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Reproducing And Pseudo Reproducing Kernels And Their Application To The Partial Differential Equations Of Physics
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Book Synopsis Reproducing and Pseudo-reproducing Kernels and Their Application to the Partial Differential Equations of Physics by : Nachman Aronszajn
Download or read book Reproducing and Pseudo-reproducing Kernels and Their Application to the Partial Differential Equations of Physics written by Nachman Aronszajn and published by . This book was released on 1948 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Reproducing Kernels and Applications by : Saburou Saitoh
Download or read book Theory of Reproducing Kernels and Applications written by Saburou Saitoh and published by Springer. This book was released on 2016-10-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications.In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of reproducing kernels with basic applications in a self-contained way. Many fundamental operations among reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book.Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing kernels with applications to numerical and practical solutions of bounded linear operator equations.In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented by applying the Tikhonov regularization, where the reproducing kernels play a key role in the results.Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete results for various fundamental partial differential equations. In Chapter 7, typical integral equations are presented with discretization methods. These chapters are applications of the general theories of Chapter 3 with the purpose of practical and numerical constructions of the solutions.In Chapter 8, hot topics on reproducing kernels are presented; namely, norm inequalities, convolution inequalities, inversion of an arbitrary matrix, representations of inverse mappings, identifications of nonlinear systems, sampling theory, statistical learning theory and membership problems. Relationships among eigen-functions, initial value problems for linear partial differential equations, and reproducing kernels are also presented. Further, new fundamental results on generalized reproducing kernels, generalized delta functions, generalized reproducing kernel Hilbert spaces, andas well, a general integral transform theory are introduced.In three Appendices, the deep theory of Akira Yamada discussing the equality problems in nonlinear norm inequalities, Yamada's unified and generalized inequalities for Opial's inequalities and the concrete and explicit integral representation of the implicit functions are presented.
Book Synopsis Kernel Functions and Elliptic Differential Equations in Mathematical Physics by : Stefan Bergman
Download or read book Kernel Functions and Elliptic Differential Equations in Mathematical Physics written by Stefan Bergman and published by Courier Corporation. This book was released on 2013-01-23 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the theory of boundary value problems in partial differential equations and discusses a portion of the theory from a unifying point of view while providing an introduction to each branch of its applications. 1953 edition.
Book Synopsis Kernel Functions and Differential Equations by :
Download or read book Kernel Functions and Differential Equations written by and published by Academic Press. This book was released on 2009-08-31 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kernel Functions and Differential Equations
Book Synopsis Theory of Reproducing Kernels and Its Applications by : Saburou Saitoh
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:
Book Synopsis Construction and Applications of Conformal Maps by : Institute for Numerical Analysis (U.S.)
Download or read book Construction and Applications of Conformal Maps written by Institute for Numerical Analysis (U.S.) and published by . This book was released on 1952 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Reproducing Kernels by : Nachman Aronszajn
Download or read book Theory of Reproducing Kernels written by Nachman Aronszajn and published by . This book was released on 1951 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Real Analysis written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-11-02 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
Book Synopsis Variational Methods for Eigenvalue Problems by : S. H. Gould
Download or read book Variational Methods for Eigenvalue Problems written by S. H. Gould and published by Courier Corporation. This book was released on 2012-05-24 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Purely mathematical treatment offers simple exposition of general theory of variational methods with special reference to the vibrating plate. No math beyond basic calculus. Includes exercises. 1957 edition.
Book Synopsis Methods of Intermediate Problems for Eigenvalues: Theory and Ramifications by : A. Weinstein
Download or read book Methods of Intermediate Problems for Eigenvalues: Theory and Ramifications written by A. Weinstein and published by Elsevier. This book was released on 1972-06-23 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Book Synopsis Reproducing Kernel Hilbert Spaces by : Howard L. Weinert
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:
Book Synopsis Integral Transforms, Reproducing Kernels and Their Applications by : Saburou Saitoh
Download or read book Integral Transforms, Reproducing Kernels and Their Applications written by Saburou Saitoh and published by CRC Press. This book was released on 2020-11-26 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.
Book Synopsis Linear Partial Differential Equations by : Paul C. Rosenbloom
Download or read book Linear Partial Differential Equations written by Paul C. Rosenbloom and published by . This book was released on 1957 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the Symposium on Spectral Theory and Differential Problems by : Oklahoma State University
Download or read book Proceedings of the Symposium on Spectral Theory and Differential Problems written by Oklahoma State University and published by . This book was released on 1955 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Publications by : Harvard University. Graduate School of Engineering
Download or read book Publications written by Harvard University. Graduate School of Engineering and published by . This book was released on 1949 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Inner Product Structures by : V.I. Istratescu
Download or read book Inner Product Structures written by V.I. Istratescu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 909 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis Nonlinear Partial Differential Equations and Their Applications by : Doina Cioranescu
Download or read book Nonlinear Partial Differential Equations and Their Applications written by Doina Cioranescu and published by CRC Press. This book was released on 1998-08-15 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of selected lectures on recent work in the field of nonlinear partial differential equations delivered by leading international experts at the well-established weekly seminar held at the Collège de France. Emphasis is on applications to numerous areas, including control theory, theoretical physics, fluid and continuum mechanics, free boundary problems, dynamical systems, scientific computing, numerical analysis, and engineering. Proceedings of this seminar will be of particular interest to postgraduate students and specialists in the area of nonlinear partial differential equations.
