Eigenfunctions of the Laplace-Beltrami Operator on Hyperboloids

Eigenfunctions of the Laplace-Beltrami operator on a hyperboloid are studied in the spirit of the treatment of the spherical harmonics by Stein and Weiss. As a special case, a simple self-contained proof of Laplace's integral for a Legendre function is obtained.Comment: 5 page

Inductive Algebras for Finite Heisenberg Groups

A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite Heisenberg groups.Comment: 5 page

A generalization of a result of Minakshisundaram and Pleijel

Minakshisundaram and Pleijel gave an asymptotic formula for the sum of squares of the pointwise values of the eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold, with eigenvalues less than a fixed number. Here, a generalization is given, where the pointwise values are replaced by the Fourier coefficients of a smooth measure supported on a compact submanifold.Comment: 13 page