Blaschke products and their applications [electronic resource] /
Mashreghi, Javad.editor.
Fricain, Emmanuel.editor.
Fields Institute for Research in Mathematical Sciences.
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.
Description based upon print version of record.
Blaschke Products and Their Applications; Preface; Contents; Applications of Blaschke Products to the Spectral Theory of Toeplitz Operators; 1 Introduction; 2 Spectra of Toeplitz Operators; 3 Compositions with Blaschke Products and the Ap Condition; 4 More on the Spectra of Toeplitz Operators; 5 Modelling of Monotone Functions with the Help of Blaschke Products; 6 Applications to the KdV Equation; 7 Some Open Problems; References; Approximating the Riemann Zeta-Function by Strongly Recurrent Functions; 1 Introduction; 2 Symmetric Function Theory; 3 Frequent Hypercyclicity
4 Proof of Theorem 35 Proof of Theorem 4; References; A Survey on Blaschke-Oscillatory Differential Equations, with Updates; 1 Prologue; 2 Introduction; 3 Typical Requirements for Blaschke Sequences; 3.1 Measurements for the Quantity of Points; 3.2 Measurements for the Density of Points; 4 The Converse Direction; 4.1 Improvement of (4); 4.2 Basic Properties of Solutions; 4.3 Solutions in F\N are Possible; 5 Disconjugate, Non-oscillatory and Oscillatory; 5.1 Pointwise Growth Restrictions for A(z); 5.2 Integrated Growth Restrictions for A(z); 6 Univalent Coefficient Function
7 Logarithmic Derivatives of Blaschke Products7.1 Pointwise Estimates; 7.2 Integrated Estimates; 8 One Infinite Prescribed Zero Sequence; 9 Two Infinite Prescribed Zero Sequences; 9.1 New Result Involving Two Sequences; 9.2 Interpolation in the BMOA Space; 9.3 Wiman-Valiron Theory in D; 9.4 Proof of Theorem 21; 10 Finite Prescribed Zero Sequences; 11 Blaschke-Oscillatory Equations of Arbitrary Order; 12 Critical Points and Blaschke-Critical Equations; 12.1 Zeros Versus Critical Points; 12.2 Necessary and Sufficient Conditions; 12.3 Prescribed Critical Points; 13 Concluding Remarks; References
Bi-orthogonal Expansions in the Space L2(0,infty)1 Introduction; 2 Two Systems of Analytic Functions in H2+; 3 Bi-orthogonal Expansions in H2+; 4 Main Results and Their Proofs; References; Blaschke Products as Solutions of a Functional Equation; 1 Introduction; 2 A Two-Sided Blaschke Sequence; Open Question; 3 A Surjective Composition Operator on KB; References; Cauchy Transforms and Univalent Functions; 1 Introduction; 2 Definitions and Known Results; 3 The Primitive of a CT Function; 4 The Connection to Univalent Functions; 5 Connection to BMOA and Teichmuller Space; 6 Questions; References
Critical Points, the Gauss Curvature Equation and Blaschke Products1 Critical Points of Bounded Analytic Functions; 2 Conformal Metrics and Maximal Blaschke Products; 2.1 Conformal Metrics and Developing Maps; 2.2 Maximal Conformal Pseudometrics and Maximal Blaschke Products; 3 Some Properties of Maximal Blaschke Products; 3.1 Schwarz' Lemmas; 3.2 Related Extremal Problems in Hardy and Bergman Spaces; 3.3 Boundary Behaviour of Maximal Blaschke Products; 3.4 Heins' Results on Maximal Functions; 4 The Gauss Curvature PDE and the Berger-Nirenberg Problem; Berger-Nirenberg Problem; References
Growth, Zero Distribution and Factorization of Analytic Functions of Moderate Growth in the Unit Disc
Includes bibliographical references.
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.
Functions of complex variables.
Functional analysis.
Difference equations.
Functional equations.
Functions of a Complex Variable.
Functional Analysis.
Difference and Functional Equations.