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The Resource Slice hyperholomorphic Schur analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Slice hyperholomorphic Schur analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Label
Slice hyperholomorphic Schur analysis
Title
Slice hyperholomorphic Schur analysis
Statement of responsibility
Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Creator
Contributor
Author
Subject
Language
eng
Summary
This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Alpay, Daniel
Dewey number
  • 515/.98
  • 510
Index
index present
LC call number
QA331.7
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
Operator theory: Advances and applications,
Series volume
volume 256
http://library.link/vocab/subjectName
  • Schur functions
  • Mathematical analysis
Label
Slice hyperholomorphic Schur analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Prologue; Part I Classical Schur Analysis; Chapter 1 Preliminaries; 1.1 Some history; 1.2 Krein spaces, Pontryagin spaces,and negative squares; 1.3 The Wiener algebra; 1.4 The Nehari extension problem; 1.5 The Carathéodory-Toeplitz extension problem; 1.6 Various classes of functions and realization theorems; Chapter 2 Rational Functions; 2.1 Rational functions and minimal realizations; 2.2 Minimal factorization; 2.3 Rational functions J-unitary on the imaginary line; 2.4 Rational functions J-unitary on the unit circle; Chapter 3 Schur Analysis; 3.1 The Schur algorithm
  • 3.2 Interpolation problems3.3 First-order discrete systems; 3.4 The Schur algorithm and reproducing kernel spaces; Part II Quaternionic Analysis; Chapter 4Finite-dimensional Preliminaries; 4.1 Some preliminaries on quaternions; 4.2 Polynomials with quaternionic coefficients; 4.3 Matrices with quaternionic entries; 4.4 Matrix equations; Chapter 5 Quaternionic Functional Analysis; 5.1 Quaternionic locally convex linear spaces; 5.2 Quaternionic inner product spaces; 5.3 Quaternionic Hilbert spaces. Main properties; 5.4 Partial majorants; 5.5 Majorant topologies and inner product spaces
  • 5.6 Quaternionic Hilbert spaces. Weak topology5.7 Quaternionic Pontryagin spaces; 5.8 Quaternionic Krein spaces; 5.9 Positive definite functions and reproducing kernel quaternionic Hilbert spaces; 5.10 Negative squares and reproducing kernel quaternionic Pontryagin spaces; Chapter 6 Slice Hyperholomorphic Functions; 6.1 The scalar case; 6.2 The Hardy space of the unit ball; 6.3 Blaschke products (unit ball case); 6.4 The Wiener algebra; 6.5 The Hardy space of the open half-space; 6.6 Blaschke products (half-space case); Chapter 7 Operator-valued Slice Hyperholomorphic Functions
  • 7.1 Definition and main properties7.2 S-spectrum and S-resolvent operator; 7.3 Functional calculus; 7.4 Two results on slice hyperholomorphic extension; 7.5 Slice hyperholomorphic kernels; 7.6 The space H2H(B) and slice backward-shift invariant subspaces; Part III Quaternionic Schur Analysis; Chapter 8 Reproducing Kernel Spaces and Realizations; 8.1 Classes of functions; 8.2 The Potapov-Ginzburg transform; 8.3 Schur and generalized Schur functions of the ball; 8.4 Contractive multipliers, inner multipliers and Beurling-Lax theorem; 8.5 A theorem on convergence of Schur multipliers
  • 8.6 The structure theorem8.7 Carathéodory and generalizedCarathéodory functions; 8.8 Schur and generalized Schur functions of the half-space; 8.9 Herglotz and generalized Herglotz functions; Chapter 9 Rational Slice HyperholomorphicFunctions; 9.1 Definition and first properties; 9.2 Minimal realizations; 9.3 Realizations of unitary rational functions; 9.4 Rational slice hyperholomorphic functions; 9.5 Linear fractional transformation; 9.6 Backward-shift operators; Chapter 10 First Applications: Scalar Interpolation and First-order Discrete Systems; 10.1 The Schur algorithm
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319425146
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
ocn965904374
Label
Slice hyperholomorphic Schur analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Prologue; Part I Classical Schur Analysis; Chapter 1 Preliminaries; 1.1 Some history; 1.2 Krein spaces, Pontryagin spaces,and negative squares; 1.3 The Wiener algebra; 1.4 The Nehari extension problem; 1.5 The Carathéodory-Toeplitz extension problem; 1.6 Various classes of functions and realization theorems; Chapter 2 Rational Functions; 2.1 Rational functions and minimal realizations; 2.2 Minimal factorization; 2.3 Rational functions J-unitary on the imaginary line; 2.4 Rational functions J-unitary on the unit circle; Chapter 3 Schur Analysis; 3.1 The Schur algorithm
  • 3.2 Interpolation problems3.3 First-order discrete systems; 3.4 The Schur algorithm and reproducing kernel spaces; Part II Quaternionic Analysis; Chapter 4Finite-dimensional Preliminaries; 4.1 Some preliminaries on quaternions; 4.2 Polynomials with quaternionic coefficients; 4.3 Matrices with quaternionic entries; 4.4 Matrix equations; Chapter 5 Quaternionic Functional Analysis; 5.1 Quaternionic locally convex linear spaces; 5.2 Quaternionic inner product spaces; 5.3 Quaternionic Hilbert spaces. Main properties; 5.4 Partial majorants; 5.5 Majorant topologies and inner product spaces
  • 5.6 Quaternionic Hilbert spaces. Weak topology5.7 Quaternionic Pontryagin spaces; 5.8 Quaternionic Krein spaces; 5.9 Positive definite functions and reproducing kernel quaternionic Hilbert spaces; 5.10 Negative squares and reproducing kernel quaternionic Pontryagin spaces; Chapter 6 Slice Hyperholomorphic Functions; 6.1 The scalar case; 6.2 The Hardy space of the unit ball; 6.3 Blaschke products (unit ball case); 6.4 The Wiener algebra; 6.5 The Hardy space of the open half-space; 6.6 Blaschke products (half-space case); Chapter 7 Operator-valued Slice Hyperholomorphic Functions
  • 7.1 Definition and main properties7.2 S-spectrum and S-resolvent operator; 7.3 Functional calculus; 7.4 Two results on slice hyperholomorphic extension; 7.5 Slice hyperholomorphic kernels; 7.6 The space H2H(B) and slice backward-shift invariant subspaces; Part III Quaternionic Schur Analysis; Chapter 8 Reproducing Kernel Spaces and Realizations; 8.1 Classes of functions; 8.2 The Potapov-Ginzburg transform; 8.3 Schur and generalized Schur functions of the ball; 8.4 Contractive multipliers, inner multipliers and Beurling-Lax theorem; 8.5 A theorem on convergence of Schur multipliers
  • 8.6 The structure theorem8.7 Carathéodory and generalizedCarathéodory functions; 8.8 Schur and generalized Schur functions of the half-space; 8.9 Herglotz and generalized Herglotz functions; Chapter 9 Rational Slice HyperholomorphicFunctions; 9.1 Definition and first properties; 9.2 Minimal realizations; 9.3 Realizations of unitary rational functions; 9.4 Rational slice hyperholomorphic functions; 9.5 Linear fractional transformation; 9.6 Backward-shift operators; Chapter 10 First Applications: Scalar Interpolation and First-order Discrete Systems; 10.1 The Schur algorithm
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319425146
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
ocn965904374

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