Approximation problems and representations of Hardy spaces in circular domains
Chalendar, I. ; Partington, J.
Studia Mathematica, Tome 133 (1999), p. 255-269 / Harvested from The Polish Digital Mathematics Library

We derive various approximation results in the theory of Hardy spaces on circular domains G. Two applications are given, one to operators which admit a nice representation of H(G), and the other to extremal problems with links to the theory of differential equations.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:216670
@article{bwmeta1.element.bwnjournal-article-smv136i3p255bwm,
     author = {I. Chalendar and J. Partington},
     title = {Approximation problems and representations of Hardy spaces in circular domains},
     journal = {Studia Mathematica},
     volume = {133},
     year = {1999},
     pages = {255-269},
     zbl = {0952.30033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv136i3p255bwm}
}
Chalendar, I.; Partington, J. Approximation problems and representations of Hardy spaces in circular domains. Studia Mathematica, Tome 133 (1999) pp. 255-269. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv136i3p255bwm/

[00000] [1] J. Agler, Rational dilation on an annulus, Ann. of Math. 121:537-563, 1985. | Zbl 0609.47013

[00001] [2] J. A. Ball and K. F. Clancey, Reproducing kernels for Hardy spaces on multiply connected domains, Integral Equations Operator Theory 25:35-57, 1996. | Zbl 0867.30038

[00002] [3] L. Baratchart and J. Leblond, Hardy approximation to Lp functions on subsets of the circle with 1 ≤ p < ∞, Constr. Approx. 14:41-56, 1998. | Zbl 0894.30023

[00003] [4] L. Baratchart, J. Leblond and J. R. Partington, Hardy approximation to L functions on subsets of the circle, ibid. 12:423-436, 1996. | Zbl 0853.30022

[00004] [5] H. Bercovici, C. Foiaş and C. Pearcy, Two Banach space methods and dual operator algebras, J. Funct. Anal. 78:306-345, 1988. | Zbl 0661.46004

[00005] [6] H. Bercovici, C. Hernandez-Garciadiego and V. Paulsen, Universal compressions of representations of H(G), Math. Ann. 281:177-191, 1988.

[00006] [7] J. Bourgain, Some consequences of Pisier's approach to interpolation, Israel J. Math. 77:165-185, 1992. | Zbl 0788.46070

[00007] [8] I. Chalendar and J. Esterle, L1-factorization for C00-contractions with isometric functional calculus, J. Funct. Anal. 154:174-194, 1998. | Zbl 0914.47013

[00008] [9] B. Chevreau and W. S. Li, On certain representations of H(G) and the reflexivity of associated operator algebras, ibid. 128:341-373, 1995. | Zbl 0871.47034

[00009] [10] B. Chevreau, C. Pearcy and A. L. Shields, Finitely connected domains G, representations of H(G), and invariant subspaces, J. Operator Theory 6:375-405, 1981. | Zbl 0525.47004

[00010] [11] R. G. Douglas and V. Paulsen, Completely bounded maps and hypo-Dirichlet algebras, Acta Sci. Math. (Szeged) 50:143-157, 1986. | Zbl 0649.46053

[00011] [12] G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Amer. Math. Soc., Providence, 1969 (translated from Russian). | Zbl 0183.07502

[00012] [13] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, 1965.

[00013] [14] P. W. Jones, L estimates for the ¯-problem in a half-plane, Acta Math. 150:137-152, 1983. | Zbl 0516.35060

[00014] [15] S. V. Kisliakov, Quantitative aspect of correction theorems, Zap. Nauchn. Sem. LOMI 92:182-191, 1979. | Zbl 0434.42017

[00015] [16] S. V. Kisliakov, A sharp correction theorem, Studia Math. 113:177-196, 1995. | Zbl 0833.42009

[00016] [17] J. Leblond and J. R. Partington, Constrained approximation and interpolation in Hilbert function spaces, J. Math. Anal. Appl., to appear. | Zbl 0961.41025

[00017] [18] G. Pisier, Interpolation between Hp spaces and non-commutative generalizations I, Pacific J. Math. 155:341-368, 1992. | Zbl 0747.46050

[00018] [19] W. Rudin, Analytic functions of class Hp, Trans. Amer. Math. Soc. 78:46-66, 1955. | Zbl 0064.31203

[00019] [20] W. Rudin, Real and Complex Analysis, McGraw-Hill, third ed., 1986.

[00020] [21] X. Zheng, Functional calculus and its application to operator algebras, Integral Equations Operator Theory 24:484-496, 1996. | Zbl 0846.47013