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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Distance estimates and pointwise bounded density
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by A. M. Davie, T. W. Gamelin and J. Garnett PDF
Trans. Amer. Math. Soc. 175 (1973), 37-68 Request permission

Abstract:

Let U be a bounded open subset of the complex plane, and let H be a closed subalgebra of ${H^\infty }(U)$, the bounded analytic functions on U. If E is a subset of $\partial U$, let ${L_E}$ be the algebra of all bounded continuous functions on U which extend continuously to E, and set ${H_E} = H \cap {L_E}$. This paper relates distance estimates of the form $d(h,H) = d(h,{H_E})$, for all $h \in {L_E}$, to pointwise bounded density of ${H_E}$ in H. There is also a discussion of the linear space $H + {L_E}$, which turns out often to be a closed algebra.
References
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 175 (1973), 37-68
  • MSC: Primary 30A78; Secondary 30A98, 46J15
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0313514-8
  • MathSciNet review: 0313514