MATE 3322 Int Análisis Armónico (Inglés)
In this course we will study a basic tool of analysis: the Fourier series. We will start with basic notions related to the Fourier series and their pointwise convergence as well as convergence in the norm. Then there are several possibilities how to proceed further. For example, we could continue with Hardy spaces and notions related to the theory of analytic functions in the unit disc; discuss lacunary series and their relations to Probability Theory; turn to the noncommutative case on the group SO(3), etc. For the most part we will follow the book by Katznelson and cover chapter I and II, and possibly III and V. For the part about the lacunary series we would use the book by Zygmund. Depending on the additional material we will cover, we might use some additional literature.
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