"The rapid development of quantum mechanics stimulated research in and theory. Initiated during the mid-twenties, intensive study of s and their representations led to Haar's discovery of the basic construction of invariant integration on a topological group. Bohr's theory of s influenced the work of Wiener, Bochner and many other analysts. They enriched the technical arsenal of harmonic analysis and the scope of its applications (statistical mechanics, ergodic theory, , etc.) The new notion of the generalized made it possible to consider Plancherel's theory simultaneously with Bohr's theory, the continuous spectrum with the discrete. The Pontrjagin-van Kampen duality opened the way for an unobstructed development of on locally compact s, allowing , Fourier integrals and expansions via numerical characters to be viewed as objects of the same kind. The Peter–Weyl theory made it possible for von Neumann to analyze almost periodic functions on groups by connecting them to group representation theory. Along with the many other discoveries of that period, this led to the inclusion of group theorethical methods into the tool kit of harmonic analysis."