Peetre-Slovák's theorem revisited

2014/11/27 by J. Navarro, Navarro, J., J. B. Sancho +1 · 1 voice
Mathematics · #58J99 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AP #math.DG #math.GT #msc:58J99

paper · pdf · doi:10.48550/arxiv.1411.7499

17 pages

arxiv created 2016/01/19 · arxiv updated 2016/01/20

Abstract

In 1960, J. Peetre proved the finiteness of the order of linear local operators. Later on, J. Slovák vastly generalized this theorem, proving the finiteness of the order of a broad class of (non-linear) local operators. In this paper, we use the language of sheaves and ringed spaces to prove a simpler version of Slovák's result. The statement we prove, adapting Slovák's original ideas, deals with local operators defined between the sheaves of smooth sections of fibre bundles, and thus covers many of the applications of Slovák's theorem.

Discussions

• Short answer: yes, but only after the statement is reformulated — and the extra hypothesis you are looking for is the existence of smooth partitions of unity . Let me first explain why the reformulati [stackexchange, 1 points]

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