On the dimension of divergence sets of Schrödinger equation with complex time

Yuan, Jiye; Zhao, Tengfei; Zheng, Jiqiang

doi:10.1016/j.na.2021.112312

Cited by 3 publications

(1 citation statement)

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“…(ii) In R, using stationary phase analysis and the T T * argument, Shiraki in [40] and together with Cho in [16] obtained the pointwise convergence for the Schrödinger equation along the non-tangential lines and the tangential lines respectively. The authors in [46] and together with Zheng in [44,45] studied these several variants of the pointwise convergence problem for the fractional Schrödinger operator with complex time. However, because of the different properties between the space T d and R d such as Dirichlet lemma and Hardy-Littlwood circle method, here we only obtain the pointwise convergence along rational non-tangential lines.…”

Section: (D+1)mentioning

confidence: 99%

Maximal estimates for the Weyl sums on $\mathbb{T}^{d}$

Miao¹,

Yuan²,

Zhao³

2022

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In this paper, we obtain the maximal estimate for the Weyl sums on the torus T d with d ≥ 2, which is sharp up to the endpoint. We also consider two variants of this problem which include the maximal estimate along the rational lines and on the generic torus. Applications, which include some new upper bound on the Hausdorff dimension of the sets associated to the large value of the Weyl sums, reflect the compound phenomenon between the square root cancellation and the constructive interference.

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Section: (D+1)mentioning

confidence: 99%