A Complete System of Orthogonal Step Functions
David Torney
Los Alamos National Labs\\
Tuesday, January 14, 2003 15:0016:00, Room 145, NIST North (820) Gaithersburg Tuesday, January 14, 2003 13:0014:00, 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 PaleyWalsh 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 almosteverywhere convergent Fourierseries
expansion if and only if it has an almosteverywhere 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) 9753668;
at least 24 hours in advance.
