The “Full Müntz Theorem” Revisited
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We give an elementary proof of the "convergent sum part" of the full Müntz Theorem in Lp(A) and in C(A), together with the "Clarkson - Erdös-Schwartz phenomenon" for all p (0,∞), and for all compact A ⊂ [0,∞) with positive lower density at 0. This extends earlier results of Müntz, Szász, Clarkson and Erdös, L. Schwartz, P. Borwein and Erdélyi, and Operstein, and offers an arguably shorter and more elementary approach to reprove a large part of the result W. B. Johnson achieved with the author. This approach does not require the usage of Bastero's extension of the Krivine-Maurey stable theory. It requires only a standard undergraduate level familiarity with real and complex analysis. © 2004 Springer Scinece+Business Media, Inc.
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