On a new class of reproducing kernel spaces and a new generalization of the Iohvidov laws

Daniel Alpay, Harry Dym

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

A new class of finite dimensional reproducing kernel spaces of m × 1 vector valued analytic functions on a fairly general domain Ω+ is introduced. The reproducing kernels of these spaces have a special form which is based on an m × m matrix valued function Θ, which is J unitary on the boundary of Ω+. Every invertible Hermitian matrix can be interpreted as the Gram matrix of a suitably chosen basis in such a space, where m is equal to the appropriately defined displacement rank of the given matrix. Orthogonal decompositions of the space are developed in terms of Schur complements of the matrix and factorizations of the Θ, much as in the classical cases wherein Ω+ is either the unit disc or the half plane. Finally, a new generalization of the Iohvidov laws (which extends earlier generalizations by the same authors) is deduced as an application of the theory.

Original languageEnglish
Pages (from-to)109-183
Number of pages75
JournalLinear Algebra and Its Applications
Volume178
Issue numberC
DOIs
StatePublished - 1 Jan 1993

ASJC Scopus subject areas

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

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