论文标题
卷积运算符在非政策对称空间上的溢流
Surjectivity of Convolution Operators on Noncompact Symmetric Spaces
论文作者
论文摘要
让$μ$为$ k $ invariant紧凑型分布，在不兼容的riemannian对称空间上$ x = g/k $。如果球形傅立叶变换$ \widetildeμ（λ）$正在缓慢减少，则众所周知，正确的卷积操作员$c_μ\ colon f \ colon f \ mapsto f*μ$ maps $ \ mathcal $ \ mathcal e（x）$ to $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Mathcal E（x）$。在本文中，我们证明了这一结果的相反。我们还证明，$C_μ$只有$ \widetildeμ（λ）$缓慢减少时，才具有基本解决方案。
Let $μ$ be a $K$-invariant compactly supported distribution on a noncompact Riemannian symmetric space $X=G/K$. If the spherical Fourier transform $\widetildeμ(λ)$ is slowly decreasing, it is known that the right convolution operator $c_μ\colon f\mapsto f*μ$ maps $\mathcal E(X)$ onto $\mathcal E(X)$. In this paper, we prove the converse of this result. We also prove that $c_μ$ has a fundamental solution if and only if $\widetildeμ(λ)$ is slowly decreasing.
