Harmonic and Complex Analysis and its Applications

Description

This volume highlights the main results of the research performed within the network “Harmonic and Complex Analysis and its Applications” (HCAA), which was a five-year (2007–2012) European Science Foundation Programme intended to explore and to strengthen the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. It coordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings, potential theory, Banach spaces of analytic functions and their applications to the problems of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveys written as a result of activities of the Programme and will be interesting and useful for professionals and novices in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader will undoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme. Front Matter....Pages i-viii Function Spaces of Polyanalytic Functions....Pages 1-38 Classical and Stochastic Löwner–Kufarev Equations....Pages 39-134 The Schwarz Lemma: Rigidity and Dynamics....Pages 135-230 Coorbit Theory and Bergman Spaces....Pages 231-259 Quadrature Domains and Their Two-Phase Counterparts....Pages 261-285 Exponential Transforms, Resultants and Moments....Pages 287-323 From the Virasoro Algebra to Krichever–Novikov Type Algebras and Beyond....Pages 325-358