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The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of Co-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigr

Semigroups of operators. --- Operators, Semigroups of --- Operator theory

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Semigroups of operators --- 512.54 --- Operators, Semigroups of --- Operator theory --- 512.54 Groups. Group theory --- Groups. Group theory --- Group theory

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In this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and develops a symbolic calculus; in addition, it deals with special approaches, such as subordination in the sense of Bochner. The second part handles capacities, function spaces associated with continuous negative definite functions, Lp -sub-Markovian sem

Semigroups of operators. --- Pseudodifferential operators. --- Potential theory (Mathematics) --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory --- Operators, Semigroups of

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The book gives a streamlined and systematic introduction to strongly continuous semigroups of bounded linear operators on Banach spaces. It treats the fundamental Hille-Yosida generation theorem as well as perturbation and approximation theorems for generators and semigroups. The special feature is its treatment of spectral theory leading to a detailed qualitative theory for these semigroups. This theory provides a very efficient tool for the study of linear evolution equations arising as partial differential equations, functional differential equations, stochastic differential equations, and others. Therefore, the book is intended for those wanting to learn and apply functional analytic methods to linear time dependent problems arising in theoretical and numerical analysis, stochastics, physics, biology, and other sciences. It should be of interest to graduate students and researchers in these fields.

Semigroups of operators. --- Linear operators. --- Banach spaces. --- Functions of complex variables --- Generalized spaces --- Topology --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Operators, Semigroups of --- Operator theory. --- Global analysis (Mathematics). --- Operator Theory. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- Functional analysis --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis

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This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event. They will be a valuable and inspiring source of information for graduate students and established researchers.

Calculus --- Mathematics --- Physical Sciences & Mathematics --- Semigroups of operators. --- Operators, Semigroups of --- Mathematics. --- Functional analysis. --- Operator theory. --- Partial differential equations. --- Mathematical physics. --- Partial Differential Equations. --- Operator Theory. --- Mathematical Applications in the Physical Sciences. --- Functional Analysis. --- Operator theory --- Differential equations, partial. --- Functional analysis --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Physical mathematics --- Physics