Analysis on compact groups

Abstract

In this chapter, we take up a number of special topics in harmonic analysis on compact groups. Section 34 deals with the algebra of absolutely convergent Fourier series, an entity about which a good deal although far from everything is known. Sections 35 and 36 are a detailed treatment of multipliers for various classes of Fourier transforms on compact groups; some facts about locally compact Abelian groups are obtained as well. In § 37, we study lacunary Fourier transforms, again on compact groups, and in § 38, ideal theory for certain convolution algebras of functions on compact groups.