Download or read book An Introduction to the Theory of Reproducing Kernel Hilbert Spaces written by Vern I. Paulsen and published by Cambridge University Press. This book was released on 2016-04-11 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.
Download or read book Reproducing Kernel Spaces and Applications written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2003-08-29 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Primer on Reproducing Kernel Hilbert Spaces written by Jonathan H. Manton and published by . This book was released on 2015-11-20 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert space theory is an invaluable mathematical tool in numerous signal processing and systems theory applications. Hilbert spaces satisfying certain additional properties are known as Reproducing Kernel Hilbert Spaces (RKHSs). This primer gives a gentle and novel introduction to RKHS theory. It also presents several classical applications. It concludes by focusing on recent developments in the machine learning literature concerning embeddings of random variables. Parenthetical remarks are used to provide greater technical detail, which some readers may welcome, but they may be ignored without compromising the cohesion of the primer. Proofs are there for those wishing to gain experience at working with RKHSs; simple proofs are preferred to short, clever, but otherwise uninformative proofs. Italicised comments appearing in proofs provide intuition or orientation or both. A Primer on Reproducing Kernel Hilbert Spaces empowers readers to recognize when and how RKHS theory can profit them in their own work.
Download or read book A Primer on Hilbert Space Theory written by Carlo Alabiso and published by Springer Nature. This book was released on 2021-03-03 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to the Theory of Reproducing Kernel Hilbert Spaces written by Vern I. Paulsen and published by Cambridge University Press. This book was released on 2016-04-11 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reproducing kernel Hilbert spaces have developed into an important tool in many areas, especially statistics and machine learning, and they play a valuable role in complex analysis, probability, group representation theory, and the theory of integral operators. This unique text offers a unified overview of the topic, providing detailed examples of applications, as well as covering the fundamental underlying theory, including chapters on interpolation and approximation, Cholesky and Schur operations on kernels, and vector-valued spaces. Self-contained and accessibly written, with exercises at the end of each chapter, this unrivalled treatment of the topic serves as an ideal introduction for graduate students across mathematics, computer science, and engineering, as well as a useful reference for researchers working in functional analysis or its applications.
Download or read book Reproducing Kernel Hilbert Spaces in Learning Theory written by Minh Ha Quang and published by . This book was released on 2006 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Survey on Hilbert Spaces and Reproducing Kernels written by Baver Okutmuştur and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this chapter is to provide a brief review of Hilbert space with its fundamental features and introduce reproducing kernels of the corresponding spaces. We separate our analysis into two parts. In the first part, the basic facts on the inner product spaces including the notion of norms, pre-Hilbert spaces, and finally Hilbert spaces are presented. The second part is devoted to the reproducing kernels and the related Hilbert spaces which is called the reproducing kernel Hilbert spaces (RKHS) in the complex plane. The operations on reproducing kernels with some important theorems on the Bergman kernel for different domains are analyzed in this part.
Download or read book Reproducing Kernel Hilbert Spaces and Their Multipliers written by Lucinda M. Zmarzly and published by . This book was released on 1998 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reproducing Kernel Hilbert Spaces written by Howard L. Weinert and published by . This book was released on 1982 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book REPRODUCING KERNEL HILBERT SPACES written by Baver Okutmustur and published by LAP Lambert Academic Publishing. This book was released on 2010 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a series of lectures we have held during the academic year 2004-2005 at the Department of Mathematics of the Bilkent University in the seminar of operator theory. The theory of reproducing kernel Hilbert spaces has important applications to boundary value problems, integral operators, harmonic and analytic functions, in conformal mappings of simply- and multiply-connected domains, in pseudo-conformal mappings, in the study of invariant Riemann metrics, in probability theory, interpolation of functions, and in many other subjects. In this short presentation, we consider an introduction to this subject by emphasizing first the abstract theory, the Bergman kernels, and some of their applications to interpolation of functions in the unit disc. The book is aimed to a broader audience of graduate students, mathematicians, physicists, and engineers, and all those having an interest in getting a quick, but carefully presented, mathematically sound basic knowledge on this domain.
Download or read book Reproducing Kernel Spaces and Applications written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-11-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Hilbert Space and the Theory of Spectral Multiplicity written by Paul Richard Halmos and published by . This book was released on 1951 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces written by Sergei Pereverzyev and published by Springer Nature. This book was released on 2022-05-17 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an in-depth exploration of statistical learning with reproducing kernels, an active area of research that can shed light on trends associated with deep neural networks. The author demonstrates how the concept of reproducing kernel Hilbert Spaces (RKHS), accompanied with tools from regularization theory, can be effectively used in the design and justification of kernel learning algorithms, which can address problems in several areas of artificial intelligence. Also provided is a detailed description of two biomedical applications of the considered algorithms, demonstrating how close the theory is to being practically implemented. Among the book’s several unique features is its analysis of a large class of algorithms of the Learning Theory that essentially comprise every linear regularization scheme, including Tikhonov regularization as a specific case. It also provides a methodology for analyzing not only different supervised learning problems, such as regression or ranking, but also different learning scenarios, such as unsupervised domain adaptation or reinforcement learning. By analyzing these topics using the same theoretical framework, rather than approaching them separately, their presentation is streamlined and made more approachable. An Introduction to Artificial Intelligence Based on Reproducing Kernel Hilbert Spaces is an ideal resource for graduate and postgraduate courses in computational mathematics and data science.
Download or read book Theory of Reproducing Kernels and Its Applications written by Saburou Saitoh and published by Longman. This book was released on 1988 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Reproducing Kernels for Hilbert Spaces of Vector Valued Functins written by George B. Pedrick and published by . This book was released on 1957 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of H b Spaces written by Emmanuel Fricain and published by Cambridge University Press. This book was released on 2016-05-26 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is volume 1 of a 2 volume set.
Download or read book Reproducing Kernel Hilbert Spaces written by Nicholas Gauguin Houghton-Larsen and published by . This book was released on 2014 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
