Symbol of a differential operator: Difference between revisions

Revision as of 22:50, 13 June 2007

Revision as of 10:19, 20 June 2007

Line 25:

:<math> \sigma(P): S^{k} (T^*X) \otimes E_{1} \to E_{2} </math>.

View the symbol <math> \sigma(P) </math> as a homogeneous polynomial orof degree <math> k </math> in <math> T^* X </math> with values in <math> Hom(E_1, E_2) </math>.

The differential operator <math> P </math> is elliptic if its symbol is invertible; that is for each nonzero <math> \theta \in T^*X </math> the bundle map <math> \sigma(P) (\theta, \dots, \theta)</math> is invertible.