The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators

The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators
A Book

by Volodymyr Koshmanenko,Mykola Dudkin

  • Publisher : Birkhäuser
  • Release : 2016-07-08
  • Pages : 237
  • ISBN : 3319295357
  • Language : En, Es, Fr & De
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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 δ-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.

Singular Quadratic Forms in Perturbation Theory

Singular Quadratic Forms in Perturbation Theory
A Book

by Volodymyr Koshmanenko

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 312
  • ISBN : 9401146195
  • Language : En, Es, Fr & De
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The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense. Numerous physical models are based on the use of Hamiltonians containing perturba tion terms with singular properties. Typical examples of such expressions are Schrodin ger operators with O-potentials (-~ + AD) and Hamiltonians in quantum field theory with perturbations given in terms of operators of creation and annihilation (P(

Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology

Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology
Ronald G. Douglas Memorial Volume

by Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu

  • Publisher : Springer Nature
  • Release : 2020-12-12
  • Pages : 534
  • ISBN : 3030433803
  • Language : En, Es, Fr & De
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This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.

Singular Quadratic Forms in Perturbation Theory

Singular Quadratic Forms in Perturbation Theory
A Book

by Volodymyr Koshmanenko

  • Publisher : Springer
  • Release : 1999-04-30
  • Pages : 312
  • ISBN : 079235625X
  • Language : En, Es, Fr & De
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The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense. Numerous physical models are based on the use of Hamiltonians containing perturba tion terms with singular properties. Typical examples of such expressions are Schrodin ger operators with O-potentials (-~ + AD) and Hamiltonians in quantum field theory with perturbations given in terms of operators of creation and annihilation (P(

Methods of Modern Mathematical Physics

Methods of Modern Mathematical Physics
Functional Analysis

by Michael Reed

  • Publisher : Elsevier
  • Release : 2012-12-02
  • Pages : 344
  • ISBN : 0323155006
  • Language : En, Es, Fr & De
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Methods of Modern Mathematical Physics, Volume I: Functional Analysis discusses the fundamental principles of functional analysis in modern mathematical physics. This book also analyzes the influence of mathematics on physics, such as the Newtonian mechanics used to interpret all physical phenomena. Organized into eight chapters, this volume starts with an overview of the functional analysis in the study of several concrete models. This book then discusses how to generalize the Lebesgue integral to work with functions on the real line and with Borel sets. This text also explores the properties of finite-dimensional vector spaces. Other chapters discuss the normed linear spaces, which have the property of being complete. This monograph further examines the general class of topologized vector spaces and the spaces of distributions that arise in a wide variety of physical problems and functional situations. This book is a valuable resource for mathematicians and physicists. Students and researchers in the field of geometry will also find this book extremely useful.

Conservative Realizations of Herglotz-Nevanlinna Functions

Conservative Realizations of Herglotz-Nevanlinna Functions
A Book

by Yuri Arlinskii,Sergey Belyi,Eduard Tsekanovskii

  • Publisher : Springer Science & Business Media
  • Release : 2011-06-21
  • Pages : 530
  • ISBN : 3764399961
  • Language : En, Es, Fr & De
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This book is devoted to conservative realizations of various classes of Stieltjes, inverse Stieltjes, and general Herglotz-Nevanlinna functions as impedance functions of linear systems. The main feature of the monograph is a new approach to the realization theory profoundly involving developed extension theory in triplets of rigged Hilbert spaces and unbounded operators as state-space operators of linear systems. The connections of the realization theory to systems with accretive, sectorial, and contractive state-space operators as well as to the Phillips-Kato sectorial extension problem, the Krein-von Neumann and Friedrichs extremal extensions are provided. Among other results the book contains applications to the inverse problems for linear systems with non-self-adjoint Schrödinger operators, Jacobi matrices, and to the Nevanlinna-Pick system interpolation.

From Classical to Quantum Mechanics

From Classical to Quantum Mechanics
An Introduction to the Formalism, Foundations and Applications

by Giampiero Esposito,Giuseppe Marmo,George Sudarshan

  • Publisher : Cambridge University Press
  • Release : 2004-03-11
  • Pages : 592
  • ISBN : 1139450549
  • Language : En, Es, Fr & De
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This 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.

Reviews in Partial Differential Equations, 1980-86, as Printed in Mathematical Reviews

Reviews in Partial Differential Equations, 1980-86, as Printed in Mathematical Reviews
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1988
  • Pages : 3998
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Mathematical Reviews

Mathematical Reviews
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2006
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Communications in Applied Analysis

Communications in Applied Analysis
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2004
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Homogenization in Time of Singularly Perturbed Mechanical Systems

Homogenization in Time of Singularly Perturbed Mechanical Systems
A Book

by Folkmar Bornemann

  • Publisher : Springer
  • Release : 2006-11-15
  • Pages : 158
  • ISBN : 3540697845
  • Language : En, Es, Fr & De
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This book is about the explicit elimination of fast oscillatory scales in dynamical systems, which is important for efficient computer-simulations and our understanding of model hierarchies. The author presents his new direct method, homogenization in time, based on energy principles and weak convergence techniques. How to use this method is shown in several general cases taken from classical and quantum mechanics. The results are applied to special problems from plasma physics, molecular dynamics and quantum chemistry. Background material from functional analysis is provided and explained to make this book accessible for a general audience of graduate students and researchers.

Index of Mathematical Papers

Index of Mathematical Papers
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1985
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Chemical Abstracts

Chemical Abstracts
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2002
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Current Research in Britain

Current Research in Britain
Physical Sciences. Part 2, Indexes

by British Library

  • Publisher : Unknown Publisher
  • Release : 1990
  • Pages : 1242
  • ISBN : 9780712320702
  • Language : En, Es, Fr & De
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Nuclear Science Abstracts

Nuclear Science Abstracts
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1966
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Physics Briefs

Physics Briefs
Physikalische Berichte

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1984
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Monthly List of Russian Accessions

Monthly List of Russian Accessions
A Book

by Library of Congress. Processing Department

  • Publisher : Unknown Publisher
  • Release : 1964-04
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Monthly Index of Russian Accessions

Monthly Index of Russian Accessions
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1964
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Probability Theory Subject Indexes from Mathematical Reviews

Probability Theory Subject Indexes from Mathematical Reviews
A Book

by American Mathematical Society

  • Publisher : Amer Mathematical Society
  • Release : 1987
  • Pages : 470
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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