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Springer Monographs in Mathematics

Extremal Polynomials and Riemann Surfaces

Authors: Bogatyrev, Andrei

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  • Includes numerous problems and  exercises which provide a deep insight in the subject and allow  to conduct independent research  in this topic
  • Contains many pictures which  visualize involved theory
  • Description of effective  computational algorithms for higher genus algebraic curves provides wide opportunities for  numerical experiments in  mathematics and theoretical physics
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eBook $84.99
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  • ISBN 978-3-642-25634-9
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Hardcover $109.99
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About this book

The problems of conditional optimization of the uniform (or C-) norm for polynomials and rational functions arise in various branches of science and technology. Their numerical solution is notoriously difficult in case of high degree functions. The book develops the classical Chebyshev's approach which gives analytical representation for the solution in terms of Riemann surfaces. The techniques born in the remote (at the first glance) branches of mathematics such as complex analysis, Riemann surfaces and Teichmüller theory, foliations, braids, topology are applied to  approximation problems.  

The key feature of this book is the usage of beautiful ideas of contemporary mathematics for the solution of applied problems and their effective numerical realization. This is one of the few books  where the computational aspects of the higher genus Riemann surfaces are illuminated. Effective work with the moduli spaces of algebraic curves provides wide opportunities for numerical experiments in mathematics and theoretical physics.​

About the authors

The author is working in the field of complex analysis, Riemann surfaces and moduli, optimization of numerical algorithms, mathematical physics. He was awarded the S.Kowalewski Prize in 2009 by the Russian Academy of Sciences

Reviews

From the reviews:

“This book develops the classical Chebyshev approach to optimization problems in polynomial spaces. This approach yields an analytical representation for the solution in terms of Riemann surfaces. The text includes numerous problems, exercises, and illustrations. … In this book, methods from various areas of mathematics are used. … It has more than 150 pages throughout which the author makes a lot of effort to give as many results as possible, and yet provide lots of details to make the reading easier.” (Konstantin Malyutin, Zentralblatt MATH, Vol. 1252, 2012)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-642-25634-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
Softcover $109.99
price for USA in USD
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Extremal Polynomials and Riemann Surfaces
Authors
Translated by
Kruzhilin, N.G.
Series Title
Springer Monographs in Mathematics
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-25634-9
DOI
10.1007/978-3-642-25634-9
Hardcover ISBN
978-3-642-25633-2
Softcover ISBN
978-3-642-44332-9
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XXVI, 150
Additional Information
Original Russian edition published by MCCME, Moscow, 2005
Topics