具有公度时滞的常系数线性微分方程的Escherapreis-Malgrange型定理的剩余流方法
Residue current approach to Ehrenpreis-Malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags
摘要：
我们引入了由H. Glüsing-Lürßen构造了一般的$DΔ$算子，并研究了它的上同调性质.将这一环论观察与M.安德森，我们解决了一个特定类型的划分与界限。在第四章中，我们证明了该环上各种函数模的内射性以及$DΔ$方程的谱综合型定理。
英文摘要：
We introduce the ring of partial differential operators with constant coefficients and commensurate time lags (we use the terminology D$Δ$ operators from now) initially defined by H. Glüsing-Lürßen for ordinary $DΔ$ operators and investigate its cohomological properties. Combining this ring theoretic observation with the integral representation technique developed by M. Andersson, we solve a certain type of division with bounds. In the last chapter, we prove the injectivity property of various function modules over this ring as well as spectral synthesis type theorems for $DΔ$ equations.
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