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Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions by Daniel Alpay at Abbey's Bookshop,
Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions
— —
Daniel Alpay Fabrizio Colombo

Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions

Daniel Alpay,  Fabrizio Colombo,  Irene Sabadini

$385.95   $308.92

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English
Birkhauser Verlag AG
10 December 2024
Functional analysis & transforms
Series: Operator Theory: Advances and Applications
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.
By:   , ,
Imprint:   Birkhauser Verlag AG
Country of Publication:   Switzerland
Edition:   2024 ed.
Volume:   304
Dimensions:   Height: 235mm,  Width: 155mm, 
ISBN:   9783031734298
ISBN 10:   3031734297
Series:   Operator Theory: Advances and Applications
Pages:   348
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
- 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.

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.

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