Title | Reproducing Kernel Spaces and Applications [electronic resource] / edited by Daniel Alpay |
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Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003 |

Connect to | http://dx.doi.org/10.1007/978-3-0348-8077-0 |

Descript | XV, 344 p. online resource |

SUMMARY

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

Realization of Functions into the Symmetrised Bidisc -- A Basic Interpolation Problem for Generalized Schur Functions and Coisometric Realizations -- Formal Reproducing Kernel Hilbert Spaces: The Commutative and Noncommutative Settings -- On Realizations of Rational Matrix Functions of Several Complex Variables II -- Bergman Projection and Weighted Holomorphic Functions -- Linear Fractional Transformations, Riccati Equations and Bitangential Interpolation, Revisited -- A Class of Matrix-valued Schrรถdinger Operators with Prescribed Finite-band Spectra -- Laplace Transforms Asymptotics, Bergman Kernels and Composition Operators -- On the Structure of Self-similar Systems: A Hilbert Space Approach -- Reproducing Kernels and a Family of Bounded Linear Operators -- Multipliers in the Reproducing Kernel Hilbert Space, Subnormality and Noncommutative Complex Analysis -- Existence of Unitary Dilations as a Moment Problem

Mathematics
Functional analysis
Functions of complex variables
Integral transforms
Operational calculus
Operator theory
Partial differential equations
Mathematics
Operator Theory
Functional Analysis
Functions of a Complex Variable
Integral Transforms Operational Calculus
Partial Differential Equations