Noch Fragen? 0800 / 33 82 637

Harmonic Analysis on Semigroups

Theory of Positive Definite and Related Functions

Produktform: E-Buch Text Elektronisches Buch in proprietärem

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.weiterlesen

Dieser Artikel gehört zu den folgenden Serien

Elektronisches Format: PDF

Sprache(n): Englisch

ISBN: 978-1-4612-1128-0 / 978-1461211280 / 9781461211280

Verlag: Springer US

Erscheinungsdatum: 06.12.2012

Seiten: 292

Autor(en): C. van den Berg, J. P. R. Christensen, P. Ressel

53,49 € inkl. MwSt.
Recommended Retail Price
kostenloser Versand

lieferbar - Lieferzeit 10-15 Werktage

zurück