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One-Parameter Semigroups for Linear Evolution Equations
Klaus-Jochen Engel,Rainer Nagel +1 more
TLDR
In this paper, Spectral Theory for Semigroups and Generators is used to describe the exponential function of a semigroup and its relation to generators and resolvents.Abstract:
Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.- Semigroups Everywhere.- A Brief History of the Exponential Function.read more
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Stochastic Equations in Infinite Dimensions
Giuseppe Da Prato,Jerzy Zabczyk +1 more
TL;DR: In this paper, the existence and uniqueness of nonlinear equations with additive and multiplicative noise was investigated. But the authors focused on the uniqueness of solutions and not on the properties of solutions.
Book
Observation and Control for Operator Semigroups
Marius Tucsnak,George Weiss +1 more
TL;DR: The main topics of interest about observation and control operators are admissibility, observability, controllability, stabilizability and detectability as discussed by the authors, which is a mature area of functional analysis, which is still very active.
MonographDOI
Impulsive Differential Equations and Inclusions
TL;DR: Ben-chohra as discussed by the authors dedicates this book to his family members who complete us, and his children, Mohamed, Maroua, and Abdelillah; J. Henderson dedicates to his wife, Darlene and his descendants, Kathy.
Journal ArticleDOI
The Laplace Transform
TL;DR: The theory of Fourier integrals arises out of the elegant pair of reciprocal formulae The Laplace Transform By David Vernon Widder as mentioned in this paper, which is the basis of our theory of integrals.
Introduction to stochastic partial differential equations
Mihály Kovács,Stig Larsson +1 more
TL;DR: In this paper, the Hilbert space-valued Wiener process and the corresponding stochastic integral of Ito type were introduced and used together with semigroup theory to obtain existence and uniqueness of weak solutions of linear and semilinear stochiastic evolution problems in Hilbert space.
References
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Semigroups of Linear Operators and Applications to Partial Differential Equations
TL;DR: In this article, the authors considered the generation and representation of a generator of C0-Semigroups of Bounded Linear Operators and derived the following properties: 1.1 Generation and Representation.
Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Book
Introduction to Fourier Analysis on Euclidean Spaces.
Elias M. Stein,Guido Weiss +1 more
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.