Editors:
- Focus on new results and original research
- Most approaches and techniques presented for the first time in an easily understandable format
- Topics covered reflect new trends in Schur analysis and new areas for future studies
- Includes supplementary material: sn.pub/extras
Part of the book series: Operator Theory: Advances and Applications (OT, volume 226)
Part of the book sub series: Linear Operators and Linear Systems (LOLS)
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Table of contents (6 chapters)
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Front Matter
About this book
The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices.
This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
Reviews
From the reviews:
“The contributors of this volume are very productive and they have published a large number of papers in many journals and books. … It may take a while for the reader to get used to it, but once familiar with these habits and the constructs involved, it is good reading. It will be of high interest to anyone who is involved from far or near with Schur analysis and the whole universe of related topics that I sketched in the beginning.” (A. Bultheel, The European Mathematical Society, September, 2012)
Editors and Affiliations
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Dept. Mathematics & Computer Science, Ben-Gurion University of the Negev, Beer Sheva, Israel
Daniel Alpay
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, Mathematisches Institut, Universität Leipzig, Leipzig, Germany
Bernd Kirstein
Bibliographic Information
Book Title: Interpolation, Schur Functions and Moment Problems II
Editors: Daniel Alpay, Bernd Kirstein
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-0348-0428-8
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2012
Hardcover ISBN: 978-3-0348-0427-1Published: 24 July 2012
Softcover ISBN: 978-3-0348-0742-5Published: 09 August 2014
eBook ISBN: 978-3-0348-0428-8Published: 25 July 2012
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: VI, 302
Topics: Operator Theory, Integral Transforms, Operational Calculus, Functions of a Complex Variable