| Autor: |
de Ávila Silva, Fernando, Gonzalez, Rafael Borro, Kirilov, Alexandre, de Medeira, Cleber |
| Zdroj: |
Journal of Fourier Analysis & Applications; Aug2019, Vol. 25 Issue 4, p1717-1758, 42p |
| Abstrakt: |
We show that an obstruction of number-theoretical nature appears as a necessary condition for the global hypoellipticity of the pseudo-differential operator L = D t + (a + i b) (t) P (D x) on T t 1 × T x N . This condition is also sufficient when the symbol p (ξ) of P (D x) has at most logarithmic growth. If p (ξ) has super-logarithmic growth, we show that the global hypoellipticity of L depends on the change of sign of certain interactions of the coefficients with the symbol p (ξ). Moreover, the interplay between the order of vanishing of coefficients with the order of growth of p (ξ) plays a crucial role in the global hypoellipticity of L. We also describe completely the global hypoellipticity of L in the case where P (D x) is homogeneous. Additionally, we explore the influence of irrational approximations of a real number in the global hypoellipticity. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
Full text from SpringerLink