Structured invariant spaces of vector valued rational functions, hermitian matrices, and a generalization of the lohvidov laws

Daniel Aron Alpay, Harry Dym

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Finite dimensional indefinite inner product spaces of vector valued rational functions which are (1) invariant under the generalized backward shift and (2) subject to a structural identity, and subspaces and "superspaces" thereof are studied. The theory of these spaces is then applied to deduce a generalization of a pair of rules due to lohvidov for evaluating the inertia of certain subblocks of Hermitian Toeplitz and Hermitian Hankel matrices. The connecting link rests on the identification of a Hermitian matrix as the Gram matrix of a space of vector valued functions of the type considered in the first part of the paper. Corresponding generalizations of another pair of theorems by lohvidov on the rank of certain subblocks of non-Hermitian Teoplitz and non-Hermitian Hankel matrices are also stated, but the proofs will be presented elsewhere.

Original languageEnglish
Pages (from-to)137-181
Number of pages45
JournalLinear Algebra and Its Applications
Volume137-138
Issue numberC
DOIs
StatePublished - 1 Jan 1990
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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