Lectures related to Heisenberg Groups: Introduction

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Explores optimal transport in heat equations and metric spaces.

Covers the concept of outer measure and properties of measurable sets.

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.