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Analytic operator functions with compact spectrum. II. Spectral pairs and factorization

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Abstract

Using the technique introduced in the first part of this paper, various problems concerning factorization and divisibility of analytic operator functions with compact spectrum are studied in terms of spectral pairs of operators. The basic properties of such pairs are derived. Using these properties, stability of spectral divisors is proved and necessary and sufficient conditions (in terms of moments of the inverse function) are given in order that an analytic operator function with compact spectrum admits a generalized Wiener-Hopf factorization.

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Research supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).

This paper was written while the third author was a senior visiting fellow at the Vrije Universiteit at Amsterdam.

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Kaashoek, M.A., van der Mee, C.V.M. & Rodman, L. Analytic operator functions with compact spectrum. II. Spectral pairs and factorization. Integr equ oper theory 5, 791–827 (1982). https://doi.org/10.1007/BF01694064

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Keywords

  • Analytic Operator
  • Basic Property
  • Operator Function
  • Inverse Function
  • Spectral Pair