论文标题
各向异性Gelfand-Shilov Wave Fronts的传播
Propagation of anisotropic Gelfand-Shilov wave front sets
论文作者
论文摘要
我们展示了与Schwartz内核的线性运算符的各向异性Gelfand-Shilov Wave Front集的繁殖结果，这是Gelfand--Shilov--Shilov-Shilov beurling类型。此各向异性波前集由两个正面参数进行参数，这些参数与空间和频率变量有关。假定操作员的Schwartz内核的各向异性Gelfand--Shilov Wave Front集可以满足图类型标准。结果应用于一类进化方程，该方程将自由粒子的schrödinger方程推广。 Laplacian被由符号定义的部分差分操作员取代，该符号是一个多项式，具有实际系数和秩序至少两个。
We show a result on propagation of the anisotropic Gelfand--Shilov wave front set for linear operators with Schwartz kernel which is a Gelfand--Shilov ultradistribution of Beurling type. This anisotropic wave front set is parametrized by two positive parameters relating the space and frequency variables. The anisotropic Gelfand--Shilov wave front set of the Schwartz kernel of the operator is assumed to satisfy a graph type criterion. The result is applied to a class of evolution equations that generalizes the Schrödinger equation for the free particle. The Laplacian is replaced by a partial differential operator defined by a symbol which is a polynomial with real coefficients and order at least two.
