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Semigroups of Linear Operators : With Applications to Analysis, Probability and Physics - David Applebaum

Semigroups of Linear Operators

With Applications to Analysis, Probability and Physics

By: David Applebaum

eBook | 15 August 2019

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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 Levy 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.

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Non-FictionSciencePhysicsClassical MathematicsDynamics & StaticsMathematicsCalculus & Mathematical AnalysisDifferential Calculus & EquationsApplied MathematicsStochasticsMathematical Physics

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