Global regularity for ordinary differential operators with polynomial coefficients

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Nicola, Fabio^1,2  Rodino, Luigi^1,2 

[1] Politecn Torino, Dipartimento Sci Matemat, I-10129 Turin, Italy

[2] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy

关键词: Global regularity;    Puiseaux expansions;    Symmetric functions;    Elimination theory;   

DOI  :  10.1016/j.jde.2013.07.022

来源: Elsevier

【 摘 要 】

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 is an element of S'(R) and Pu is an element of S(R) imply u is an element of 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 xi = xi(j)(x) of the equation p(x, xi) = 0, where p(x,) is the (Weyl) symbol of P. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free