is a morphism of sheaves which is linear on sections such that the support of "D" is non-increasing: "supp Ds" ⊆ "supp s" for every smooth section "s" of "E". The original Peetre theorem asserts that, for every point "p" in "M", there is a neighborhood "U" of "p" and an integer "k" (depending on "U") such that "D" is a differential operator of order "k" over "U". This means that "D" factors through a linear mapping "i""D" from the "k"-jet of sections of "E" into the space of smooth sections of "F":