Sze-Man Ngai

activity

20142025

most citedOne-dimensional wave equations defined by fractal Laplacians

18 citations · 19 across the 10 of their papers we have counts for

collaborators

Showing 2024Show all

5 papers · 1 filter

math.DS2024

Iterated relation systems on Riemannian manifolds

Jie Liu, Sze-Man Ngai, Lei Ouyang

For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as fractal sets are often defined by relations that are multivalue…

math.FA2024

Nodal sets and continuity of eigenfunctions of Krein-Feller operators on Riemannian manifolds

Sze-Man Ngai, Wen-Quan Zhao

Let $d \geq 1$ , $Ω$ be a bounded domain of a smooth complete Riemannian d-manifold M, and $μ$ be a positive finite Borel measure with compact support in $Ω$ . We prove the Co…

math.AP2024

Nodal sets and continuity of eigenfunctions of Kre\uı-Feller operators

Sze-Man Ngai, Meng-Ke Zhang, Wen-Quan Zhao

Let $μ$ be a compactly supported positive finite Borel measure on $R^{d}$ . Let $0 < λ_{1} \leq λ_{2} \leq \dots$ be eigenvalues of the Kre $ı ˘$ n-Feller operator $Δ_{μ}$ . We prove t…

math.FA2024

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 $- Δ_{μ}$ on a complete Riemannian $n$ -manifolds $M$ , where $μ$ is a finite po…

math.FA2024

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…