## Tuesday Seminar of Analysis

Date, time & place Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

### 2015/04/21

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Saiei Matsubara (Graduate School of Mathematical Sciences, the University of Tokyo)
Residue current techniques with application to a general theory of
linear delay-differential equations with constant coefficients (Japanese)
[ Abstract ]
We introduce the ring of 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 observe that various function modules enjoy good cohomological properties over this ring. %After revising the notion of the residue current in the spirit of M. Andersson and E. Wulcan, we introduce the multidimensional version of the ring D$\Delta$ operators.
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.