
Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
Springer (Publisher)
Published on 4. April 2014
Book
Paperback/Softback
XV, 95 pages
978-3-319-05109-3 (ISBN)
Description
This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this may serve for many different developments, just like the usual functional analysis with complex scalars and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schur analysis.
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Research
Illustrations
3 farbige Abbildungen
XV, 95 p. 3 illus. in color.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 7 mm
Weight
184 gr
ISBN-13
978-3-319-05109-3 (9783319051093)
DOI
10.1007/978-3-319-05110-9
Schweitzer Classification
Other editions
Additional editions

Daniel Alpay | Maria Elena Luna-Elizarrarás | Michael Shapiro
Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
E-Book
03/2014
1st Edition
Springer
€53.49
Available for download
Persons
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. He is the author of "An Advanced Complex Analysis Problem Book" (Birkhäuser, 2015). Together with co-authors, he has written seven books and close to 240 research papers, and edited fifteen books of research papers, and in particular the Springer Reference Work on Operator Theory.
Content
1. Bicomplex and hyperbolic numbers.- 2. Bicomplex functions and matrices.- 3. BC-modules.- 4. Norms and inner products on BC-modules.- 5. Linear functionals and linear operators on BC-modules.- 6. Schur analysis.