Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis

• Κύριοι συγγραφείς: Alpay, Daniel (Συγγραφέας), Luna-Elizarrarás, Maria Elena (Συγγραφέας), Shapiro, Michael (Συγγραφέας), Struppa, Daniele C. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: SpringerBriefs in Mathematics,
• Θέματα: Mathematics.; Functional analysis.; Functions of complex variables.; Operator theory.; System theory.; Functions of a Complex Variable.; Functional Analysis.; Operator Theory.; Systems Theory, Control.
• Φυσική περιγραφή: XV, 95 p. 3 illus. in color. online resource.
• ISBN: 9783319051109
• ISSN: 2191-8198

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.