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電子ブック
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1. Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis
by Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: SpringerBriefs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-3-319-05110-9
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1. Bicomplex and hyperbolic numbers
2. Bicomplex functions and matrices
3. BC-modules
4. Norms and inner products on BC-modules
5. Linear functionals and linear operators on BC-modules
6. Schur analysis
1. Bicomplex and hyperbolic numbers
2. Bicomplex functions and matrices
3. BC-modules
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電子ブック
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2. Operator Theory
edited by Daniel Alpay
出版情報: Basel : Springer Basel : Imprint: Springer, 2015
オンライン: http://dx.doi.org/10.1007/978-3-0348-0667-1
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General aspects of quaternionic and Clifford analysis
Further developments of quaternionic and Clifford analysis
Infinite dimensional analysis
Non-commutative theory
Multivariable operator theory
Reproducing kernel Hilbert spaces
de Branges spaces
Indefinite inner product spaces
Schur analysis
Linear system theory
General aspects of quaternionic and Clifford analysis
Further developments of quaternionic and Clifford analysis
Infinite dimensional analysis
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電子ブック
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3. An Advanced Complex Analysis Problem Book : Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions. 1st ed. 2015
by Daniel Alpay
出版情報: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015
オンライン: http://dx.doi.org/10.1007/978-3-319-16059-7
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Prologue
Part I, Analytic functions
1 Some algebra
2 Exercises in complex variables
Part II, Topology and functional analysis
3 Topological spaces
4 Normed spaces
5 Locally convex topological vector spaces
6 Some functional analysis
Part III, Hilbert spaces of analytic functions
7 Reproducing kernel Hilbert spaces
8 Hardy spaces
9 de Branges-Rovnyak spaces
10 Bergman spaces
11 Fock spaces
Index
Name index
Notation index
Prologue
Part I, Analytic functions
1 Some algebra
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電子ブック
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4. Quaternionic de Branges Spaces and Characteristic Operator Function. 1st ed. 2020
by Daniel Alpay, Fabrizio Colombo, Irene Sabadini
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2020
シリーズ名: SpringerBriefs in Mathematics ;
オンライン: https://doi.org/10.1007/978-3-030-38312-1
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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
Preliminaries
Quaternions and matrices
Slice hyperholomorphic functions
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電子ブック
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5. New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative : Chapman University, November 2019. 1st ed. 2021
edited by Daniel Alpay, Ronen Peretz, David Shoikhet, Mihaela B. Vajiac
出版情報: Cham : Springer International Publishing : Imprint: Birkhäuser, 2021
シリーズ名: Linear Operators and Linear Systems ; 286
オンライン: https://doi.org/10.1007/978-3-030-76473-9
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Editorial Introduction
On Parseval Frames of Kernel Functions in de Branges Spaces of Entire Vector Valued Functions
Differential Subordinations in Harmonic Mappings
The Segal-Bargmann Transform in Clifford Analysis
On the Carathéodory-Fejér interpolation problem for Stieltjes functions
Harmonic Analysis of some arithmetical functions
Symmetric measures, continuous networks, and dynamics
Multi Variable Semicircular Processes From - Homomorphisms and Operators
Representation formulae for the determinant in a neighborhood of the identity
Parametrization of the Solution Set of a Matricial Truncated Hamburger Moment Problem by a Schur Type Algorithm
The Wiener algebra and singular integrals
Techniques to derive estimates for integral means and other geometric quantities related to conformal mappings
Complex Ternary Analysis and Applications
Editorial Introduction
On Parseval Frames of Kernel Functions in de Branges Spaces of Entire Vector Valued Functions
Differential Subordinations in Harmonic Mappings