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Infinite Hankel Block Matrices, Extremal Problems

  • Lev Sakhnovich
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)

Abstract

In this paper we use the matrix analogue of eigenvalue ρ min 2 to formulate and to solve the extremal Nehari problem. Our approach coincides with Arov, Adamyan, Krein approach when ρ min 2 is a scalar matrix.

Keywords

Matrix Nehari problem minimal solution matrix analogue of eigenvalue Communicated by V. Bolotnikov 

Mathematics Subject Classification (2000)

Primary 15A57 Secondary 47B10 

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References

  1. [1]
    V.M. Adamyan, D.Z. Arov and M.G. Krein, Infinite Hankel Block Matrices and Related Extension Problems, Amer. Math. Soc. Transl. 111 (1978), 133–156.zbMATHGoogle Scholar
  2. [2]
    B. Fritzsche, B. Kirstein and L.A. Sakhnovich, Extremal Classical Interpolation Problems (matrix case), Lin. Alg. Appl. 430 (2009), 762–781.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    J.W. Helton and L.A. Sakhnovich, Extremal Problems of Interpolation Theory, Rocky Mount. J. Math., 35 (2005), 819–841.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Z. Nehari, On Bounded Linear Forms, Ann. of Math. 65 (1957), 153–162.CrossRefMathSciNetGoogle Scholar
  5. [5]
    V.V. Peller and N.J. Joung, Superoptimal Analytic Approximation of Matrix Functions, J. Funct. Anal. 120 (1994), 300–343.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    A.C.M. Ran and M.C.B. Reurings A Nonlinear Matrix Equation Connected to Interpolation Theory, Lin. Alg. Appl. 379 (2004), 289–302.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    L.A. Sakhnovich, Interpolation Theory and its Applications, Kluwer, Dordrecht, 1997.zbMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Lev Sakhnovich
    • 1
  1. 1.MilfordUSA

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