Harmonic-Counting Measures and Spectral Theory of Lens Spaces

H. Mohades; B. Honari

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arXiv · 1602.06528

Harmonic-Counting Measures and Spectral Theory of Lens Spaces

H. Mohades·B. Honari

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Abstract

In this article, associated with each lattice $T\subseteq \mathbb{Z}^n$ the concept of a harmonic-counting measure $\nu_T$ on a sphere $S^{n-1}$ is introduced and it is applied to determine the asymptotic behavior of the eigenfunctions of the Laplace-Beltrami operator on a lens space. In fact, the asymptotic behavior of the cardinality of the set of independent eigenfunctions associated with the elements of $T$ which lie in a cone is determined when $T$ is the lattice of a lens space.

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BibTeX RIS

H. Mohades, B. Honari. 2016-02-21. Harmonic-Counting Measures and Spectral Theory of Lens Spaces. https://arxiv.org/abs/1602.06528

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