论文标题
自然歼灭者和恒定等级的运营商超过$ \ mathbb {c} $
Natural annihilators and operators of constant rank over $\mathbb{C}$
论文作者
论文摘要
即使对于每个非平凡相位空间变量的两个常数级别差分运算符的傅立叶符号具有相同的nullspace，这些差分运算符的零空域也可能因无限的维度空间而有所不同。在$ \ mathbb {c} $以上的恒定等级的自然条件下，我们确定傅立叶符号级别上的nullspaces的平等性已经意味着$ \ mathscr {d}'$ modulo多项式在固定度的固定度多项式中的nullspace的相等性。特别是，这种情况允许在差异操作员的复合物框架内谈论自然歼灭者。作为应用程序，我们为在二维中具有恒定复杂等级的差异操作员建立了庞加莱型引理。
Even if the Fourier symbols of two constant rank differential operators have the same nullspace for each non-trivial phase space variable, the nullspaces of those differential operators might differ by an infinite dimensional space. Under the natural condition of constant rank over $\mathbb{C}$, we establish that the equality of nullspaces on the Fourier symbol level already implies the equality of the nullspaces of the differential operators in $\mathscr{D}'$ modulo polynomials of a fixed degree. In particular, this condition allows to speak of natural annihilators within the framework of complexes of differential operators. As an application, we establish a Poincaré-type lemma for differential operators of constant complex rank in two dimensions.
