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arXiv · 1301.4806

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

Agapitos N. Hatzinikitas
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Abstract

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.

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Agapitos N. Hatzinikitas. 2013-01-21. Spectral Properties of the Dirichlet Operator $\sum_{i=1}^d (-\partial_i^2)^s$ on Domains in d-Dimensional Euclidean Space. https://doi.org/10.1063/1.4823481

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