Reproducing Kernel Spaces and Applications

Daniel Alpay

ISBN 10: 376430068X / ISBN 13: 9783764300685

Editore: Birkhäuser Basel, Birkhäuser Basel Aug 2003, 2003

Riguardo questo articolo

Neuware -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.Birkhäuser Verlag GmbH, Im Westfeld 8, 4055 Basel 364 pp. Englisch.

Codice articolo 9783764300685

Dati bibliografici

• Titolo: Reproducing Kernel Spaces and Applications
• Editore: Birkhäuser Basel, Birkhäuser Basel Aug 2003
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 376430068X
• ISBN 13: 9783764300685
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 260 L x 183 A x 26 P (millimetri) 260 millimetri di larghezza per 183 millimetri di altezza per 26 millimetri di profondità
• Peso: 881 grammi

Descrizione articolo

Riassunto

The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochastic processes, linear systems theory, operator theory, and the theory of analytic functions. Also they are relevant for many applications, for example to statistical learning theory and pattern recognition.
The present volume contains a selection of papers which deal with different aspects of reproducing kernel Hilbert spaces. Topics considered include one complex variable theory, differential operators, the theory of self-similar systems, several complex variables, and the non-commutative case.
The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

Contenuti

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 Schrödinger 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.