Описание: Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares.
Описание: for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug- gesting the publication of these notes as a book.
Автор: Saitoh Название: Theory of Reproducing Kernels and Applications ISBN: 981100529X ISBN-13(EAN): 9789811005299 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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.
Автор: Daniel Alpay Название: Reproducing Kernel Spaces and Applications ISBN: 3034894309 ISBN-13(EAN): 9783034894302 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Описание: Covering the fundamental underlying theory as well as a range of applications, this unique text provides a unified overview of reproducing kernel Hilbert spaces. It offers an unrivalled and accessible introduction to the field, ideal for graduate students and researchers working in functional analysis or its applications.
Автор: Barlow Название: Random Walks and Heat Kernels on Graphs ISBN: 1107674425 ISBN-13(EAN): 9781107674424 Издательство: Cambridge Academ Рейтинг: Цена: 9186.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This introduction to random walks on infinite graphs, in both discrete and continuous time, gives a systematic account of transition densities, including useful but hard-to-find results. The book is aimed at researchers and graduate students in mathematics who have a basic familiarity with analysis and some familiarity with probability.
Автор: Lev A. Sakhnovich Название: Integral Equations with Difference Kernels on Finite Intervals ISBN: 3319307630 ISBN-13(EAN): 9783319307633 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M.
Автор: Lev A. Sakhnovich Название: Integral Equations with Difference Kernels on Finite Intervals ISBN: 3319164880 ISBN-13(EAN): 9783319164885 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M.
Автор: Vladimir Maz`ya; Alexander Movchan; Michael Nieves Название: Green`s Kernels and Meso-Scale Approximations in Perforated Domains ISBN: 3319003569 ISBN-13(EAN): 9783319003566 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Part I: Green's functions in singularly perturbed domains: Uniform asymptotic formulae for Green's functions for the Laplacian in domains with small perforations.- Mixed and Neumann boundary conditions for domains with small holes and inclusions. Uniform asymptotics of Green's kernels.- Green's function for the Dirichlet boundary value problem in a domain with several inclusions.- Numerical simulations based on the asymptotic approximations.- Other examples of asymptotic approximations of Green's functions in singularly perturbed domains.- Part II: Green's tensors for vector elasticity in bodies with small defects: Green's tensor for the Dirichlet boundary value problem in a domain with a single inclusion.- Green's tensor in bodies with multiple rigid inclusions.- Green's tensor for the mixed boundary value problem in a domain with a small hole.- Part III Meso-scale approximations. Asymptotic treatment of perforated domains without homogenization: Meso-scale approximations for solutions of Dirichlet problems.- Mixed boundary value problems in multiply-perforated domains.
Автор: S. Saitoh; Daniel Alpay; Joseph A. Ball; Takeo Ohs Название: Reproducing Kernels and their Applications ISBN: 0792356187 ISBN-13(EAN): 9780792356189 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The First International Congress of the International Society for Analysis, its Applications and Computations (ISAAC`97) was held at the University of Delaware from 3 to 7 June 1997. Rather than restricting the papers to Congress participants, we asked the Ieading mathematicians in the field of the theory of reproducing kern eIs to submit papers.
Автор: Lev A. Sakhnovich Название: Integral Equations with Difference Kernels on Finite Intervals ISBN: 3034898568 ISBN-13(EAN): 9783034898560 Издательство: Springer Рейтинг: Цена: 14673.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Avramidi Ivan Название: Heat Kernel Method and its Applications ISBN: 3319262653 ISBN-13(EAN): 9783319262659 Издательство: Springer Рейтинг: Цена: 13275.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented.The book consists of four parts: Analysis, Geometry, Perturbations and Applications.
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