By Yurii I. Lyubich
The thought of workforce representations performs a massive roie in glossy arithmetic and its applica~ions to traditional sciences. within the obligatory college curriculum it's incorporated as a department of algebra, facing representations of finite teams (see, for instance, the textbook of A. I. Kostrikin ). The illustration conception for compact, in the neighborhood compact Abelian, and Lie teams is co vered in graduate classes, focused round sensible research. the writer of the current boo~ has lectured for a few years on useful research at Khar'kov collage. He therefore con tinued those lectures within the kind of a graduate direction at the idea of team representations, within which specific realization used to be dedicated to a retrospective exposition of operator conception and harmo nic research of capabilities from the perspective of illustration thought. during this procedure it used to be normal to contemplate not just uni tary, but additionally Banach representations, and never merely representations of teams, but in addition of semigroups.