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Residue current approach to Ehrenpreis-Malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags. (arXiv:1507.06757v2 [math.AP] UPDATED)
来源于:arXiv
We introduce the ring of partial differential operators with constant
coefficients and commensurate time lags (we use the terminology D$\Delta$
operators from now) initially defined by H. Gl\"using-L\"ur\ss en for ordinary
$D\Delta$ 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 $D\Delta$
equations. 查看全文>>