Hilbert spaces of analytic functions, inverse scattering and operator models.I

Daniel Alpay, Harry Dym

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


This paper develops a method for obtaining linear fractional representations of a given n×n matrix valued function which is analytic and contractive in either the unit disc or the open upper half plane. The method depends upon the theory of reproducing kernel Hilbert spaces of vector valued functions developed by de Branges. A self-contained account of the relevant aspects of these spaces to this study is included. In addition, the methods alluded to above are used in conjunction with some ideas of Krein, to develop models for simple, closed symmetric [resp. isometric] operators with equal deficiency indices. A number of related issues and applications are also discussed.

Original languageEnglish
Pages (from-to)589-641
Number of pages53
JournalIntegral Equations and Operator Theory
Issue number5
StatePublished - 1 Sep 1984
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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