Integral Equations and Operator Theory

, Volume 6, Issue 1, pp 184–205 | Cite as

Connection colligations of the second order

  • Hillel Gauchman
Article
Received:

Abstract

The paper deals with a study of connection colligations of the second order, that is the colligations for which not only the connection, but also the curvature operator satisfies the colligation condition. The gyration operators in the coupling space and the coupling system of partial differential equations are introduced and used for investigations of the basic problem of finding all regular connection colligations with vanishing curvature.

Keywords

Differential Equation Partial Differential Equation Coupling System Basic Problem Curvature Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gauchman, H.: Operator colligations on differentiable manifolds. Toeplitz Centennial, Operator Theory and Applications, vol. 4, Birkhäuser (1982), 271–302.Google Scholar
  2. 2.
    Gauchman, H.: Connection colligations on Hilbert bundles, Integral Equations and Operator Theory, to appear.Google Scholar
  3. 3.
    Greub, W., Halperin, S., and Vanstone, R.: Connections, Curvature, and Cohomology, vol. I, Academic Press, 1973.Google Scholar
  4. 4.
    Kravitsky, N.: Regular colligations for several operators in Banach space. Integral Equations and Operator Theory, to appear.Google Scholar
  5. 5.
    Livšic, M.S.: Operator waves in Hilbert space and related partial differential equations. Integral Equations and Operator Theory, vol. 2/1 (1979), 25–47.Google Scholar
  6. 6.
    Livšic, M.S.: A method for constructing triangular canonical models of commuting operators based on connections with algebraic curves. Integral Equations and Operator Theory, vol. 3/4 (1980), 489–507.Google Scholar
  7. 7.
    Livšic, M.S.: Commuting operators and fields of systems distributed in Euclidean space. Toeplitz Centennial, Operator Theory and Applications, vol. 4, Birkhäuser (1982), 377–413.Google Scholar

Copyright information

© Birkhäuser Verlag 1983

Authors and Affiliations

  • Hillel Gauchman
    • 1
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael

Personalised recommendations