论文标题
一般赫尔姆霍尔茨的本地化
Localization for general Helmholtz
论文作者
论文摘要
在\ cite {gmw2022}中，关，穆鲁甘和魏建立了经典的helmholtz方程与``分数helmholtz''方程式，在该方程中，laplacian操作员替换了非局部分数分数laplacian cortions and Explorte and Exports sounders and suffe and suffers offer。我们为这个Helmholtz等效问题介绍了一种新颖的设置。
In \cite{gmw2022}, Guan, Murugan and Wei established the equivalence of the classical Helmholtz equation with a ``fractional Helmholtz" equation in which the Laplacian operator is replaced by the nonlocal fractional Laplacian operator. More general equivalence results are obtained for symbols which are complete Bernstein and satisfy additional regularity conditions. In this work we introduce a novel and general set-up for this Helmholtz equivalence problem. We show that under very mild and easy-to-check conditions on the Fourier multiplier, the general Helmholtz equation can be effectively reduced to a localization statement on the support of the symbol.
