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 |  | 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 | doi | https://doi.org/10.1007/978-1-4612-1128-0 | isbn_softcover | 978-1-4612-7017-1 | isbn_ebook | 978-1-4612-1128-0Series ISSN 0072-5285 Series E-ISSN 2197-5612 | issn_series | 0072-5285 | copyright | Springer Science+Business Media New York 1984 |
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