This handbook contains a collection of reference papers which survey the many aspects of modern operator theory and its applications. It begins with sections exploring real and complex reproducing kernel spaces, indefinite inner product spaces, de Branges spaces, and linear systems theory. Multivariable operator theory, infinite dimensional analysis, and quaternionic and hypercomplex analysis are considered in the following parts. For this
Second Edition
, the material has been updated throughout these sections, and many new papers have been added. The remaining sections are entirely new and cover operators and function spaces of analytic functions; non-commutative analysis; operators and superoscillations; operators for quantum particles and fields; the Koopman operator; and analysis and spectral problems in materials science.
Editors-in-Chief:Daniel Alpay, Schmidt College of Science and Technology, Chapman University, Orange, CA, USAFabrizio Colombo, Dipartimento di Matematica, Politecnico di Milano, Milan, ItalyIrene Sabadini, Dipartimento di Matematica, Politecnico di Milano, Milan, ItalyEditorial Board:Anton Baranov, Department of Mathematics and Mechanics, St. Petersburg State University, Pedrodvorets, RussiaKirill Cherednichenko, University of Bath, Bath, UKElena Cherkaev, Department of Mathematics, University of Utah, Salt Lake City, Utah, USAMichele Correggi, Politecnico di Milano, Milan, ItalyRaul Curto,University of Iowa, Iowa City, Iowa, USAIlan Hirshberg, Ben Gurion University, Beersheba, IsraelPalle E.T. Jorgensen, Department of Mathematics, The University of Iowa, Iowa City, IA, USAMatthias Langer, Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland, UK Javad Mashreghi, Université Laval Canada, Quebec City, Quebec, CanadaMamadou Mboup, Université de Reims Champagne Ardenne, CReSTIC - UFR des Sciences Exactes et Naturelles Moulin de la Housse, Reims, FranceScott McCullogh,University of Florida, Gainesville, FL, USAMihai Putinar, UC Santa Barbara, Santa Barbara, CA, USAOrr Shalit, Technion Israel of Technology, Haifa, IsraelDaniele C. Struppa, Schmid College of Science and Technology, Chapman University, Orange, CA, USAFranciszek Hugon Szafraniec, Instytut Matematyki, Uniwersytet Jagiellónski, Kraków, PolandMichal Wojtylak, Jagellonian University, Krakow, PolandHarald Woracek, Institut for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria Prof. Daniel Alpay is a faculty member of the Schmid College of Science and Technology at Chapman University, United States. He holds the Foster G. and Mary McGaw Professorship in Mathematical Sciences. 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. Together with co-authors, he has written 10 books and more than 310 research papers, and edited 18 books.
Prof. Fabrizio Colombo is a faculty member of the Department of Mathematics at Politecnico di Milano. He has the PhD in Mathematics (Università Statale di Milano, 1997). His research interest include operator theory, spectral theory on the S-spectrum,hypercomplex analysis and the theory of superoscillations. Together with co-authors, he has written 9 books and over 230 research papers. He is editor in some mathematical journals.
Prof. Irene Sabadini is a faculty of the Department of Mathematics at Politecnico di Milano. She has the PhD in Mathematics (Università Statale di Milano, 1996). Her research includes the algebraic analysis of Dirac and generalized Cauchy-Riemann operators over noncommutative algebras, complex and hypercomplex analysis. She is co-author of about 220 papers, 8 books, co-editor of 12 volumes and various journals.
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.
