For natural numbers n ≥ 3 and r ≥ 1 all natural operators transforming functions from n-manifolds into affinors (i.e. tensor fields of type (1,1)) on the r-cotangent bundle are classified.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-6, author = {W. M. Mikulski}, title = {Natural operators lifting functions to affinors on higher order cotangent bundles}, journal = {Annales Polonici Mathematici}, volume = {83}, year = {2004}, pages = {49-55}, zbl = {1056.58005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-6} }
W. M. Mikulski. Natural operators lifting functions to affinors on higher order cotangent bundles. Annales Polonici Mathematici, Tome 83 (2004) pp. 49-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-1-6/