Residue current approach to Ehrenpreis-Malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags
Analysis of PDEs
2019-04-02 v3 Commutative Algebra
Complex Variables
Abstract
We introduce the ring of partial differential operators with constant coefficients and commensurate time lags (we use the terminology D operators from now) initially defined by H. Gl\"using-L\"ur\ss en for ordinary 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 equations.
Keywords
Cite
@article{arxiv.1507.06757,
title = {Residue current approach to Ehrenpreis-Malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags},
author = {Saiei-Jaeyeong Matsubara-Heo},
journal= {arXiv preprint arXiv:1507.06757},
year = {2019}
}