Finite Blaschke Products and Their Connections

Authors: Garcia, Stephan Ramon, Mashreghi, Javad, Ross, William

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  • Explains connections in complex analysis, linear algebra, operator theory, and electrical engineering
  • Accessible to undergraduate students, graduate students, and researchers familiar with complex analysis
  • Offers numerous exercises that equip the reader with a working knowledge of the material
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eBook $44.99
$54.99 (listprice)
price for USA in USD (gross)
valid through June 30, 2019
  • ISBN 978-3-319-78247-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
$99.99 (listprice)
price for USA in USD
valid through June 30, 2019
  • ISBN 978-3-319-78246-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2019
  • ISBN 978-3-030-08655-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

Stephan Ramon Garcia is a professor of mathematics at Pomona College

Javad Mashreghi is a professor in the Department of Mathematics and Statistics at Laval University, Alexandre-Vachon. 

William T. Ross is a professor of mathematics and the Chair of the Department of Math and Computer Sciences at the University of Richmond.

Reviews

“The book under consideration is concerned with finite Blaschke products. … The book is designed for students and researchers familiar with basic real and complex analysis and linear algebra. The proofs are detailed and dozens illustrations are provided. At the end of each chapter, the authors include exercises so that the reader can gain greater technical fluency with the material and appreciate the beauty of the subject.” (Leonid Golinskii, zbMATH 1398.30002, 2018)

Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook $44.99
$54.99 (listprice)
price for USA in USD (gross)
valid through June 30, 2019
  • ISBN 978-3-319-78247-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
$99.99 (listprice)
price for USA in USD
valid through June 30, 2019
  • ISBN 978-3-319-78246-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2019
  • ISBN 978-3-030-08655-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Finite Blaschke Products and Their Connections
Authors
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-78247-8
DOI
10.1007/978-3-319-78247-8
Hardcover ISBN
978-3-319-78246-1
Softcover ISBN
978-3-030-08655-8
Edition Number
1
Number of Pages
XIX, 328
Number of Illustrations
39 b/w illustrations, 10 illustrations in colour
Topics