Dispersive estimates and optimality for Schrödinger equations on product cones
Abstract
Abstract In this paper, we study time decay estimates for the Schrödinger propagator on the product cone ( X , g ) {(X,g)} , where X = C ( ρ 𝕊 n - 1 ) = ( 0 , ∞ ) × ρ 𝕊 n - 1 {X=C(\rho\mathbb{S}^{n-1})=(0,\infty)\times\rho\mathbb{S}^{n-1}} . We prove that the usual dispersive estimate holds when the radius ρ is greater than or equal to 1 and fails otherwise. A part of the former result was already established in a recent paper by Jia and Zhang. The method used here relies purely on harmonic analysis, whereas Jia and Zhang employed microlocal analysis to capture the precise asymptotic behavior of the propagator.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Numerical methods in inverse problems
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Forum Mathematicum
- Publisher
- Walter de Gruyter GmbH
- Volume
- 38
- Issue
- 4
- Pages
- 1043–1059
- Publication date
- 1 January 2026
- Language
- EN