Dimension of divergence sets of oscillatory integrals with concave phase
arXiv (Cornell University)(2022)
摘要
We study the Hausdorff dimension of the sets on which the pointwise convergence of the solutions to the fractional Schr\"odinger equation $e^{it(-\Delta)^\frac m2}f$ fails when $m\in(0,1)$ in one spatial dimension. The pointwise convergence along a non-tangential curve and a set of lines are also considered, where we find different nature from the case when $m\in(1,\infty)$. In particular, non-tangential curves are no longer regarded as vertical lines.
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关键词
oscillatory integrals,divergence sets
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