A Primer On Reproducing Kernel Hilbert Spaces
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A Primer on Reproducing Kernel Hilbert Spaces
![A Primer on Reproducing Kernel Hilbert Spaces](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Jonathan H. Manton,Pierre-Olivier Amblard |
Publsiher | : Unknown |
Total Pages | : 126 |
Release | : 2015 |
Genre | : Hilbert space |
ISBN | : 1680830937 |
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Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious. The novel viewpoint is that reproducing kernel Hilbert space theory studies extrinsic geometry, associating with each geometric configuration a canonical overdetermined coordinate system. This coordinate system varies continuously with changing geometric configurations, making it well-suited for studying problems whose solutions also vary continuously with changing geometry. This primer can also serve as an introduction to infinite-dimensional linear algebra because reproducing kernel Hilbert spaces have more properties in common with Euclidean spaces than do more general Hilbert spaces.
An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
Author | : Vern I. Paulsen,Mrinal Raghupathi |
Publsiher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 2016-04-11 |
Genre | : Mathematics |
ISBN | : 9781107104099 |
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A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.
Reproducing Kernel Hilbert Spaces
Author | : Howard L. Weinert |
Publsiher | : Unknown |
Total Pages | : 680 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : STANFORD:36105031984888 |
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Reproducing Kernel Spaces and Applications
Author | : Daniel Alpay |
Publsiher | : Birkhäuser |
Total Pages | : 355 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9783034880770 |
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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.
A Primer on Hilbert Space Theory
Author | : Carlo Alabiso,Ittay Weiss |
Publsiher | : Springer Nature |
Total Pages | : 343 |
Release | : 2021-03-03 |
Genre | : Science |
ISBN | : 9783030674175 |
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This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
J Contractive Matrix Functions Reproducing Kernel Hilbert Spaces and Interpolation
Author | : Harry Dym |
Publsiher | : American Mathematical Soc. |
Total Pages | : 159 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : 9780821807224 |
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Presents an introduction to the theory and applications of $J$ inner matrices. This book discusses matrix interpolation problems including two-sided tangential problems of both the Nevanlinna-Pick type and the Caratheodory-Fejer type, as well as mixtures of these.
Reproducing Kernel Spaces and Applications
![Reproducing Kernel Spaces and Applications](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Daniel Alpay |
Publsiher | : Birkhauser |
Total Pages | : 344 |
Release | : 2003-01 |
Genre | : Mathematics |
ISBN | : 081760068X |
Download Reproducing Kernel Spaces and Applications Book in PDF, Epub and Kindle
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.
Generalized Mercer Kernels and Reproducing Kernel Banach Spaces
Author | : Yuesheng Xu,Qi Ye |
Publsiher | : American Mathematical Soc. |
Total Pages | : 122 |
Release | : 2019-04-10 |
Genre | : Banach spaces |
ISBN | : 9781470435509 |
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This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .