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.
Описание: The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.
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.
Автор: Sears William Rees, Sears W. R. Название: Small Perturbation Theory ISBN: 0691626022 ISBN-13(EAN): 9780691626024 Издательство: Wiley Рейтинг: Цена: 4752.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Part of the Princeton Aeronautical Paperback series designed to bring to students and research engineers outstanding portions of the twelve-volume High Speed Aerodynamics and Jet Propulsion series. These books have been prepared by direct reproduction of the text from the original series and no attempt has been made to provide introductory material
Описание: The book provides a general, broad approach to aspects of perturbation theory. The aim has been to cover all topics of interest, from construction, analysis, and summation of perturbation series to applications. Emphasis is placed on simple methods, as well as clear, intuitive ideas stemming from the physics of systems of interest.
Автор: Krishnaswami Alladi; Manjul Bhargava; David Savitt Название: Quadratic and Higher Degree Forms ISBN: 1493901443 ISBN-13(EAN): 9781493901449 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Preface.- Toy Models for D. H. Lehmer's Conjecture II (E. Bannai, T. Miezaki).- On the Representation of an Integer by X2+Y2+Z2 and the Modular Equations of Degree 3 and 5 (A. Berkovich).- Almost Universal Ternary Sums of Squares and Triangular Numbers (W. Chan, A. Haensch).- Weighted Generating Functions for Type II Lattices and Codes (N. Elkies, S. Kominers).- Quadratic and Automorphic Forms (J. Hanke).- Integral Positive Ternary Quadratic Forms (W. Jagy).- Some Aspects of the Algebraic Theory of Quadratic Forms (R. Parimala).- On the Length of Binary Forms (B. Reznick).- Representation of Quadratic Forms by Integral Quadratic Forms (R. Schulze-Pillot).- Identifying the Matrix Ring (J. Voight).
Автор: Krishnaswami Alladi; Manjul Bhargava; David Savitt Название: Quadratic and Higher Degree Forms ISBN: 1461474876 ISBN-13(EAN): 9781461474876 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Preface.- Toy Models for D. H. Lehmer's Conjecture II (E. Bannai, T. Miezaki).- On the Representation of an Integer by X2+Y2+Z2 and the Modular Equations of Degree 3 and 5 (A. Berkovich).- Almost Universal Ternary Sums of Squares and Triangular Numbers (W. Chan, A. Haensch).- Weighted Generating Functions for Type II Lattices and Codes (N. Elkies, S. Kominers).- Quadratic and Automorphic Forms (J. Hanke).- Integral Positive Ternary Quadratic Forms (W. Jagy).- Some Aspects of the Algebraic Theory of Quadratic Forms (R. Parimala).- On the Length of Binary Forms (B. Reznick).- Representation of Quadratic Forms by Integral Quadratic Forms (R. Schulze-Pillot).- Identifying the Matrix Ring (J. Voight).
Автор: Prof. Kevin F. Clancey; Prof. Israel Gohberg Название: Factorization of Matrix Functions and Singular Integral Operators ISBN: 3034854943 ISBN-13(EAN): 9783034854948 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A few years aga the authors started a project of a book on the theory of systems of one-dimensional singular integral equa- tions which was planned as a continuation of the monograph by one of the authors and N.
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.
Описание: This monograph combines a thorough introduction to the mathematical foundations of n-body Schrodinger mechanics with numerous new results. Originally published in 1971. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton Universi
Автор: Farrukh Mukhamedov; Nasir Ganikhodjaev Название: Quantum Quadratic Operators and Processes ISBN: 3319228366 ISBN-13(EAN): 9783319228365 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes.
Автор: Steve Wright Название: Quadratic Residues and Non-Residues ISBN: 3319459546 ISBN-13(EAN): 9783319459547 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory.The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
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