Ebook: Reproducing Kernel Spaces and Applications
- Tags: Operator Theory, Functional Analysis, Functions of a Complex Variable, Integral Transforms Operational Calculus, Partial Differential Equations
- Series: Operator Theory: Advances and Applications 143
- Year: 2003
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
20. Pattern recognition and statistical learning theory (the theory of support vector machines). See [40], [58]. In this last volume we refer in particular to the papers [63] and [64]. Since this topic is maybe less known to the operator theory community we mention that the support vector method is a general approach to function estimation problems. See [63, p. 26]. We note that the above list and the given references are by no way exhaustive. We refer to the first section of the paper of S. Saitoh in the present volume for another (and mainly different) list of topics where reproducing kernel spaces appear. Quite often a given question is best understood in a reproducing kernel Hilbert space (for instance when using Cauchy's formula in the Hardy space H ) 2 and one finds oneself as Mr Jourdain of Moliere' Bourgeois Gentilhomme speaking Prose without knowing it [48, p. 51]: Par ma foil il y a plus de quarante ans que je dis de la prose sans que l j'en susse rien.
Content:
Front Matter....Pages i-xv
Realization of Functions into the Symmetrised Bidisc....Pages 1-37
A Basic Interpolation Problem for Generalized Schur Functions and Coisometric Realizations....Pages 39-76
Formal Reproducing Kernel Hilbert Spaces: The Commutative and Noncommutative Settings....Pages 77-134
On Realizations of Rational Matrix Functions of Several Complex Variables II....Pages 135-146
Bergman Projection and Weighted Holomorphic Functions....Pages 147-169
Linear Fractional Transformations, Riccati Equations and Bitangential Interpolation, Revisited....Pages 171-212
A Class of Matrix-valued Schr?dinger Operators with Prescribed Finite-band Spectra....Pages 213-253
Laplace Transform Asymptotics, Bergman Kernels and Composition Operators....Pages 255-272
On the Structure of Self-similar Systems: A Hilbert Space Approach....Pages 273-302
Reproducing Kernels and a Family of Bounded Linear Operators....Pages 303-312
Multipliers in the Reproducing Kernel Hilbert Space, Subnormality and Noncommutative Complex Analysis....Pages 313-331
Existence of Unitary Dilations as a Moment Problem....Pages 333-344
Content:
Front Matter....Pages i-xv
Realization of Functions into the Symmetrised Bidisc....Pages 1-37
A Basic Interpolation Problem for Generalized Schur Functions and Coisometric Realizations....Pages 39-76
Formal Reproducing Kernel Hilbert Spaces: The Commutative and Noncommutative Settings....Pages 77-134
On Realizations of Rational Matrix Functions of Several Complex Variables II....Pages 135-146
Bergman Projection and Weighted Holomorphic Functions....Pages 147-169
Linear Fractional Transformations, Riccati Equations and Bitangential Interpolation, Revisited....Pages 171-212
A Class of Matrix-valued Schr?dinger Operators with Prescribed Finite-band Spectra....Pages 213-253
Laplace Transform Asymptotics, Bergman Kernels and Composition Operators....Pages 255-272
On the Structure of Self-similar Systems: A Hilbert Space Approach....Pages 273-302
Reproducing Kernels and a Family of Bounded Linear Operators....Pages 303-312
Multipliers in the Reproducing Kernel Hilbert Space, Subnormality and Noncommutative Complex Analysis....Pages 313-331
Existence of Unitary Dilations as a Moment Problem....Pages 333-344
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