Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions / by Daniel Alpay, Fabrizio Colombo, Irene Sabadini.

Format:

Book

Author/Creator:

Alpay, Daniel.

Contributor:

Colombo, Fabrizio.

Sabadini, Irene.

Series:

Operator Theory: Advances and Applications, 2296-4878 ; 304

Language:

English

Subjects (All):

Operator theory.

Operator Theory.

Local Subjects:

Operator Theory.

Physical Description:

1 online resource (352 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024.

Summary:

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.

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-73430-0

OCLC:

1478698017