等共振复值势与对称性
Isoresonant complex-valued potentials and symmetries
摘要：
设$X$是连通黎曼流形，使得自由拉普拉斯算子$(Δ-z)^{-1}, z\in\C\setminus\R^{+},$的预解式有一个通过$\R^{+}$的亚纯延拓.这种延拓的极点称为共振。当$X$具有某些对称性时，我们构造复值位势$V$，使得$Δ+V$的预解式也具有亚纯延拓，与自由拉普拉斯算子具有相同的重数共振.
英文摘要：
Let $X$ be a connected Riemannian manifold such that the resolvent of the free Laplacian $(Δ-z)^{-1}, z\in\C\setminus\R^{+},$ has a meromorphic continuation through $\R^{+}$. The poles of this continuation are called resonances. When $X$ has some symmetries, we construct complex-valued potentials, $V$, such that the resolvent of $Δ+V$, which has also a meromorphic continuation, has the same resonances with multiplicities as the free Laplacian.
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