论文标题
Gelfand--Shilov空间的微局部分析
Microlocal analysis for Gelfand--Shilov spaces
论文作者
论文摘要
我们介绍了Gelfand-Shilov超级分布的各向异性全球波锋，其定期性和衰减不同。该概念是由于短期傅立叶变换的相位空间中沿功率类型曲线沿功率类型曲线缺乏超指数衰减而定义的。该波前集捕获了功率单型振荡的相空间行为，即k a chirp信号。相对于伪造的运算符证明了微局部的结果，其符号类别会导致gelfand-shilov空间上的连续运算符。我们确定了Dirac Delta的某些衍生物和指数函数的波前集。
We introduce an anisotropic global wave front set of Gelfand--Shilov ultradistributions with different indices for regularity and decay at infinity. The concept is defined by the lack of super-exponential decay along power type curves in the phase space of the short-time Fourier transform. This wave front set captures the phase space behaviour of oscillations of power monomial type, a k a chirp signals. A microlocal result is proved with respect to pseudodifferential operators with symbol classes that give rise to continuous operators on Gelfand--Shilov spaces. We determine the wave front set of certain series of derivatives of the Dirac delta, and exponential functions.
