2008/11/09 by D. Grigoriev, Grigoriev, D.
Mathematics · #35C10 #35D05 #68W30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AP #math.RA #msc:35C10 #msc:35D05 #msc:68W30
paper · pdf · doi:10.48550/arxiv.0811.1367
arxiv created 2008/11/09 · arxiv updated 2009/12/01
We introduce a concept of a fractional-derivatives series and prove that any linear partial differential equation in two independent variables has a fractional-derivatives series solution with coefficients from a differentially closed field of zero characteristic. The obtained results are extended from a single equation to D-modules having infinite-dimensional space of solutions (i. e. non-holonomic D-modules). As applications we design algorithms for treating first-order factors of a linear partial differential operator, in particular for finding all (right or left) first-order factors.