2024/05/27 by Patrick Erik Bradley, Bradley, Patrick Erik · 3 citations
Computer Science · Mathematics · #14H30 #Advanced Mathematical Modeling in Engineering #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2405.17586
openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A parametrised diffusion operator on the regular domain Ω of a p-adic Schottky group is constructed. It is defined as an integral operator on the complex-valued functions on Ω which are invariant under the Schottky group Γ, where integration is against the measure defined by an invariant regular differential 1-form ω. It is proven that the space of Schottky invariant L2-functions on Ω outside the zeros of ω has an orthonormal basis consiting of Γ-invariant extensions of Kozyrev wavelets which are eigenfunctions of the operator. The eigenvalues are calculated, and it is shown that the heat equation for this operator provides a unique solution for its Cauchy problem with Schottky-invariant continuous initial conditions supportes outside the zero set of ω, and gives rise to a strong Markov process on the corresponding orbit space for the Schottky group whose paths are càdlàg.