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Matrix functions with arbitrarily prescribed left and right partial indices

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Abstract

We prove that ifn≥2 and ϱ, χ are two given vectors inZ n, then there exists a matrix function inL n×n∞ (T) which has a right Wiener-Hopf factorization inL 2 with the partial indices ϱ and a left Wiener-Hopf factorization inL 2 with the partial indices χ.

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Authors and Affiliations

  1. Fakultät für Mathematik, TU Chemnitz, 09107, Chemnitz, Germany

    A. Böttcher

  2. Faculty of Mechanics and Mathematics, Rostov-on-Don State University, Bolshaya Sadovaya 105, 344711, Rostov-on-Don, Russian Federation

    S. M. Grudsky

  3. Department of Mathematics, The College of William and Mary, 23187-8795, Williamsburg, VA, USA

    I. M. Spitkovsky

Authors
  1. A. Böttcher
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  2. S. M. Grudsky
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  3. I. M. Spitkovsky
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Böttcher, A., Grudsky, S.M. & Spitkovsky, I.M. Matrix functions with arbitrarily prescribed left and right partial indices. Integr equ oper theory 36, 71–91 (2000). https://doi.org/10.1007/BF01236287

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  • DOI: https://doi.org/10.1007/BF01236287

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