£100.99

Spectral Theory for Bounded Functions & Applications to Evolution Equations (Mathematics Research Developments)

Differential Equations

Price data checked 1 day ago

View at Amazon

Price History & Forecast

Last 90 days • 90 data points

Historical

Generating forecast...

Price Distribution

Price distribution over 90 days • 1 price levels

Days at Price

Price Analysis

Most common price: £101 (90 days, 100.0%)

Price range: £101 - £101

Price levels: 1 different prices over 90 days

Description

One of the central questions in the qualitative theory of difference and differential equations is to find the conditions of existence and asymptotic behavior of bounded solutions. For equations with almost periodic coefficients, the problem concerns Favard and Perron. A remarkable theory has been developed in harmonic analysis with outstanding contributions by Loomis, Arendt, Batty, Lyubic, Phong, Naito, Minh and many others, when the Carleman spectrum of the functions is countable. Uniform continuity in this case plays a key role. In the absence of this condition, the theory does not apply. This led to the introduction over the last decade of new types of spectrum functions which helped solve the problem, especially in the case of almost automorphic functions by using the theory of commutating operators. This monograph presents a unique and unified manner of recent developments in the theory of bounded continuous functions, including the space of (Bohr) almost periodic functions and some of their generalisations, and the spaces of (Bochner) almost automorphic functions and almost automorphic sequences. Classical concepts from harmonic analysis such as the Bohr spectrum, Beurling spectrum and Carleman spectrum are also presented with some examples. Special attention is devoted to the recently introduced concepts of uniform spectrum and circular spectrum of bounded functions derived from the study of linear differential equation solutions, whose forcing terms are not necessarily uniformly continuous. Connections between these various types of spectra are also investigated. The book provides a semigroup-free study of the existence and asymptotic behavior of mild solutions concerning evolution equations of the first and second order as well as difference equations. Bibliographical and historical notes complete the major chapters. An appendix reviewing basic results on the theory of commutating operators is given. The content is presented in a way that is easily accessible to readers who are working in differential equations, but are not familiar with harmonic analysis and advanced functional analysis. Its our hope that this first monograph ever on this topic will attract more researchers.

Product Specifications

Format: paperback
ASIN: 1536121126
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Differential Equations
Domain: Amazon UK
Release Date: 01 July 2017
Listed Since: 10 May 2017

Barcode

No barcode data available

Spectral Theory for Bounded Functions & Applications to Evolution Equations (Mathematics Research Developments)

Price History & Forecast

Price Distribution

Price Analysis

Description

Product Specifications

Barcode

Similar Products You Might Like

Oscillation Theory for Difference and Functional Differential Equations

Numerical Range of Holomorphic Mappings and Applications

Nonlinear Spectral Theory (de Gruyter Series In Nonlinear Analysis And Applications): 10

Sturm-Liouville Theory: Past and Present

Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations (Springer Monographs in Mathematics)

Extended States for the Schrodinger Operator with Quasi-Periodic Potential in Dimension Two (Memoirs of the American Mathematical Society)

Functional Dynamic Equations on Time Scales

Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications: 550 (Mathematics and Its Applications, 550)

Differential Inclusions in a Banach Space: 524 (Mathematics and Its Applications, 524)

Critical Point Theory: Sandwich and Linking Systems

A Short Course on Spectral Theory: 209 (Graduate Texts in Mathematics, 209)

Theory of Commuting Nonselfadjoint Operators: 332 (Mathematics and Its Applications, 332)

Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications (Springer Monographs in Mathematics)

Fredholm and Local Spectral Theory, with Applications to Multipliers

Difference Equations in Normed Spaces: Stability and Oscillations (Volume 206) (North-Holland Mathematics Studies, Volume 206)

Functional Analytic Methods for Heat Green Operators: Heat Kernel Asymptotics via the Weyl-Hörmander Calculus: 2354 (Lecture Notes in Mathematics, 2354)

Numerical Analysis

Algebraic Methods in Nonlinear Perturbation Theory: 88 (Applied Mathematical Sciences, 88)

Asymptotic Characteristics of Entire Functions and Their Applications in Mathematics and Biophysics: 559 (Mathematics and Its Applications, 559)

Harmonic Analysis in China: v. 327 (Mathematics and its Applications)

Gaussian Harmonic Analysis (Springer Monographs in Mathematics)

Basic Theory Of Fractional Differential Equations

Ordinary Differential Equations And Boundary Value Problems - Volume II: Boundary Value Problems: 8 (Trends in Abstract and Applied Analysis)

Spectral Methods: Fundamentals in Single Domains (Scientific Computation)