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Dispersive estimates and optimality for Schr\"odinger equations on product cones
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abstract
In this paper, we study time decay estimates for the Schr\"odinger propagator on the product cone $(X,g)$, where $X=C(\rho \mathbb{S}^{n-1})=(0,\infty)\times \rho\mathbb{S}^{n-1}$. We prove that the usual dispersive estimate holds when the radius $\rho$ 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-Zhang. The method used here relies purely on harmonic analysis, whereas Jia-Zhang employed microlocal analysis to capture the precise asymptotic behavior of the propagator.
Forward citations
Cited by 2 Pith papers
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Decay and Strichartz estimates for critical electromagnetic wave equations on conic manifolds
The authors establish microlocalized pointwise decay and Strichartz estimates for electromagnetic wave equations on n-dimensional product cones, with the admissible p-range restricted by the smallest eigenvalue of the...
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Pointwise dispersive estimates for Schrodinger and wave equations in a conical singular space
On product cones over closed manifolds with conjugate radius larger than pi, the Schrödinger and half-wave propagators satisfy global pointwise dispersive estimates with the Euclidean decay rate times an angular weight.
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