LEADER 03402nam  22004815  450 
001 9910300102403321
005 20251113203412.0
010   $a3-319-78247-9
024 7 $a10.1007/978-3-319-78247-8
035   $a(CKB)4100000004243847
035   $a(MiAaPQ)EBC5401122
035   $a(DE-He213)978-3-319-78247-8
035   $a(PPN)227406567
035   $a(EXLCZ)994100000004243847
100   $a20180524d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aFinite Blaschke Products and Their Connections /$fby Stephan Ramon Garcia, Javad Mashreghi, William T. Ross
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (340 pages)
311 08$a3-319-78246-0 
327   $aPreface -- Notations -- 1. Geometry of the Schur class -- 2. Elementary hyperbolic geometry -- 3. Finite Blaschke products: the basics -- 4. Approximation by finite Blaschke products -- 5. Zeros and residues -- 6. Critical points -- 7. Interpolation -- 8. The Bohr radius -- 9. Finite Blaschke products and group theory -- 10. Finite Blaschke products and operator theory -- 11. Real complex functions -- 12. Finite-dimensional model spaces -- 13. The Darlington synthesis problem -- A. Some reminders -- Index.
330   $aThis 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.
606   $aFunctional analysis
606   $aOperator theory
606   $aFunctional Analysis
606   $aOperator Theory
615  0$aFunctional analysis.
615  0$aOperator theory.
615 14$aFunctional Analysis.
615 24$aOperator Theory.
676   $a515.9
700   $aGarcia$b Stephan Ramon$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768246
702   $aMashreghi$b Javad$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aRoss$b William T$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910300102403321
996   $aFinite Blaschke Products and Their Connections$92102300
997   $aUNINA