Lacunary Müntz systems
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The classical theorem of Müntz and Szász says that the span of [formula omtted] is dense in C[0,1] in the uniform norm if and only if [formula omtted]. We prove that, if [formula omtted] is lacunary, we can replace the underlying interval [0,1] by any set of positive measure. The key to the proof is the establishment of a bounded Remeztype inequality for lacunary Müntz systems. Namely if A c [0,1] and its Lebesgue measure μ(A) is at least ε>0 then [formula omtted] i = 0 A where c depends only on ε and A (not on n and A) and where [formula omtted]. © 1993, Edinburgh Mathematical Society. All rights reserved.
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Borwein, P., & Erdélyi, T.
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