Analysis Seminar

A celebrated theorem of C.L. Siegel from 1929 shows that the multiplicity of eigenvalues for the Laplace eigenfunctions on the unit disk is at most two. More precisely, Siegel shows that positive zeros of Bessel functions are transcendental.

We study the fourth order clamped plate problem, showing that the multiplicity of eigenvalues is uniformly bounded (by not more than six). Our method is based on Siegel-Shidlovskii theory and new recursion formulas.

The talk is based on a joint work with Yuri Lvovski.