Operator Theory

Editors: Alpay, Daniel (Ed.)

  • Embraces the long history, diversity and wide range of topics relating to operator theory
  • Explores notions such as positivity and reproducing kernel through interconnected sections
  • Describes multiple applications and connections with other fields of mathematics, physics and Engineering
  • Provides a timely reference work on operator theory
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About this Reference Work

A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.

About the authors

Editorial Board:

  • Daniel Alpay (Editor-in-Chief), Earl Katz Chair in Algebraic System   Theory, Department of Mathematics, Ben-Gurion University of the Negev, Be’er Sheva, Israel
  • Joseph A. Ball, Department of Mathematics, Virginia Tech, Blacksburg, VA, USA
  • Anton Baranov, Department of Mathematics and Mechanics, St. Petersburg State University, Pedrodvorets, Russia
  • Fabrizio Colombo, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
  • Palle E.T. Jorgensen, Department of Mathematics, The University of Iowa, Iowa City, IA, USA
  • Matthias Langer, Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland, UK 
  • Mamadou Mboup, Université de Reims Champagne Ardenne, CReSTIC - UFR des Sciences Exactes et Naturelles Moulin de la Housse, Reims, France
  • Irene Sabadini, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy
  • Michael Shapiro, Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, del Instituto Politécnico Nacional, Mexico City, Mexico
  • Franciszek Hugon Szafraniec,Instytut Matematyki, Uniwersytet Jagiellónski, Kraków, Poland
  • Harald Woracek, Institut for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria

Prof. Daniel Alpay is a faculty member of the department of mathematics at Ben-Gurion University, Beer-Sheva, Israel. He is the incumbent of the Earl Katz Family chair in algebraic system theory. He has a double formation of electrical engineer (Telecom Paris, graduated 1978) and mathematician (PhD, Weizmann Institute, 1986). His research includes operator theory, stochastic analysis, and the theory of linear systems. Daniel Alpay is one of the initiators and responsible of the dual track electrical-engineering mathematics at Ben-Gurion University. Together with co-authors, he has written two books and close to 190 research papers, and edited ten books of research papers.


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Table of contents (64 chapters)

  • The Reproducing Kernel Property and Its Space: The Basics

    Szafraniec, Franciszek Hugon

    Pages 3-30

  • The Reproducing Kernel Property and Its Space: More or Less Standard Examples of Applications

    Szafraniec, Franciszek Hugon

    Pages 31-58

  • The Use of Kernel Functions in Solving the Pick Interpolation Problem

    Agler, Jim (et al.)

    Pages 59-71

  • Bergman Kernel in Complex Analysis

    Kosiński, Łukasz (et al.)

    Pages 73-86

  • Sampling Theory and Reproducing Kernel Hilbert Spaces

    García, Antonio G.

    Pages 87-110

Buy this book

Print + eBook $1,560.00
price for USA
  • ISBN 978-3-0348-0668-8
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
Print $999.00
price for USA
  • ISBN 978-3-0348-0666-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
eReference $999.00
price for USA (gross)
  • ISBN 978-3-0348-0667-1
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Operator Theory
Editors
  • Daniel Alpay
Copyright
2015
Publisher
Springer Basel
Copyright Holder
Springer Basel
Print + eBook ISBN
978-3-0348-0668-8
Print ISBN
978-3-0348-0666-4
eReference ISBN
978-3-0348-0667-1
Edition Number
1
Number of Pages
XIX, 1860
Number of Illustrations and Tables
33 b/w illustrations, 18 illustrations in colour
Topics