## Two little remarks on sphere

1. “Take a sphere of radius in dimensions, large; then most points inside the sphere are in fact very close to the surface.” David Ruelle Let and . Let The fraction of the volume of to the volume of is … Continue reading

## Matrix multiplication as a convolution

1. The product of two power series/polynomials is The coefficients given by is sometimes called the Cauchy product. This is a convolution. 2. Let be a finite group and be the group algebra with complex coefficients. Let be two elements … Continue reading

## From combinatorics to entropy

Let and . Then by Stirling’s formula. This is probably well-known to people who have studied statistical physics, but some of us including myself may not be very aware of this kind of relation. I wonder if this was the … Continue reading

## A meta post, and two articles

1. Is there any way to support MathJax here? It can translate directly the latex code to display math. It is supported on blogspot, I find it more convenient. 2. I believe many of us come across some very good articles … Continue reading

Posted in Dynamical system, Uncategorized | 2 Comments

## Fourier coefficients as eigenvalues/spectrum

In this post I want to make a connection between Fourier coefficients and eigenvalues/spectrum. Let me put the claim up front: If , then is not invertible with respect to the convolution product. Please feel free to jump directly to … Continue reading