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One-Sided Tangential Interpolation for Hilbert-Schmidt Operator Functions with Symmetries on the Bidisk

  • M.C.B. Reurings
  • L. Rodman
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 157)

Abstract

One-sided tangential interpolation problems for functions with symmetries having values in the set of Hilbert-Schmidt operators and defined on the bidisk are studied. General solutions are described as well as solutions with the minimal scalar and operator-valued norms. Two types of symmetries are considered: (a) componentwise symmetries that operate separately on each component of a general point in the bidisk; (b) interchange symmetry that interchanges the two components of a general point in the bidisk. Applications are made to multipoint tangential interpolation problems of special form.

Keywords Tangential interpolation symmetries Hilbert Schmidt operators 

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References

  1. [1]
    D. Alpay and V. Bolotnikov, On the tangential interpolation problem for matrix-valued H2-finctions of two variables, Proceedings of the Amer. Math. Soc. 127 (1999), 76–105.Google Scholar
  2. [2]
    D. Alpay and V. Bolotnikov, Two-sided interpolation for matrix functions with entries in the Hardy space, Linear Algebra Appl., 223/224 (1995), 31–56.CrossRefGoogle Scholar
  3. [3]
    D. Alpay, V. Bolotnikov, and Ph. Loubaton, On two-sided residue interpolation for matrix-valued H2-finctions with symmetries, J. Math. Anal. and Appl 200 (1996), 76–105.CrossRefGoogle Scholar
  4. [4]
    D. Alpay, V. Bolotnikov, and Ph. Loubaton, An interpolation with symmetry and related questions, Zeitschrift für Analysis und ihrer Anwand., 15 (1996), 19–29.Google Scholar
  5. [5]
    D. Alpay, V. Bolotnikov, and Ph. Loubaton, On interpolation for Hardy functions in a certain class of domains under moment type constraints, Houston J. of Math. 23 (1997), 539–571.Google Scholar
  6. [6]
    D. Alpay, V. Bolotnikov, and Ph. Loubaton, On a new positive extension problem for block Toeplitz matrices, Linear Algebra Appl. 268 (1998), 247–287.CrossRefGoogle Scholar
  7. [7]
    D. Alpay, V. Bolotnikov, and L. Rodman, Tangential interpolation with symmetries and two-point interpolation problem for matrix-valued H2-finctions, Integral Equations and Operator Theory 32 (1998), 1–28.CrossRefGoogle Scholar
  8. [8]
    D. Alpay, V. Bolotnikov, and L. Rodman, Two-sided tangential interpolation for Hilbert-Schmidt operator functions on polydisks, Operator Theory: Advances and Applications 124 (2001), 63–87.Google Scholar
  9. [9]
    D. Alpay, V. Bolotnikov, and L. Rodman, One-sided tangential interpolation for operator-valued Hardy functions on polydisks, Integral Equations and Operator Theory 35 (1999), 253–270.CrossRefGoogle Scholar
  10. [10]
    D. Alpay, V. Bolotnikov, and L. Rodman, Two-sided residue interpolation in matrix H2 spaces with symmetries: conformal conjugate involutions, Linear Algebra Appl. 351/352 (2002), 27–68.CrossRefGoogle Scholar
  11. [11]
    J.A. Ball, I. Gohberg, and L. Rodman, Interpolation of Rational Matrix Functions, Birkhäuser Verlag, Basel, 1990.Google Scholar
  12. [12]
    J.A. Ball, I. Gohberg, and L. Rodman, Two sided tangential interpolation of real rational matrix functions, Operator Theory: Advances and Applications, 64, Birkhäuser Verlag, Basel, 1993, 73–102.Google Scholar
  13. [13]
    J.A. Ball and J. Kim, Bitangential interpolation problems for symmetric rational matrix functions, Linear Algebra and Appl. 241/243 (1996), 133–152.CrossRefGoogle Scholar
  14. [14]
    H. Dym, J Contractive Matrix Functions. Reproducing Kernel Hilbert Spaces and Interpolation, CBMS Reg. Conf. Ser. in Math, Vol. 71, Amer. Math. Soc., 1989.Google Scholar
  15. [15]
    C. Foias and A.E. Frazho, The Commutant Lifting Approach to Interpolation Problems, Birkhäuser Verlag, Basel, 1990.Google Scholar
  16. [16]
    A. A. Nudel’man, A new problem of the type of the moment problem, Soviet Math. Dokl. 18 (1977), 792–795.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • M.C.B. Reurings
    • 1
  • L. Rodman
    • 1
  1. 1.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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