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Analytic approximation of matrix functions and dual extremal functions
Author(s):
V.
V.
Peller
Journal:
Proc. Amer. Math. Soc.
137
(2009),
205-210.
MSC (2000):
Primary 47B35, 46E40, 30D55, 30E10
Posted:
August 4, 2008
MathSciNet review:
2439442
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Additional information
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:
-
- [F]
- B. A. Francis, A Course in
 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
 , 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
DOI:
10.1090/S0002-9939-08-09623-8
PII:
S 0002-9939(08)09623-8
Keywords:
Best approximation,
badly approximable matrix functions,
dual extremal function,
Hankel operator,
maximizing vector
Received by editor(s):
December 18, 2007
Posted:
August 4, 2008
Additional Notes:
The author is partially supported by NSF grant DMS 0700995
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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