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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)

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
Creator
Contributor
Subject
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 so-called S-spectrum and S-resolvent 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 J-contractive functions, where J is self-adjoint and unitary, and we also treat the inverse problem, namely to characterize which J-contractive 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, non-linear partial differential equations and are studied in the last section of this book
Member of
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)
Instantiates
Publication
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 -- J-contractive 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
  • 10.1007/978-3-030-38
  • 10.1007/978-3-030-38312-1
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)
Publication
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 -- J-contractive 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
  • 10.1007/978-3-030-38
  • 10.1007/978-3-030-38312-1
Quality assurance targets
unknown
Reformatting quality
unknown
Specific material designation
remote
System control number
  • on1138673066
  • (OCoLC)1138673066

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