Non-Linear Eigenvalues and Analytic Hypoellipticity

Abstract

Motivated by the problems of analytic hypoellipticity, we show that a special family of compact non self-adjoint operators has a non-zero eigenvalue. We recover old results by Christ,Hanges, Himonas, Pham-The-Lai and Robert proved by using ordinary differential equations. We show our method applies to higher dimensional cases, giving in particular a new class of hypoelliptic but not analytic hypoelliptic operators.

22 pages, theorem 4.3 in new version is improved from m>18(old) to m>5(new) Proofs simplified considerably and typos fixed