Illinois/Missouri Applied
Harmonic Analysis Seminar
Affine synthesis onto Lp for 0 < p < 1

Richard S. Laugesen

Abstract:

Analysis and synthesis are fundamental operations of applied harmonic analysis. I investigate them on the Lebesgue space Lp for 0 < p < 1, using affine systems of the form {g(aj x - k)}.

Analysis is shown to map Lp boundedly into the sequence space lp, provided it is preceded by a nonlinear stretch of the signal. Synthesis clearly maps lp into Lp. The real challenge is to find when synthesis maps onto Lp (preferably using an explicit construction).

As time permits, I'll mention related results for p>1, and for Hardy space.

To download the slides, please click the title of the talk above

Washington University in St. Louis
Mathematics Department
Campux Box 1146
St. Louis, MO 63130
Phone: (314) 935-6760   FAX: (314) 935-6839.