Fourier and Abel in cooperation

Abstract:

In his work on the stationary heat distribution in a unit disc, Fourier introduced the method of expressing functions as series involving trigonometric functions. In Fourier's case, the functions were functions from the unit circle in R² to C, but the concept can be generalized. In this talk, we show that the approach can also be used for functions in the space L²(G), i.e., the space of functions from some finite Abelian group G to C.