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Variants of Dirichlet's theorem on Fourier series - Math Stack Exchange
Unlike rigorous drill books, Körner's Fourier Analysis (1988) is designed to be accessible to undergraduates with two years of mathematical background. It treats Fourier analysis as a subject born in physics that grew into a cornerstone of pure mathematics, emphasizing that the same techniques used for heat equations can also be applied to number theory and statistics.
The beginning of the book is deceptively simple. It deals with the representation of periodic functions as sums of sines and cosines. However, Körner quickly moves past the "nice" functions that students are used to.
He is not afraid to tell you that a proof is "ugly" or that a historical figure was "stubborn." This narrative style makes the book readable in a way that few advanced math texts are. He guides the reader through the thicket of Lebesgue integrals and $L^p$ spaces with a narrative thread that keeps you turning pages.
To convince you to acquire this text legally, let’s break down what you will find inside.
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