Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers

This book on recent research in noncommutative harmonic analysis treats the L^p boundedness of Riesz transforms associated with Markovian semigroups of either Fourier multipliers on non-abelian groups or Schur multipliers. The detailed study of these objects is then continued with a proof of the boundedness of the holomorphic functional calculus for Hodge–Dirac operators, thereby answering a question of Junge, Mei and Parcet, and presenting a new functional analytic approach which makes it p...