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)
Gaithersburg
Tuesday, January 14, 2003 13:00-14:00,
Room 4550
Boulder
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. HuntNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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