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Blaschke Products and Their Applications presents a collection of survey articles that examine Blaschke products and several of its applications to fields such as approximation theory, differential equations, dynamical systems, harmonic analysis, to name a few. Additionally, this volume illustrates the historical roots of Blaschke products and highlights key research on this topic. For nearly a century, Blaschke products have been researched. Their boundary behaviour, the asymptomatic growth of various integral means and their derivatives, their applications within several branches of mathematics, and their membership in different function spaces and their dynamics, are a few examples of where Blaschke products have shown to be important. The contributions written by experts from various fields of mathematical research will engage graduate students and researches alike, bringing the reader to the forefront of research in the topic. The readers will also discover the various open problems, enabling them to better pursue their own research.
List of contents
-Preface. - Applications of Blaschke products to the spectraltheory of Toeplitz operators (Grudsky, Shargorodsky). -Asurvey on Blaschke-oscillatory differential equations, with updates (Heittokangas.). - Bi-orthogonal expansions in the space L2(0,1) ( Boivin, Zhu). - Blaschkeproducts as solutions of a functional equation (Mashreghi.). - CauchyTransforms and Univalent Functions( Cima, Pfaltzgraff). - Critical points, the Gauss curvature equation andBlaschke products (Kraus, Roth). - Growth, zero distribution and factorizationof analytic functions of moderate growth in the unit disc, (Chyzhykov, Skaskiv).- Hardy means of a finite Blaschke product and its derivative ( Gluchoff, Hartmann).-Hyperbolic derivatives determine a function uniquely (Baribeau). - Hyperbolic wavelets and multiresolution in the Hardyspace of the upper half plane (Feichtinger, Pap). - Normof composition operators induced by finite Blaschke products on Mobiusinvariant spaces (Martin, Vukotic). - Onthe computable theory of bounded analytic functions (McNicholl). - Polynomials versus finite Blaschke products (Tuen Wai Ng, Yin Tsang). -Recent progress on truncated Toeplitz operators (Garcia,Ross).
Summary
Blaschke Products and Their Applications presents a collection of survey articles that examine Blaschke products and several of its applications to fields such as approximation theory, differential equations, dynamical systems, harmonic analysis, to name a few. Additionally, this volume illustrates the historical roots of Blaschke products and highlights key research on this topic. For nearly a century, Blaschke products have been researched. Their boundary behaviour, the asymptomatic growth of various integral means and their derivatives, their applications within several branches of mathematics, and their membership in different function spaces and their dynamics, are a few examples of where Blaschke products have shown to be important. The contributions written by experts from various fields of mathematical research will engage graduate students and researches alike, bringing the reader to the forefront of research in the topic. The readers will also discover the various open problems, enabling them to better pursue their own research.
