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Analytic approximation of matrix functions and dual extremal functions

Author: V. V. Peller
Journal: Proc. Amer. Math. Soc. 137 (2009), 205-210
MSC (2000): Primary 47B35, 46E40, 30D55, 30E10
Published electronically: August 4, 2008
MathSciNet review: 2439442
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Abstract: We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions, for which a dual extremal function exists in terms of the existence of a maximizing vector of the corresponding Hankel operator and in terms of certain special factorizations that involve thematic matrix functions.

References [Enhancements On Off] (What's this?)

  • [F] B. A. Francis, A Course in $ H^\infty$ Control Theory, Lecture Notes in Control and Information Sciences, No. 88, Springer-Verlag, Berlin, 1987. MR 0932459 (89i:93002)
  • [Kh] S. Havinson, On some extremal problems of the theory of analytic functions, Uchen. Zapiski Mosk. Universiteta, Matem. 148:4 (1951), 133-143. English Translation: Amer. Math. Soc. Translations (2) 32 (1963), 139-154. MR 0049322 (14:155f)
  • [P] V.V. Peller, Hankel operators and their applications, Springer-Verlag, New York, 2003. MR 1949210 (2004e:47040)
  • [PY] V.V. Peller and N.J. Young, Superoptimal analytic approximations of matrix functions, J. Funct. Anal. 120 (1994), 300-343. MR 1266312 (94m:47030)
  • [S] D. Sarason, Generalized interpolation in $ H^\infty$, Trans. Amer. Math. Soc. 127 (1967), 179-203. MR 0208383 (34:8193)

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Additional Information

V. V. Peller
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Keywords: Best approximation, badly approximable matrix functions, dual extremal function, Hankel operator, maximizing vector
Received by editor(s): December 18, 2007
Published electronically: August 4, 2008
Additional Notes: The author is partially supported by NSF grant DMS 0700995
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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