Pseudo Differential Operators And Markov Processes, Volume I: Fourier Analysis And Semigroups PDF Download
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Author: Niels Jacob
Publisher: World Scientific
ISBN: 178326134X
Category : Mathematics
Languages : en
Pages : 517
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Book Description
After recalling essentials of analysis — including functional analysis, convexity, distribution theory and interpolation theory — this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students./a
Author: Niels Jacob
Publisher: World Scientific
ISBN: 178326134X
Category : Mathematics
Languages : en
Pages : 517
Get Book Here
Book Description
After recalling essentials of analysis — including functional analysis, convexity, distribution theory and interpolation theory — this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students./a
Author: Niels Jacob
Publisher: World Scientific
ISBN: 9781860949746
Category : Mathematics
Languages : en
Pages : 528
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Book Description
After recalling essentials of analysis OCo including functional analysis, convexity, distribution theory and interpolation theory OCo this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students. Sample Chapter(s). Introduction: Pseudo Differential Operators and Markov Processes (207 KB). Chapter 1: Introduction (190 KB). Contents: Essentials from Analysis: Calculus Results; Convexity; Some Interpolation Theory; Fourier Analysis and Convolution Semigroups: The PaleyOCoWienerOCoSchwartz Theorem; Bounded Borel Measures and Positive Definite Functions; Convolution Semigroups and Negative Definite Functions; The L(r)vyOCoKhinchin Formula for Continuous Negative Definite Functions; Bernstein Functions and Subordination of Convolution Semigroups; Fourier Multiplier Theorems; One Parameter Semigroups: Strongly Continuous Operator Semigroups; Subordination in the Sense of Bochner for Operator Semigroups; Generators of Feller Semigroups; Dirichlet Forms and Generators of Sub-Markovian Semigroups; and other papers. Readership: Graduate students, researchers and lecturers in analysis & differential equations, stochastics, probability & statistics, and mathematical physics."
Author: C. van den Berg
Publisher: Springer Science & Business Media
ISBN: 146121128X
Category : Mathematics
Languages : en
Pages : 299
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Book Description
The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, Bernstein-Widder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk» is positive definite for all finite choices of elements St, . . . , Sn from S. The three basic results mentioned above correspond to (~, +, x* = -x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffding-type inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space.
Author: Niels Jacob
Publisher: World Scientific
ISBN: 1860942938
Category : Mathematics
Languages : en
Pages : 517
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Book Description
This work covers two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated.
Author: Niels Jacob
Publisher:
ISBN:
Category :
Languages : en
Pages : 493
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Book Description
Author: Kalyan B. Sinha
Publisher: Springer
ISBN: 9811048649
Category : Mathematics
Languages : en
Pages : 176
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Book Description
The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in each chapter, partly to initiate and motivate the theory developed and partly to underscore the applications. The choice of topics in this vastly developed book is a difficult one, and the authors have made an effort to stay closer to applications instead of bringing in too many abstract concepts.
Author: David Applebaum
Publisher: Cambridge University Press
ISBN: 1108623522
Category : Mathematics
Languages : en
Pages : 235
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Book Description
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.
Author: David Applebaum
Publisher: Cambridge University Press
ISBN: 1108483097
Category : Mathematics
Languages : en
Pages : 235
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Book Description
Provides a graduate-level introduction to the theory of semigroups of operators.
Author: Robert Dautray
Publisher: Springer Science & Business Media
ISBN: 3642580904
Category : Mathematics
Languages : en
Pages : 754
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Book Description
299 G(t), and to obtain the corresponding properties of its Laplace transform (called the resolvent of - A) R(p) = (A + pl)-l , whose existence is linked with the spectrum of A. The functional space framework used will be, for simplicity, a Banach space(3). To summarise, we wish to extend definition (2) for bounded operators A, i.e. G(t) = exp( - tA) , to unbounded operators A over X, where X is now a Banach space. Plan of the Chapter We shall see in this chapter that this enterprise is possible, that it gives us in addition to what is demanded above, some supplementary information in a number of areas: - a new 'explicit' expression of the solution; - the regularity of the solution taking into account some conditions on the given data (u , u1,f etc ... ) with the notion of a strong solution; o - asymptotic properties of the solutions. In order to treat these problems we go through the following stages: in § 1, we shall study the principal properties of operators of semigroups {G(t)} acting in the space X, particularly the existence of an upper exponential bound (in t) of the norm of G(t). In §2, we shall study the functions u E X for which t --+ G(t)u is differentiable.
Author: Walter Rudin
Publisher: John Wiley & Sons
ISBN: 1118165640
Category : Mathematics
Languages : en
Pages : 298
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Book Description
In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained.
