國立虎尾科技大學 |

Finite Blaschke Products and Their Connections

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Finite Blaschke Products and Their Connections/ by Stephan Ramon Garcia, Javad Mashreghi, William T. Ross.
Author:	Garcia, Stephan Ramon.
other author:	Mashreghi, Javad.
Description:	XIX, 328 p. 49 illus., 10 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functional analysis. -
Online resource:	https://doi.org/10.1007/978-3-319-78247-8
ISBN:	9783319782478

Finite Blaschke Products and Their Connections
Garcia, Stephan Ramon.

Finite Blaschke Products and Their Connections[electronic resource] /by Stephan Ramon Garcia, Javad Mashreghi, William T. Ross. - 1st ed. 2018. - XIX, 328 p. 49 illus., 10 illus. in color.online resource.

Preface -- 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.

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.

ISBN: 9783319782478

Standard No.: 10.1007/978-3-319-78247-8doiSubjects--Topical Terms:

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Finite Blaschke Products and Their Connections
LDR:03209nam a22003975i 4500 001 993901
003 DE-He213
005 20200704092522.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319782478 $9 978-3-319-78247-8
024 7 $a 10.1007/978-3-319-78247-8 $2 doi
035 $a 978-3-319-78247-8
050 4 $a QA319-329.9
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
100 1 $a Garcia, Stephan Ramon. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1205157
245 1 0 $a Finite Blaschke Products and Their Connections $h [electronic resource] / $c by Stephan Ramon Garcia, Javad Mashreghi, William T. Ross.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a XIX, 328 p. 49 illus., 10 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a Preface -- 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.
520 $a 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.
650 0 $a Functional analysis. $3 527706
650 0 $a Operator theory. $3 527910
650 1 4 $a Functional Analysis. $3 672166
650 2 4 $a Operator Theory. $3 672127
700 1 $a Mashreghi, Javad. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1072508
700 1 $a Ross, William T. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 792266
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319782461
776 0 8 $i Printed edition: $z 9783319782485
776 0 8 $i Printed edition: $z 9783030086558
856 4 0 $u https://doi.org/10.1007/978-3-319-78247-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)