Dispersive estimates and optimality for Schrödinger equations on product cones
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909555296829440 |
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| author | Taira, Kouichi |
| author_facet | Taira, Kouichi |
| contents | In this paper, we study time decay estimates for the Schrödinger propagator on the product cone $(X,g)$, where $X=C(ρ\mathbb{S}^{n-1})=(0,\infty)\times ρ\mathbb{S}^{n-1}$. 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-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_21527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dispersive estimates and optimality for Schrödinger equations on product cones Taira, Kouichi Analysis of PDEs 35Q41, 35R01 In this paper, we study time decay estimates for the Schrödinger propagator on the product cone $(X,g)$, where $X=C(ρ\mathbb{S}^{n-1})=(0,\infty)\times ρ\mathbb{S}^{n-1}$. 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-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. |
| title | Dispersive estimates and optimality for Schrödinger equations on product cones |
| topic | Analysis of PDEs 35Q41, 35R01 |
| url | https://arxiv.org/abs/2503.21527 |