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Homotopy Classes of Elliptic Transmission Problems over C*-Algebras

Homotopy Classes of Elliptic Transmission Problems over C*-Algebras The topological aspects of B.Bojarski's approach to Riemann–Hilbert problems are developed in terms of infinite-dimensional grassmanians and generalized to the case of transmission problems over C*-algebras. In particular, the homotopy groups of certain grassmanians related to elliptic transmission problems are expressed through K-groups of the basic algebra. Also, it is shown that the considered grassmanians are homogeneous spaces of appropriate operator groups. Several specific applications of the obtained results to singular operators are given, and further perspectives of our approach are outlined. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal Springer Journals

Homotopy Classes of Elliptic Transmission Problems over C*-Algebras

Georgian Mathematical Journal , Volume 5 (5) – Oct 4, 2004

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 1998 by Plenum Publishing Corporation
Subject
Mathematics; Mathematics, general
ISSN
1072-947X
eISSN
1572-9176
DOI
10.1023/B:GEOR.0000008116.53411.d0
Publisher site
See Article on Publisher Site

Abstract

The topological aspects of B.Bojarski's approach to Riemann–Hilbert problems are developed in terms of infinite-dimensional grassmanians and generalized to the case of transmission problems over C*-algebras. In particular, the homotopy groups of certain grassmanians related to elliptic transmission problems are expressed through K-groups of the basic algebra. Also, it is shown that the considered grassmanians are homogeneous spaces of appropriate operator groups. Several specific applications of the obtained results to singular operators are given, and further perspectives of our approach are outlined.

Journal

Georgian Mathematical JournalSpringer Journals

Published: Oct 4, 2004

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