5 papers · 1 filter
Nodal sets and continuity of eigenfunctions of Krein-Feller operators on Riemannian manifolds
Sze-Man Ngai, Wen-Quan Zhao
Let , be a bounded domain of a smooth complete Riemannian d-manifold M, and be a positive finite Borel measure with compact support in . We prove the Co…
Differential equations defined by Kre\uın-Feller operators on Riemannian manifolds
Sze-Man Ngai, Lei Ouyang
We study linear and semi-linear wave, heat, and Schrödinger equations defined by Kre\uın-Feller operator on a complete Riemannian -manifolds , where is a finite po…
Hodge Theorem for Krein-Feller operators on compact Riemannian manifolds
Sze-Man Ngai, Lei Ouyang
For an open set in a compact smooth oriented Riemannian n-manifold and a positive finite Borel measure with support contained in the closure of the open set, we define an associate…
Separation conditions for iterated function systems with overlaps on Riemannian manifolds
Sze-Man Ngai, Yangyang Xu
We formulate the weak separation condition and the finite type condition for conformal iterated function systems on Riemannian manifolds with nonnegative Ricci curvature, and gener…
Existence of -dimension and entropy dimension of self-conformal measures on Riemannian manifolds
Sze-Man Ngai, Yangyang Xu
Peres and Solomyak proved that on , the limits defining the -dimension for any , and the entropy dimension of a self-conformal measu…