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Interpolation and local data for meromorphic matrix and operator functions

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Abstract

The main result of this paper is a generalization of the Mittag-Leffler theorem to matrix and operator valued meromorphic functions. Namely, a meromorphic matrix or operator valued function is constructed when the singular parts of the function and if its inverse are given in all singular points (which are assumed to be isolated). The paper contains also interpolation theorems based on other forms of local data (Jordan chains from left and right of the function and its inverse). An analysis of the local data, which is used in the proofs of these theorems is also included.

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Authors and Affiliations

  1. Raymond and Beverly Sackler Faculty of Exact Sciences School of Mathematical Sciences, Tel-Aviv University, 69978, Tel-Aviv, Ramat Aviv, Israel

    I. Gohberg & L. Rodman

Authors
  1. I. Gohberg
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  2. L. Rodman
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Dedicated to the memory of D.P. Milman

The research of this author partially supported by the Fund for Basic Research administrated by the Israel Academy of Science and Humanities.

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Gohberg, I., Rodman, L. Interpolation and local data for meromorphic matrix and operator functions. Integr equ oper theory 9, 60–94 (1986). https://doi.org/10.1007/BF01257062

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  • DOI: https://doi.org/10.1007/BF01257062

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