Diophantine estimates on shifts of trigonometric polynomials on $\mathbb{T}^d$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913367582572544 |
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| author | Shi, Yunfeng Wang, W. -M. |
| author_facet | Shi, Yunfeng Wang, W. -M. |
| contents | We establish Diophantine type estimates on shifts of trigonometric polynomials on the torus $\mathbb{T}^d$, as well as that of their square roots. These estimates arise from the spectral analysis of the quasi-periodic Schrödinger and the quasi-periodic wave operators. They have applications to the nonlinear quasi-periodic Schrödinger equations (NLS) and the nonlinear quasi-periodic wave equations (NLW). One could now, for example, extend the result of Bourgain (Geom. Funct. Anal. 17(3): 682-706, 2007) to the nonlinear setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_12666 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Diophantine estimates on shifts of trigonometric polynomials on $\mathbb{T}^d$ Shi, Yunfeng Wang, W. -M. Mathematical Physics Dynamical Systems Number Theory We establish Diophantine type estimates on shifts of trigonometric polynomials on the torus $\mathbb{T}^d$, as well as that of their square roots. These estimates arise from the spectral analysis of the quasi-periodic Schrödinger and the quasi-periodic wave operators. They have applications to the nonlinear quasi-periodic Schrödinger equations (NLS) and the nonlinear quasi-periodic wave equations (NLW). One could now, for example, extend the result of Bourgain (Geom. Funct. Anal. 17(3): 682-706, 2007) to the nonlinear setting. |
| title | Diophantine estimates on shifts of trigonometric polynomials on $\mathbb{T}^d$ |
| topic | Mathematical Physics Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2309.12666 |