Residue current approach to Ehrenpreis-Malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags
Residue current approach to Ehrenpreis-Malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags
复制标题
具有常系数和相应时滞的线性微分方程的 Ehrenpreis-Malgrange 型定理的剩余电流方法
DOI：
10.1016/j.aim.2018.04.004
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发表时间：
2018
影响因子：
1.7
通讯作者：
Saiei-Jaeyeong Matsubara-Heo
中科院分区：
文献类型：
--
作者：
Nobuhiko Hamazaki;So Shimamoto;Orie Hikabe;Yohei Nishimura;Norio Hamada;Katsuhiko Hayashi;Saiei-Jaeyeong Matsubara-Heo
我们引入一个由H初始定义的常系数偏差分-微分算子环H。Glüsing-Lürßen算子的上同调性质。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。在最后一节中，我们从这个结果中推出了H上各种函数模的内射性以及偏微分-差分方程指数多项式解的密度结果。
We introduce a ring H of partial difference-differential operators with constant coefficients initially defined by H. Glüsing-Lürßen for ordinary difference-differential 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 section, we deduce from this injectivity properties of various function modules over H as well as the density results of exponential polynomial solutions for partial difference-differential equations.