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From Fractal Interpolation Functions to Wavelets: The HD Problem for Refinable Functions

Thursday, January 18, 2001 - 11:30am - 12:30pm
Keller 3-180
Doug Hardin (Vanderbilt University)
Fractal interpolation functions (Barnsley, 1986) are a class of functions with self-affine graphs. Fractal interpolation functions also naturally arise in the study of refinable functions. In fact, refinable functions are piecewise fractal interpolation functions.

In this talk we consider the so-called H-D problem for refinable functions: Given a fractal interpolation function F supported on [0,1], find all refinable functions that can be pieced together from the shifts of F. This is joint work with Tom Hogan.