Blaschke Products and Their Applications

ISBN-13: 9781461453406 / Angielski / Twarda / 2012 / 322 str.

Javad Mashreghi; Emmanuel Fricain

Opis

​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.

Spis treści

​-Preface. - Applications of Blaschke products to the spectral theory of Toeplitz operators (Grudsky, Shargorodsky). -A survey on Blaschke-oscillatory differential equations, with updates (Heittokangas.). - Bi-orthogonal expansions in the space L2(0,1) ( Boivin, Zhu). - Blaschke products as solutions of a functional equation (Mashreghi.). - Cauchy Transforms and Univalent Functions( Cima,  Pfaltzgraff). - Critical points, the Gauss curvature equation and Blaschke products (Kraus, Roth). - Growth, zero distribution and factorization of 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 Hardy space of the upper half plane (Feichtinger, Pap). - Norm of composition operators induced by finite Blaschke products on Mobius invariant spaces (Martin, Vukotic). - On the 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).​

Blurb

Blaschke products have been researched for nearly a century. They have shown to be important in several branches of mathematics through their  boundary behaviour, dynamics, membership in different function spaces,  and the asymptotic growth of various integral means of their derivatives.

 

This volume presents a collection of survey and research articles that examine Blaschke products and several of their applications to fields  such as approximation theory, differential equations, dynamical  systems, and harmonic analysis. Additionally, it illustrates the  historical roots of Blaschke products and highlights key research on this topic.

 

The contributions, written by experts from various fields of  mathematical research, include several open problems. They will  engage graduate students and researchers alike, bringing them to the forefront of research in the subject.