003.5748v1

Mathematics

Classical Analysis and ODEs

The talk was delivered in St Petersburg in June 2009, and should be published in the Proceedings.

Scientific paper

This is an expository talk on a topic of classical analysis, arising from the VMO theory of the topological degree due to Br\'ezis and Nirenberg (1995). We sketch the history of the subject and some of its recent developments. The paper is organized as a sequence of questions. Most of them, in particular the last one, deal with Fourier series of continuous functions of constant absolute value. One of them contains new results on the comparison of summation processes.

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