Continuity, Integration and Fourier Theory

Adriaan C. Zaanen

The first part in this thorough textbook is devoted to continuity properties, culminating in the theorems of Korovikin and Stone-Weierstrass. The last part consists of extensions and applications of the Fourier theory, for example the Wilbraham-Gibbs phenomenon, the Hausdorff-Young theorem, the Poisson sum formula and the heat and wave equations. Since the Lebesgue integral is indispensible for obtaining familiarity with Fourier series and Fourier transforms on a somewhat higher level, the book contains a brief survey with complete proofs of abstract integration theory. The compact and comprehensive exposition is rounded off by well-choosen exercises. The book is of interest to advanced undergraduate and graduate students. This book is a textbook on continuity properties, integration theory and Fourier theory for graduate or advanced undergraduate students in mathematics or...