各向异性 Gabor 波前集的传播

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-04-22 DOI:10.1017/s0013091524000269

Patrik Wahlberg

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引用次数: 0

摘要

我们展示了一个关于各向异性 Gabor 波前集传播的结果，该结果适用于具有调和分布 Schwartz 内核的线性算子。各向异性 Gabor 波前集的参数是空间和频率变量之间的正参数。假设 Schwartz 核的各向异性 Gabor 波前集满足图形类型标准。这一结果被应用于一类演化方程，该方程概括了自由粒子的薛定谔方程。拉普拉斯算子由任何具有常数系数、实符号和至少二阶的偏微分算子代替。

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Propagation of anisotropic Gabor wave front sets

We show a result on propagation of the anisotropic Gabor wave front set for linear operators with a tempered distribution Schwartz kernel. The anisotropic Gabor wave front set is parametrized by a positive parameter relating the space and frequency variables. The anisotropic Gabor wave front set of the Schwartz kernel 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 any partial differential operator with constant coefficients, real symbol and order at least two.

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来源期刊

Proceedings of the Edinburgh Mathematical Society 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.