Realizations for Schur upper triangular operators centered at an arbitrary point

D. Alpay, Y. Peretz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Reproducing kernel spaces introduced by L. de Branges and J. Rovnyak provide isometric, coisometric and unitary realizations for Schur functions, i.e. for matrix-valued functions analytic and contractive in the open unit disk. In our previous paper [12] we showed that similar realizations exist in the "nonstationary setting", i.e. when one considers upper triangular contractions (which appear in time-variant system theory as "transfer functions" of dissipative systems) rather than Schur functions and diagonal operators rather than complex numbers. We considered in [12] realizations centered at the origin. In the present paper we study realizations of a more general kind, centered at an arbitrary diagonal operator. Analogous realizations (centered at a point α of the open unit disk) for Schur functions were introduced and studied in [3] and [4].

Original languageEnglish
Pages (from-to)251-323
Number of pages73
JournalIntegral Equations and Operator Theory
Issue number3
StatePublished - 1 Jan 2000

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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