Modern Fourier Analysis

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Focusing on the theoretical foundation of Fourier analysis, this book is tailored for graduate mathematics students and designed for a comprehensive three-course sequence. It requires prior knowledge in measure theory, Lebesgue integration, and complex variables. The text delves deeply into selected topics, emphasizing real variable methods in Euclidean spaces while also including a chapter on analysis on the torus for its historical significance, tracing the origins of Fourier analysis to trigonometric expansions of periodic functions.