Student Mentoring 

I have some interesting problems in Harmonic analysis for LSU undergrads that we can work on together. Shoot me an email if you like to discuss any of this.

Uncertainty Principle: The uncertainty principle, originally formulated in quantum mechanics, also has significant analogs in mathematical analysis, particularly in signal processing and Fourier analysis. In the context of analysis, it states that a function and its Fourier transform cannot both be highly localized or sharply confined at the same time. In simple terms this means,  function and its Fourier transform cannot be simultaneously ”small”. 

This is similar in spirit to Heisenberg's uncertainty principle in quantum mechanics, where position and momentum (akin to time and frequency) cannot both be precisely known simultaneously. There are several versions of the uncertainty principle known to us now. In this context, we can work together some of these projects. Here I have a list of some topics:

Uncertainty Principle in Fourier Series


Paley-Wiener Theorem and Uncertainty Principle