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Статья «BOUNDED POINT DERIVATIONS ON CERTAIN FUNCTION SPACES, "Алгебра и анализ"»

Авторы:
  • BRENNAN J. E.1
стр. 174-188
Платно
1 University of Kentucky
  • SDI: 007.001.0234-0852.2019.031.002.7
Ключевые слова:
  • point derivation
  • approximate derivative
  • monogeneity
  • capacity
Аннотация:
Let X be a compact nowhere dense subset of the complex plane C, and let dA denote two-dimensional Lebesgue (or area) measure in C. Denote by R(X) the set of all rational functions having no poles on X, and by R(X) the closure of R(X) in L(X, dA) whenever 1 ? p < to. The purpose of this paper is to study the relationship between bounded derivations on R(X) and the existence of approximate derivatives provided 2 < p < to, and to draw attention to an anomaly that occurs when p = 2.

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