How to recognize polynomials in higher order Sobolev spaces

Details How to recognize polynomials in higher order Sobolev spaces How to recognize polynomials in higher order Sobolev spaces

2011-09-11

arxiv.org/abs/1109.2339v1

Mathematics

Classical Analysis and ODEs

Scientific paper

This paper extends characterizations of Sobolev spaces by Bourgain,
Br\'{e}zis, and Mironescu to the higher order case. As a byproduct, we obtain
an integral condition for the Taylor remainder term, which implies that the
function is a polynomial. Similar questions are also considered in the context
of Whitney jets.

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