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Titlebook: Harmonic Analysis on Semigroups; Theory of Positive D Christian Berg,Jens Peter Reus Christensen,Paul Re Textbook 1984 Springer Science+Bus

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书目名称Harmonic Analysis on Semigroups
副标题Theory of Positive D
编辑Christian Berg,Jens Peter Reus Christensen,Paul Re
视频video
丛书名称Graduate Texts in Mathematics
图书封面Titlebook: Harmonic Analysis on Semigroups; Theory of Positive D Christian Berg,Jens Peter Reus Christensen,Paul Re Textbook 1984 Springer Science+Bus
描述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,
出版日期Textbook 1984
关键词Fourier transform; Functions; Halbgruppe; Harmonische Analyse; Hilbert space; Positiv definite Funktion; V
版次1
doihttps://doi.org/10.1007/978-1-4612-1128-0
isbn_softcover978-1-4612-7017-1
isbn_ebook978-1-4612-1128-0Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer Science+Business Media New York 1984
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Christian Berg,Jens Peter Reus Christensen,Paul Ressel components include measures for quantifying private knowledge disclosure, data-mining models suitable for multi-agent predictive data mining, and a set of strategies by which agents can improve their classification accuracy through collaboration. The overall framework and its individual components are validated on a synthetic experimental domain.
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Christian Berg,Jens Peter Reus Christensen,Paul Resseldecisions. The developed system is based on the analysis of historical demand for products and on the information about transitions between phases in life cycles of those products. The architecture of the developed system is presented as also an analysis of testing on the real-world data results is given.
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Christian Berg,Jens Peter Reus Christensen,Paul Ressel adapt its incentives and attract more agents to its own market. Our prediction was based on the time series of the traders’ past bids, taking into account the variation of each bid compared to its history. The results proved to be of satisfactory accuracy, both in the game’s context and when compared to other existing approaches.
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ngeles, and Tokyo. We cluster these agents by their movement patterns across space and time. We also show that it is possible to infer part of the underlying transportation net- work from Tweets alone, and uncover interesting differences between the behaviors exhibited by users across these three cities.
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General Results on Positive and Negative Definite Matrices and Kernels, Instead of calling a kernel ψ negative definite, some authors call the kernel —ψ “conditionally positive definite” or “almost positive.” In this book we use mainly the larger class of “semidefinite” kernels of all kinds and therefore prefer to avoid the prefix “semi” which otherwise would appear several hundred times.
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Schoenberg-Type Results for Positive and Negative Definite Functions,t the connection between the class of Fourier transforms of (finite, nonnegative) measures in euclidean spaces and the class of Laplace transforms of (finite, nonnegative) measures on the half-line ℝ..
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0072-5285 erty 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
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