By V. P. Khavin (auth.), V. P. Khavin, N. K. Nikol’skij (eds.)

This quantity is the 1st within the sequence dedicated to the commutative harmonic research, a basic a part of the modern arithmetic. the basic nature of this topic, notwithstanding, has been made up our minds goodbye in the past, that not like in different volumes of this book, we need to commence with uncomplicated notions that have been in consistent use in arithmetic and physics. making plans the sequence as a complete, we have now assumed that harmonic research relies on a small variety of axioms, easily and obviously formulated by way of workforce concept which illustrate its resources of principles. despite the fact that, our topic can't be thoroughly lowered to these axioms. This a part of arithmetic is so good built and has such a lot of diversified facets to it that no summary scheme is ready to conceal its big concreteness thoroughly. specifically, it pertains to an incredible inventory of proof gathered through the classical "trigonometric" harmonic research. furthermore, subjected to a common mathematical tendency of integration and diffusion of traditional intersubject borders, harmonic research, in its modem shape, an increasing number of rests on non-translation invariant buildings. for instance, one ofthe so much signifi­ cant achievements of latter many years, which has considerably replaced the total form of harmonic research, is the penetration during this topic of refined innovations of singular essential operators.

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