About the Book
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.
Table of Contents:
General aspects of quaternionic and Clifford analysis.- Further developments of quaternionic and Clifford analysis.- Infinite dimensional analysis.- Non-commutative theory.- Multivariable operator theory.- Reproducing kernel Hilbert spaces.- de Branges spaces.- Indefinite inner product spaces.- Schur analysis.- Linear system theory.
About the Author :
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 diMatematica, 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.
