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Approximation problems and representations of Hardy spaces in circular domains

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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.
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Bibliografia
  • [1] J. Agler, Rational dilation on an annulus, Ann. of Math. 121:537-563, 1985.
  • [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.
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  • [4] L. Baratchart, J. Leblond and J. R. Partington, Hardy approximation to $L^∞$ functions on subsets of the circle, ibid. 12:423-436, 1996.
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  • [20] W. Rudin, Real and Complex Analysis, McGraw-Hill, third ed., 1986.
  • [21] X. Zheng, Functional calculus and its application to operator algebras, Integral Equations Operator Theory 24:484-496, 1996.
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bwmeta1.element.bwnjournal-article-smv136i3p255bwm
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