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Pontryagin space structure in reproducing kernel Hilbert spaces over *-semigroups

Pontryagin space structure in reproducing kernel Hilbert spaces over *-semigroups The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of *-semigroups. It goes via the positive definite functions and related to them reproducing kernel Hilbert spaces. Our concern is in describing properties of elements of the semigroup which determine shift operators which serve as Pontryagin fundamental symmetries. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Pontryagin space structure in reproducing kernel Hilbert spaces over *-semigroups

Positivity , Volume 15 (1) – Mar 2, 2010

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References (30)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Birkhäuser / Springer Basel AG
Subject
Mathematics; Econometrics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Fourier Analysis; Potential Theory
ISSN
1385-1292
eISSN
1572-9281
DOI
10.1007/s11117-010-0048-x
Publisher site
See Article on Publisher Site

Abstract

The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of *-semigroups. It goes via the positive definite functions and related to them reproducing kernel Hilbert spaces. Our concern is in describing properties of elements of the semigroup which determine shift operators which serve as Pontryagin fundamental symmetries.

Journal

PositivitySpringer Journals

Published: Mar 2, 2010

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