This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It defines the notion of bicomplex modules and then develops the theory of linear functionals and linear operators on bicomplex modules.

Offers a self-contained introduction to functional analysis with bicomplex scalars and will serve for many subsequent developments similar to those of classic functional analysis Only book that introduces a new hyperbolic valued norm on bicomplex modules which is crucial in obtaining some of the most important results in the book First book in which Schur analysis is introduced in the bicomplex context Includes supplementary material: sn.pub/extras

Autorentext

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.

Inhalt

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.