On the spectral function of some higher order elliptic or degenerate-elliptic operators
Résumé
We study the spectral function lambda --> s(lambda) := s(-A+lambda V) where s(-A+lambda V) denotes the spectral bound of the perturbed operator -A+lambda V and V is a suitable potential. In the case where A = (-1)(m) (\alpha\=\beta\=m)Sigma D-alpha(a(alpha beta)D(beta)) is a higher order degenerate-elliptic operator on L-2(R-N) and V is an element of L-1(R-N) we show in particular that s(lambda) > 0 for all lambda > 0 provided that integral(RN) V(x)dx greater than or equal to 0, V not equal 0 and N less than or equal to 2m.