Harmonic-Counting Measures and Spectral Theory of Lens Spaces

2016/02/21 by Hossein Mohades, H. Mohades, Mohades, H. +2
Mathematics · #11P21 #34L20 #58J50 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.DG #math.SP #msc:11P21 #msc:34L20 #msc:58J50

paper · pdf · doi:10.48550/arxiv.1602.06528

arxiv created 2016/02/21 · openalex publication_date 2016/02/21 · arxiv updated 2016/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, associated with each lattice T⊆ ℤⁿ the concept of a harmonic-counting measure ν_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.

Citations

• On a Relation between Spectral Theory of Lens Spaces and Ehrhart Theory

Related

• On the Calculus of the Spectrum of the Laplacian for functions in Lens Spaces
• Isospectrality For Orbifold Lens Spaces
• On a Relation between Spectral Theory of Lens Spaces and Ehrhart Theory
• Eigenmodes of Lens and Prism Spaces
• Spectral Analysis of the Kohn Laplacian on Lens Spaces