Even today the work is a treasure-trove for every mathematician interested in harmonic analysis, containing many results in this field published for the first time in a textbook. Edwin Hewitt's name was widely known among pure mathematicians through these exemplarily constructed Abstract Harmonic Analysis volumes. 0 Z was more congenial then the filterbank property for frequency-phase analysis and for the practical formulation of the uncertainty relation of quantum physics. Nevertheless, in the course of time his increasing dissatisfaction with the purely structural conception of harmonic analysis and the virtual exclusion of its applications could not be missed. In addition to his research projects Edwin Hewitt also dedicated himself very conscientiously to teaching.
Modern analysis draws on at least five disciplines.
First, to explore measure theory, and even the structure of the real number system, one must use powerful machinery from the abstract theory of sets. Second, algebraic ideas and techniques are illuminating and sometimes essential in studying problems in analysis. Third, set-theoretic topology is needed in constructing and studying measures. We think that handling inequalities, computing with actual functions, and obtaining actual numbers, is indispensable to the training of every mathematician. All five of these subjects thus find a place in our book.