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List 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
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.
Summary
Operator theory is a very wide field, with numerous facets, both applied and theoretical. In this book we focus on 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). There are deep connections with complex analysis, functional analysis, mathematical physics, electrical engineering, machine learning and physics to name a few. Fascinating new directions and connections regularly appear, such as operator spaces, free probability, and applications to hypercomplex analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and we hope you enjoy the reading, and profit from this endeavor.
