Finite Blaschke products and their connections. ([2018])

• Record Type: Book
• Further Information: Note: Stephan Ramon Garcia, Javad Mashreghi, William T. Ross.
• Authors: Garcia, Stephan Ramon; Mashreghi, Javad; Ross, William T
• Contents: Intro; Preface; Contents; Notation; 1 Geometry of the Schur Class; 1.1 The Schwarz Lemma; 1.2 Automorphisms of the Disk; 1.3 Algebraic Structure of Aut(D); 1.4 The Schwarz-Pick Theorem; 1.5 An Extremal Problem; 1.6 Julia's Lemma; 1.7 Fixed Points; 1.8 Exercises; 2 Elementary Hyperbolic Geometry; 2.1 Pseudohyperbolic Metric; 2.2 Generalized Triangle Inequality; 2.3 Poincaré Metric; 2.4 Ahlfors's Version of the Schwarz's Lemma; 2.5 Hyperbolic Geometry in C+; 2.6 Exercises; 3 Finite Blaschke Products: The Basics; 3.1 Finite Blaschke Products; 3.2 Uniqueness and Nonuniqueness. 3.3 Finite Blaschke Products as Rational Functions3.4 Finite Blaschke Products as n-to-1 Functions; 3.5 Unimodular Elements of the Disk Algebra; 3.6 Composition of Finite Blaschke Products; 3.7 Constant Valence; 3.8 Finite Blaschke Products on C+; 3.9 Notes; Commuting Blaschke Products; Infinite Blaschke Products; 3.10 Exercises; 4 Approximation by Finite Blaschke Products; 4.1 Approximating Functions from S; 4.2 The Closed Convex Hull of the Finite Blaschke Products; 4.3 Approximating Continuous Unimodular Functions; 4.4 Approximation by Finite Blaschke Products with Simple Zeros. 7 Interpolation7.1 Lagrange Interpolation: Polynomials; 7.2 Lagrange Interpolation: Rational Functions; 7.3 Pick Interpolation Theorem; 7.4 Boundary Interpolation: Cantor-Phelps Solution; 7.5 Boundary Interpolation: A Constructive Solution; 7.6 Exercises; 8 The Bohr Radius; 8.1 The Classical Bohr Radius B0; 8.2 Computing B0; 8.3 The Generalized Bohr Radius Bk; 8.4 A Localized Bohr Radius; 8.5 Estimates of Landau and Bombieri; 8.6 A Theorem of Bombieri and Ricci; 8.7 Notes; Alternate Proofs; Other Bohr Inequalities; Harald Versus Nils; Harald Bohr, Footballer; 8.8 Exercises. 9 Finite Blaschke Products and Group Theory9.1 A Cyclic Subgroup; 9.2 Decomposable Finite Blaschke Products; 9.3 The Monodromy Group; 9.4 Examples of Monodromy Groups; 9.5 Primitive Versus Imprimitive; 9.6 Ritt's Theorem; 9.7 Examples of Decomposability; 9.8 Notes; Ritt's Theorem for Polynomials; Ritt's Theorem Redux; Ritt's Theorem and Cyclic Groups; Chebyshev Blaschke Products; An Interesting Approximation Result; Further Examples; 9.9 Exercises; 10 Finite Blaschke Products and Operator Theory; 10.1 Contractions; 10.2 Norms of Contractions; 10.3 Numerical Range; 10.4 Halmos' Conjecture.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource
• Subjects: 515/.9; Mathematics; Functions of complex variables; Blaschke products; Connections (Mathematics); MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Blaschke products; Connections (Mathematics); Functions of complex variables; Mathematics; Functional Analysis; Operator Theory; Mathematics -- Functional Analysis; Functional analysis & transforms; Functional analysis; Operator theory; Electronic books
• Languages: English
• ISBNs: 9783319782478; 3319782479
• Related ISBNs: 9783319782461; 3319782460
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed May 30, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.