This book explores globalized Fejer's theorem and its implications for Fourier analysis, highlighting the contributions of Lebesgue and Denjoy. It introduces Fourier series, transforms, and wavelets in an accessible manner for beginners, while acknowledging the depth of the subject that warrants further study.
The second edition offers an in-depth analysis of the Hahn-Banach theorem, enriched with concrete examples and historical context. It delves into the theorem's relationship with the axiom of choice and examines the uniqueness of Hahn-Banach extensions. A notable addition is a new chapter dedicated to vector-valued Hahn-Banach extensions, enhancing the book's comprehensiveness and relevance for readers seeking a thorough understanding of this mathematical concept.