Eigenfunction Expansions on Geodesic Balls and Rank One Symmetric Spaces of Compact Type
We find sharp conditions for the pointwise convergence of eigenfunction expansions associated with the Laplace operator and other rotationally invariant differential operators. Specifically, we consider this problem for expansions associated with certain radially symmetric operators and general boundary conditions and the problem in the context of Jacobi polynomial expansions. The latter has immediate application to Fourier series on rank one symmetric spaces of compact type.
Eigenfunction, Jacobi polynomials, Laplacian, Symmetric spaces
Pinsky, Mark A., and William O. Bray. "Eigenfunction expansions on geodesic balls and rank one symmetric spaces of compact type." Annals of Global Analysis and Geometry 18, no. 3 (2000): 347-369.
Annals of Global Analysis and Geometry