Let X, Y, Z, W be manifolds and π : Z → X be a surjective submersion. We characterize π-local regular operators A : C∞(X,Y) → C∞(Z,W) in terms of the corresponding maps à : J∞(X,Y) ×XZ → W satisfying the so-called local finite order factorization property.
@article{bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_69-72, author = {W\l odzimierz Mikulski}, title = {On regular local operators on smooth maps}, journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica}, volume = {69}, year = {2015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_69-72} }
Włodzimierz Mikulski. On regular local operators on smooth maps. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 69 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_69-72/
Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.
Slovak, J., Peetre theorem for nonlinear operators, Ann. Global Anal. Geom. 6 (3) (1988), 273-283.