College of Liberal Arts & Sciences

# Operator Theory Seminar

Speaker:

Paul Muhly

Topic:

Groupoid Methods in Wavelet Analysis, Redux

**Abstract:**

This series of two talks is based on joint work with Marius Ionescu. I will describe how we use groupoid methods to give new proofs of the main theorems in Stephane Mallat’s famous *Multiresolution approximations and wavelet orthonormal bases of L _{2}(R*), Trans. Amer. Math. Soc. 315 (1989). Our techniques extend to settings much more general than those considered by Mallat. One of them involves composition operators on the unit circle that are generated by finite Blaschke products whose zeros are suitably constrained. My goal is to convince the audience of the utility of groupoids and to promote the mantra:

*Groups act on sets, Groupoids act on fibred sets.*

UICapture link to recordings:

Event Date:

September 26, 2023 - 1:30pm to 2:30pm

Location:

VAN 309 or Online (See URL)

Calendar Category:

Seminar

Seminar Category:

Operator Theory