1301.4806 (Agapitos N. Hatzinikitas)

Spectral Properties of the Dirichlet Operator $\sum_{i=1}^d
(-\partial_i^2)^s$ on Domains in d-Dimensional Euclidean Space    [PDF]

Agapitos N. Hatzinikitas

In this article we investigate the distribution of eigenvalues of the Dirichlet pseudo-differential operator $\sum_{i=1}^{d}(-\partial_i^2)^{s}, \, s\in (1/2,1]$ on an open and bounded subdomain $\Omega \subset \mathbb{R}^d$ and predict bounds on the sum of the first $N$ eigenvalues, the counting function, the Riesz means and the trace of the heat kernel. Moreover, utilizing the connection of coherent states to the semi-classical approach of Quantum Mechanics we determine the sum for moments of eigenvalues of the associated Schr\"{o}dinger operator.

View original: http://arxiv.org/abs/1301.4806