The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators, Koshmanenko Volodymyr, Dudkin Mykola
Автор: Holmes Mark H Название: Introduction to Perturbation Methods ISBN: 146145476X ISBN-13(EAN): 9781461454762 Издательство: Springer Рейтинг: Цена: 5869.00 р. 8384.00-30% Наличие на складе: Есть (1 шт.) Описание: Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.One hundred new pages added including new material on transcedentally small terms, Kummer`s function, weakly coupled oscillators and wave interactions.
Описание: This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac ?-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadratic forms, and the theory of rigged Hilbert spaces. The book will appeal to researchers in mathematics and mathematical physics studying the scales of densely embedded Hilbert spaces, the singular perturbations phenomenon, and singular interaction problems.
Автор: Marchuk, Guri I. , Agoshkov, Valeri I. , Shutyae Название: Adjoint Equations and Perturbation Algorithms in Nonlinear Problems ISBN: 0367448580 ISBN-13(EAN): 9780367448585 Издательство: Taylor&Francis Рейтинг: Цена: 10104.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents the theory of adjoint equations in nonlinear problems and their applications to perturbation algorithms for solution of nonlinear problems in mathematical physics. It formulates a series of principles of construction of adjoint operators in nonlinear problems.
Описание: The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago.In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book.Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Автор: Tosio Kato Название: Perturbation Theory for Linear Operators ISBN: 354058661X ISBN-13(EAN): 9783540586616 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: From the reviews: "[...] An excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Автор: Shishkin, Grigory I. , Shishkina, Lidia P. Название: Difference Methods for Singular Perturbation Problems ISBN: 0367386828 ISBN-13(EAN): 9780367386825 Издательство: Taylor&Francis Рейтинг: Цена: 9798.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods.
The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. The authors develop a technique for constructing and justifying ε uniformly convergent difference schemes for boundary value problems with fewer restrictions on the problem data.
Containing information published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter. This part also studies both the solution and its derivatives with errors that are independent of the perturbation parameters.
Co-authored by the creator of the Shishkin mesh, this book presents a systematic, detailed development of approaches to construct ε uniformly convergent finite difference schemes for broad classes of singularly perturbed boundary value problems.
Автор: Wechselberger Martin Название: Geometric Singular Perturbation Theory Beyond the Standard Form ISBN: 3030363988 ISBN-13(EAN): 9783030363987 Издательство: Springer Рейтинг: Цена: 9781.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT).It is the first of its kind that introduces the GSPT in a coordinate-independent manner.
Описание: Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. This book offers an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. It can be used as an introductory text to the theory underpinning fitted mesh methods.
Автор: J.K. Kevorkian; J.D. Cole Название: Multiple Scale and Singular Perturbation Methods ISBN: 0387942025 ISBN-13(EAN): 9780387942025 Издательство: Springer Рейтинг: Цена: 23757.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Covers multiple scale and averaging methods. This book presents an account of the various perturbation techniques used in the sciences and engineering. It is suitable for a graduate text as well as a reference work on the subject.
Автор: K. W. Chang; F. A. Howes Название: Nonlinear Singular Perturbation Phenomena ISBN: 038796066X ISBN-13(EAN): 9780387960661 Издательство: Springer Рейтинг: Цена: 13275.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The presentation involves a study of both scalar and vector boundary value problems for ordinary dif- ferential equations, by means of the consistent use of differential in- equality techniques.
Описание: Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir- ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places.
Автор: Volodymyr Koshmanenko Название: Singular Quadratic Forms in Perturbation Theory ISBN: 079235625X ISBN-13(EAN): 9780792356257 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Deals with the presentation of the method of singular quadratic forms in the perturbation theory of self-adjoint operators. This book interprets singular quadratic form in the role of an abstract boundary condition for self-adjoint extension. It also investigates various aspects of the singularity principle.
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