عنوان

Semigroups of linear operators :

شابک

1108483097

شابک

1108716377

شابک

9781108483094

شابک

9781108716376

شابک اشتباه

9781108669658

شابک اشتباه

9781108672641

عنوان اصلي

Semigroups of linear operators :

نام عام مواد

[Book]

ساير اطلاعات عنواني

with applications to analysis, probability and physics /

نام نخستين پديدآور

David Applebaum (University of Sheffield).

محل نشرو پخش و غیره

New York, NY :

نام ناشر، پخش کننده و غيره

Cambridge University Press,

تاریخ نشرو بخش و غیره

2019.

تاریخ نشرو بخش و غیره

©2019

نام خاص و کميت اثر

x, 223 pages ;

ابعاد

23 cm.

عنوان فروست

London Mathematical Society student texts ;

مشخصه جلد

93

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

Cover; Series page; Title page; Copyright page; Dedication; Epigraph; Contents; Introduction; 1 Semigroups and Generators; 1.1 Motivation from Partial Differential Equations; 1.2 Definition of a Semigroup and Examples; 1.3 Unbounded Operators and Generators; 1.3.1 Unbounded Operators and Density of Generators; 1.3.2 Differential Equations in Banach Space; 1.3.3 Generators as Closed Operators; 1.3.4 Closures and Cores; 1.4 Norm-Continuous Semigroups; 1.5 The Resolvent of a Semigroup; 1.5.1 The Resolvent of a Closed Operator; 1.5.2 Properties of the Resolvent of a Semigroup

متن يادداشت

1.6 Exercises for Chapter 12 The Generation of Semigroups; 2.1 Yosida Approximants; 2.2 Classifying Generators; 2.3 Applications to Parabolic PDEs; 2.3.1 Bilinear Forms, Weak Solutions and the Lax-Milgram Theorem; 2.3.2 Energy Estimates and Weak Solutions to the Elliptic Problem; 2.3.3 Semigroup Solution of the Parabolic Problem; 2.4 Exercises for Chapter 2; 3 Convolution Semigroups of Measures; 3.1 Heat Kernels, Poisson Kernels, Processes and Fourier Transforms; 3.1.1 The Gauss-Weierstrass Function and the Heat Equation; 3.1.2 Brownian Motion and Itô's Formula

متن يادداشت

3.1.3 The Cauchy Distribution, the Poisson Kernel and Laplace's Equation3.2 Convolution of Measures and Weak Convergence; 3.2.1 Convolution of Measures; 3.2.2 Weak Convergence; 3.3 Convolution Semigroups of Probability Measures; 3.4 The Lévy-Khintchine Formula; 3.4.1 Stable Semigroups; 3.4.2 Lévy Processes; 3.5 Generators of Convolution Semigroups; 3.5.1 Lévy Generators as Pseudo-Differential Operators; 3.6 Extension to L[sup(p)]; 3.7 Exercises for Chapter 3; 4 Self-Adjoint Semigroups and Unitary Groups; 4.1 Adjoint Semigroups and Self-Adjointness; 4.1.1 Positive Self-Adjoint Operators

متن يادداشت

4.1.2 Adjoints of Semigroups on Banach Spaces4.2 Self-Adjointness and Convolution Semigroups; 4.3 Unitary Groups, Stone's Theorem; 4.4 Quantum Dynamical Semigroups; 4.5 Exercises for Chapter 4; 5 Compact and Trace Class Semigroups; 5.1 Compact Semigroups; 5.2 Trace Class Semigroups; 5.2.1 Hilbert-Schmidt and Trace Class Operators; 5.2.2 Trace Class Semigroups; 5.2.3 Convolution Semigroups on the Circle; 5.2.4 Quantum Theory Revisited; 5.3 Exercises for Chapter 5; 6 Perturbation Theory; 6.1 Relatively Bounded and Bounded Perturbations; 6.1.1 Contraction Semigroups; 6.1.2 Analytic Semigroups

متن يادداشت

6.2 The Lie-Kato-Trotter Product Formula6.3 The Feynman-Kac Formula; 6.3.1 The Feynman-Kac Formula via the Lie-Kato-Trotter Product Formula; 6.3.2 The Feynman-Kac Formula via Itô's Formula; 6.4 Exercises for Chapter 6; 7 Markov and Feller Semigroups; 7.1 Definitions of Markov and Feller Semigroups; 7.2 The Positive Maximum Principle; 7.2.1 The Positive Maximum Principle and the Hille-Yosida-Ray Theorem; 7.2.2 Crash Course on Distributions; 7.2.3 The Courrège Theorem; 7.3 The Martingale Problem; 7.3.1 Sub-Feller Semigroups; 8 Semigroups and Dynamics; 8.1 Invariant Measures and Entropy

بدون عنوان

0

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

بدون عنوان

8

متن يادداشت

"The theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory, introducing the notions of semigroup, generator and resolvent, and establishes the key theorems of Hille-Yosida and Lumer-Phillips that give conditions for a linear operator to generate a semigroup. He then presents a mixture of applications and further developments of the theory. This includes a description of how semigroups are used to solve parabolic partial differential equations, applications to Lévy and Feller-Markov processes, Koopmanism in relation to dynamical systems, quantum dynamical semigroups, and applications to generalisations of the Riemann-Liouville fractional integral. Along the way the reader encounters several important ideas in modern analysis including Sobolev spaces, pseudo-differential operators and the Nash inequality."

شماره استاندارد بين المللي کتاب و موسيقي

9781108669658

موضوع مستند نشده

Group theory, Textbooks.

موضوع مستند نشده

Linear operators, Textbooks.

موضوع مستند نشده

Operator theory, Textbooks.

موضوع مستند نشده

Semigroups, Textbooks.

موضوع مستند نشده

Group theory.

موضوع مستند نشده

Linear operators.

موضوع مستند نشده

Operator theory.

موضوع مستند نشده

Semigroups.

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Applebaum, David,1956-

تاريخ عمليات

20200822151432.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y