The "Full Muntz Theorem" revisited Academic Article

abstract

• We give an elementary proof of the "convergent sum part" of the full Mntz Theorem in Lp(A) and in C(A), together with the "Clarkson - Erds-Schwartz phenomenon" for all p (0,), and for all compact A [0,) with positive lower density at 0. This extends earlier results of Mntz, Szsz, Clarkson and Erds, L. Schwartz, P. Borwein and Erdlyi, 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.

authors

• Erdelyi, Tamas

published proceedings

• CONSTRUCTIVE APPROXIMATION

author list (cited authors)

• Erdelyi, T.

citation count

• 9

complete list of authors

• Erdelyi, T

publication date

• February 2005

publisher

• Springer Nature  Publisher

published in

• Constructive Approximation  Journal

keywords

• 1].
• Denseness In L-p[0,1]
• Muntz Theorem

Digital Object Identifier (DOI)

• 10.1007/s00365-004-0573-6

start page

• 319

end page

• 335

volume

• 21

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs00365-004-0573-6