The Resource Quaternionic de Branges spaces and characteristic operator function, Daniel Alpay, Fabrizio Colombo, Irene Sabadini, (electronic book)
Quaternionic de Branges spaces and characteristic operator function, Daniel Alpay, Fabrizio Colombo, Irene Sabadini, (electronic book)
Resource Information
The item Quaternionic de Branges spaces and characteristic operator function, Daniel Alpay, Fabrizio Colombo, Irene Sabadini, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Quaternionic de Branges spaces and characteristic operator function, Daniel Alpay, Fabrizio Colombo, Irene Sabadini, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the socalled Sspectrum and Sresolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. The focus of this book is the notion of characteristic operator function of a bounded linear operator A with finite real part, and we address several questions like the study of Jcontractive functions, where J is selfadjoint and unitary, and we also treat the inverse problem, namely to characterize which Jcontractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in this framework. Besides other topics, we consider canonical differential equations in the setting of slice hyperholomorphic functions and we define the lossless inverse scattering problem. We also consider the inverse scattering problem associated with canonical differential equations. These equations provide a convenient unifying framework to discuss a number of questions pertaining, for example, to inverse scattering, nonlinear partial differential equations and are studied in the last section of this book
 Language
 eng
 Extent
 1 online resource (121 p.).
 Note
 Description based upon print version of record
 Contents

 Preliminaries
 Quaternions and matrices
 Slice hyperholomorphic functions
 Rational functions
 Operator models
 Structure theorems for H(A;B) spaces
 Jcontractive functions
 The characteristic operator function
 L() spaces and linear fractional transformations
 Canonical differential systems
 Isbn
 9783030383114
 Label
 Quaternionic de Branges spaces and characteristic operator function
 Title
 Quaternionic de Branges spaces and characteristic operator function
 Statement of responsibility
 Daniel Alpay, Fabrizio Colombo, Irene Sabadini
 Language
 eng
 Summary
 This work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the socalled Sspectrum and Sresolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. The focus of this book is the notion of characteristic operator function of a bounded linear operator A with finite real part, and we address several questions like the study of Jcontractive functions, where J is selfadjoint and unitary, and we also treat the inverse problem, namely to characterize which Jcontractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in this framework. Besides other topics, we consider canonical differential equations in the setting of slice hyperholomorphic functions and we define the lossless inverse scattering problem. We also consider the inverse scattering problem associated with canonical differential equations. These equations provide a convenient unifying framework to discuss a number of questions pertaining, for example, to inverse scattering, nonlinear partial differential equations and are studied in the last section of this book
 Cataloging source
 EBLCP
 http://library.link/vocab/creatorName
 Alpay, Daniel
 Dewey number
 512/.5
 Index
 index present
 LC call number
 QA196
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1965
 http://library.link/vocab/relatedWorkOrContributorName

 Colombo, Fabrizio
 Sabadini, Irene
 Series statement
 SpringerBriefs in Mathematics
 http://library.link/vocab/subjectName
 Functions, Quaternion
 Label
 Quaternionic de Branges spaces and characteristic operator function, Daniel Alpay, Fabrizio Colombo, Irene Sabadini, (electronic book)
 Note
 Description based upon print version of record
 Antecedent source
 file reproduced from an electronic resource
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Preliminaries  Quaternions and matrices  Slice hyperholomorphic functions  Rational functions  Operator models  Structure theorems for H(A;B) spaces  Jcontractive functions  The characteristic operator function  L() spaces and linear fractional transformations  Canonical differential systems
 Dimensions
 unknown
 Extent
 1 online resource (121 p.).
 File format
 one file format
 Form of item
 online
 Isbn
 9783030383114
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number

 10.1007/978303038
 10.1007/9783030383121
 Quality assurance targets
 unknown
 Reformatting quality
 unknown
 Specific material designation
 remote
 System control number

 on1138673066
 (OCoLC)1138673066
 Label
 Quaternionic de Branges spaces and characteristic operator function, Daniel Alpay, Fabrizio Colombo, Irene Sabadini, (electronic book)
 Note
 Description based upon print version of record
 Antecedent source
 file reproduced from an electronic resource
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Preliminaries  Quaternions and matrices  Slice hyperholomorphic functions  Rational functions  Operator models  Structure theorems for H(A;B) spaces  Jcontractive functions  The characteristic operator function  L() spaces and linear fractional transformations  Canonical differential systems
 Dimensions
 unknown
 Extent
 1 online resource (121 p.).
 File format
 one file format
 Form of item
 online
 Isbn
 9783030383114
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number

 10.1007/978303038
 10.1007/9783030383121
 Quality assurance targets
 unknown
 Reformatting quality
 unknown
 Specific material designation
 remote
 System control number

 on1138673066
 (OCoLC)1138673066
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/QuaternionicdeBrangesspacesandcharacteristic/PuXRI79bmls/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/QuaternionicdeBrangesspacesandcharacteristic/PuXRI79bmls/">Quaternionic de Branges spaces and characteristic operator function, Daniel Alpay, Fabrizio Colombo, Irene Sabadini, (electronic book)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>