Global regularity for ordinary differential operators with polynomial coefficients

1Citations
Citations of this article
4Readers
Mendeley users who have this article in their library.
Get full text

Abstract

For a class of ordinary differential operators P with polynomial coefficients, we give a necessary and sufficient condition for P to be globally regular in R, i.e. u∈S'(R) and Pu∈S(R) imply u∈S(R) (this can be regarded as a global version of the Schwartz' hypoellipticity notion). The condition involves the asymptotic behavior, at infinity, of the roots ξ=ξj(x) of the equation p(x, ξ)=0, where p(x, ξ) is the (Weyl) symbol of P. © 2013 Elsevier Inc.

Cite

CITATION STYLE

APA

Nicola, F., & Rodino, L. (2013). Global regularity for ordinary differential operators with polynomial coefficients. Journal of Differential Equations, 255(9), 2871–2890. https://doi.org/10.1016/j.jde.2013.07.022

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free