Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions

by Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Overview

The purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous applications.

The book is divided into three parts. In the first part, some foundational material on quaternionic functions and functional analysis are introduced. The second part is the core of the book and contains various types of functions spaces ranging from the Hardy spaces, also in the fractional case, to the Fock space extended to the case of quaternions. The third and final part present some further generalization.

Researchers in functional analysis and hypercomplex analysis will find this book a key contribution to their field, but also researchers in mathematical physics, especially in quantum mechanics, will benefit from the insights presented.

Product Details

ISBN-13:	9783031734298
Publisher:	Springer Nature Switzerland
Publication date:	12/10/2024
Series:	Operator Theory: Advances and Applications , #304
Edition description:	2024
Pages:	348
Product dimensions:	6.10(w) x 9.25(h) x 0.00(d)

About the Author

Daniel Alpay, Foster G. and Mary McGaw Professorship in Mathematical Sciences, Chapman University

Fabrizio Colombo is professor at the Politecnico di Milano, Italy.

Irene Sabadini is professor at the Politecnico di Milano, Italy.

Table of Contents

- Part I Quaternionic functional analysis and related topics.- Functions of a Quaternionic Variable.- Quaternionic Banach and Hilbert Spaces.- Quaternionic Linear Operators on a Hilbert Space.- Reproducing Kernel Hilbert Spaces.- Part II Spaces of Slice Hyperholomorphic Functions.- Slice Hyperholomorphic Hardy Spaces.- de Branges Spaces.- Slice Hyperholomorphic Bergman Spaces.- Slice Hyperholomorphic Bloch, Besov and Dirichlet Spaces.- Slice Hyperholomorphic Fock Space.- Wiener Algebras.- Part III Various Extensions.- Slice Polyanalytic Functions.- Several Quaternionic Variables.- Function Spaces and Spectral Theories.