Joni's Math Notes

Uncertainty principles in Fourier analysis are formalizations of the following principle: A function $f$ and its Fourier transform $\hat{f}$...

In this post, we consider character sums, which are one of the central objects in the discrete Fourier analysis of the integers modulo $q$. ...

We present some classical results about the Fourier transform in $\mathbb{R}^n$ in this post, and some of them will be applied in later post...

In this post, we give an application of Fourier analysis to combinatorics, more precisely to Ramsey theory. In Ramsey theory , a typical res...

In this post, we give a proof of the law of quadratic reciprocity based on discrete Fourier analysis and more precisely Gauss sums. This cel...

In later posts, we consider properties of Fourier series (for instance, convergence and divergence results), as well as lacunary trigonomet...