2008/08/08 by Mrinal Raghupathi, Raghupathi, Mrinal · 1 citation
Mathematics · #47A57 #Advanced Operator Algebra Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:47A57
paper · pdf · doi:10.48550/arxiv.0808.1206
25 pages, no figures, preprint, submitted
arxiv created 2008/08/08 · openalex publication_date 2008/08/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize Abrahamse's interpolation theorem from the setting of a multiply connected domain to that of a more general Riemann surface. Our main result provides the scalar-valued interpolation theorem for the fixed-point subalgebra of H^∞ associated to the action of a Fuchsian group. We rely on two results from a paper of Forelli. This allows us to prove the interpolation result using duality techniques that parallel Sarason's approach to the interpolation problem for H^∞. In this process we prove a more general distance formula, very much like Nehari's theorem, and obtain relations between the kernel function for the character automorphic Hardy spaces and the Szegö kernel for the disk. Finally, we examine our interpolation results in the context of the two simplest examples of Fuchsian groups acting on the disk.