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Article
Standard Symmetric Operators in Pontryagin Spaces: A Generalized von Neumann Formula and Minimality of Boundary Coefficients
Journal of Functional Analysis (2003)
  • Branko Ćurgus, Western Washington University
  • Tomas Azizov
  • Aad Dijksma
Abstract
Certain meromorphic matrix valued functions on ℂ/ℝ , the so-called boundary coefficients, are characterized in terms of a standard symmetric operator S in a Pontryagin space with finite (not necessarily equal) defect numbers, a meromorphic mapping into the defect subspaces of S, and a boundary mapping for S. Under some simple assumptions the boundary coefficients also satisfy a minimality condition. It is shown that these assumptions hold if and only if for S a generalized von Neumann equality is valid.
Keywords
  • Indefinite inner products,
  • Pontryagin and Krein spaces,
  • Symmetric and self-adjoint operators and relations,
  • Extensions of symmetric relations,
  • Defect indices,
  • Defect subspaces,
  • Boundary operators,
  • Boundary coefficients,
  • Reproducing kernel Pontryagin spaces,
  • von Neumann's equality
Disciplines
Publication Date
March 10, 2003
Publisher Statement
Copyright © 2015 Elsevier B.V. DOI: 10.1016/S0022-1236(02)00041-1
Citation Information
Branko Ćurgus, Tomas Azizov and Aad Dijksma. "Standard Symmetric Operators in Pontryagin Spaces: A Generalized von Neumann Formula and Minimality of Boundary Coefficients" Journal of Functional Analysis Vol. 198 Iss. 2 (2003)
Available at: http://works.bepress.com/branko_curgus/33/