Fractional Cauchy Transforms

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Presenting new results along with research spanning five decades, Fractional Cauchy Transforms provides a full treatment of the topic, from its roots in classical complex analysis to its current state. Self-contained with numerous references, it includes introductory material and classical results, such as those associated with complex-valued measures on the unit circle, that form the basis of the developments that follow. The authors focus on concrete analytic questions, with functional analysis providing the general framework. Discussions include radial limits, exceptional sets, zeros, factorization, and the relations between fractional Cauchy transforms and Dirichlet and Besov spaces .