Abstract
Let E be a compact subset of the complex plane with positive dx dy measure. For each p, 1 ≤ p < ∞, let Rp(E dx dy) denote the closure in Lp(E, dx dy) of the rational functions having no poles on E. We give an example where E has empty interior and the functions in Rp(E, dx dy), p ≥ 2, are uniquely determined by their values on any set of positive dx dy measure in E. Earlier, Sinanjan (Sibirsk Mat. Ž. 6 (1965), 1365-1381) obtained a somewhat weaker result along these lines and he also proved that this phenomenon can never occur when 1 ≤ p < 2.
Original language | English |
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Pages (from-to) | 307-320 |
Number of pages | 14 |
Journal | Journal of Functional Analysis |
Volume | 12 |
Issue number | 3 |
DOIs | |
State | Published - Mar 1973 |
ASJC Scopus subject areas
- Analysis