Many branches of mathematics come together in harmonic analysis; each adds richness to the subject and provides insights into this fascinating field. DeVito’s Harmonic Analysis presents a clear, comprehensive introduction to Fourier analysis and Harmonic analysis, and provides numerous examples and models, leaving students with a clear understanding of the theory.

• Material is presented in a unified way, avoiding the “cookbook” character of many texts. For example, in Chapter one an interesting boundary value problem is solved. The discussion then leads naturally to harmonic functions, periodic functions, and Fourier series. The various ways such series can converge are investigated in three separate chapters. Roots of unity and the fast Fourier transform are discussed. Here the symbiotic interplay between algebra and analysis is emphasized and exploited. Students are brought into the discussion by providing them with problems keyed to the material being discussed. Such problems are marked with a star. Solutions to starred exercises throughout the text are provided in an appendix. The structure and format of the text is flexible, allowing the instructor to tailor it to the needs of the course and the needs of the students. There is a discussion of the number theory that arises in connection with the Fourier transform and a chapter on the relevant structures from abstract algebra

Preface / Preliminaries / Classical Harmonic Analysis / Extensions of the Classical Theory / Fourier Series in Hilbert Space / The Fourier Transform / Abstract Algebra / Linear Algebra / The Completion / Solution to the Starred Problems / Index.

Undergraduate – Graduate Students in Mathematics