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Nell Paiz Jacobsson: On the convergence and divergence of Fourier series

Time: Mon 2021-05-31 15.30 - 16.30

Location: Meeting ID: 640 6342 1581

Respondent: Nell Paiz Jacobsson

Abstract

The purpose of this thesis is to study convergence and divergence phenomena for Fourier series. In particular, we seek sufficient criteria for functions to guarantee that their Fourier series converge. We present several positive results as we discover conditions that ensure different types of convergence. On the other hand, we construct a continuous function whose Fourier series diverges at one point, establishing that continuity in a function does not in fact guarantee the convergence of its Fourier series.

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Belongs to: Department of Mathematics
Last changed: May 27, 2021