Graduate Student Seminar: Translation, Rescaling and Wavelets

Speaker: 
Nikita Lvov
Date: 
Dec 5 2017 - 12:30pm
Event type: 
Graduate Student Seminar
Room: 
Fine Hall 214
Abstract: 

Translations and dilations lie at the heart of much of analysis on the real line. Eigenfunctions of the first operator give rise to Fourier decomposition, and those of the latter to Taylor series. Combining both operations in turn gives rise to the theory of wavelets, which I will discuss in this talk. I will possibly also touch upon the simple harmonic oscillator of quantum mechanics, which also combines both structures.