论文标题
各向异性全球微局部分析
Anisotropic global microlocal analysis for tempered distributions
论文作者
论文摘要
我们在$ \ Mathbf r^d $上研究了伪差操作员的舒本演算的各向异性版本。各向异性符号和GABOR波前组是根据衰减或曲线的生长来定义的，在功率类型的相空间中，通过一个区分空间和频率变量的一个正参数参数为参数。我们表明，这给出了Shubin各向同性微积分的亚钙库，并且我们在框架中显示了微局部和微层次包含。最后，我们证明了具有真实多项式相位函数的CHIRP型振荡函数的各向异性Gabor波前组的包含。
We study an anisotropic version of the Shubin calculus of pseudodifferential operators on $\mathbf R^d$. Anisotropic symbols and Gabor wave front sets are defined in terms of decay or growth along curves in phase space of power type parametrized by one positive parameter that distinguishes space and frequency variables. We show that this gives subcalculi of Shubin's isotropic calculus, and we show a microlocal as well as a microelliptic inclusion in the framework. Finally we prove an inclusion for the anisotropic Gabor wave front set of chirp type oscillatory functions with a real polynomial phase function.
