ITLApplied  Computational Mathematics Division
ACMD Seminar Series
Attractive Image NIST

A Complete System of Orthogonal Step Functions

David Torney
Los Alamos National Labs\\

Tuesday, January 14, 2003 15:00-16:00,
Room 145, NIST North (820)
Tuesday, January 14, 2003 13:00-14:00,
Room 4550

Abstract: I will straightforwardly describe a previously overlooked orthogonal system of step functions for the interval [0,1]. This system contains the Rademacher functions, and it is distinct from the Paley-Walsh system. Its step functions are expressed in closed form, using the classical Mobius function. Each step function exhibits only one step length. Furthermore, all step heights are rational. A main result is that "a function has an almost-everywhere convergent Fourier-series expansion if and only if it has an almost-everywhere convergent expansion in terms of these step functions". This exposition will include examples and, time permitting, motivations.
Contact: F. Hunt

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Last updated: 2011-01-12.