Analogue of Newton-Puiseux series for non-holonomic D-modules and factoring

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dc.creatorGrigoriev, D.
dc.date2008-11-09
dc.date.accessioned2026-07-07T10:17:09Z
dc.date.available2026-07-07T10:17:09Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0811.1367
dc.identifierhttp://arxiv.org/abs/0811.1367
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173757
dc.subjectAnalysis of PDEs
dc.subjectRings and Algebras
dc.subject35C10, 35D05, 68W30
dc.titleAnalogue of Newton-Puiseux series for non-holonomic D-modules and factoring
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