Finite blaschke products and their connections
Garcia, Stephan Ramon
Finite blaschke products and their connections - Switzerland : Springer International Publushing, 2018. - xix, 328p. ; 49 illustrations, 10 illustrations in color.
This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered.
Topics are carefully discussed, and numerous examples and illustrations highlight crucial ideas. While thorough explanations allow the reader to appreciate the beauty of the subject, relevant exercises following each chapter improve technical fluency with the material. With much of the material previously scattered throughout mathematical history, this book presents a cohesive, comprehensive and modern exposition accessible to undergraduate students, graduate students, and researchers who have familiarity with complex analysis.
9783319782461
Functional analysis.
Operator theory.
Blaschke Products
Mobius Transformations
Polynomials
Hilbert Spaces
Complex Analysis
Finite Blaschke products
Gauss-Lucas theorem
Lagrange interpolation
Group Theory
Darlington synthesis problem
517.98 / GAR-F
Finite blaschke products and their connections - Switzerland : Springer International Publushing, 2018. - xix, 328p. ; 49 illustrations, 10 illustrations in color.
This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered.
Topics are carefully discussed, and numerous examples and illustrations highlight crucial ideas. While thorough explanations allow the reader to appreciate the beauty of the subject, relevant exercises following each chapter improve technical fluency with the material. With much of the material previously scattered throughout mathematical history, this book presents a cohesive, comprehensive and modern exposition accessible to undergraduate students, graduate students, and researchers who have familiarity with complex analysis.
9783319782461
Functional analysis.
Operator theory.
Blaschke Products
Mobius Transformations
Polynomials
Hilbert Spaces
Complex Analysis
Finite Blaschke products
Gauss-Lucas theorem
Lagrange interpolation
Group Theory
Darlington synthesis problem
517.98 / GAR-F
