The Resource Slice hyperholomorphic Schur analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Slice hyperholomorphic Schur analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Resource Information
The item Slice hyperholomorphic Schur analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Slice hyperholomorphic Schur analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.
This item is available to borrow from 1 library branch.
- 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 The book includes previously unpublished results and provides the basis for new directions of research
- Language
- eng
- Extent
- 1 online resource.
- 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
- Isbn
- 9783319425146
- Label
- Slice hyperholomorphic Schur analysis
- Title
- Slice hyperholomorphic Schur analysis
- Statement of responsibility
- Daniel Alpay, Fabrizio Colombo, Irene Sabadini
- 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
- 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
- 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
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Slice-hyperholomorphic-Schur-analysis-Daniel/WWCRBZFSIjo/" 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/Slice-hyperholomorphic-Schur-analysis-Daniel/WWCRBZFSIjo/">Slice hyperholomorphic Schur analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini</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/">Sydney Jones Library, University of Liverpool</a></span></span></span></span></div>
