论文标题
$ e^{ - \ lvertτ\ rvert} $最大化圆锥部分的傅立叶扩展名？
When does $e^{-\lvert τ\rvert }$ maximize Fourier extension for a conic section?
论文作者
论文摘要
在过去的十年中，了解最大化器的最大限制和扩展不平等的努力。几乎所有涉及限制或扩展操作员的不平等现象的最大化者都可以被成功识别为标题中问题的部分答案。在这项调查中，我们关注与此问题相关的尖锐限制理论的最新发展。我们在球形和双曲线延伸不平等的代数情况下提出了结果。我们还讨论了penrose变换的使用，导致锥体中有一些负面答案。
In the past decade, much effort has gone into understanding maximizers for Fourier restriction and extension inequalities. Nearly all of the cases in which maximizers for inequalities involving the restriction or extension operator have been successfully identified can be seen as partial answers to the question in the title. In this survey, we focus on recent developments in sharp restriction theory relevant to this question. We present results in the algebraic case for spherical and hyperbolic extension inequalities. We also discuss the use of the Penrose transform leading to some negative answers in the case of the cone.
