Two simple topics in spectral theory

Abstract

1.An expression for the smoothed counting function in terms of the fractional derivatives of the delta-function is presented. 2. The Neumann-Dirichlet (ND) boundary problem is introduced via some elementary examples based on a functorial relation between the ND, DD, NN and periodic boundary conditions.

Talk presented at the International Meeting on ``Quantum Gravity and Spectral Geometry'', Naples July 2-7, 2001. 4 pages, LaTeX