2002/11/30 by Sagun Chanillo, Bernard Helffer, Ari Laptev
Mathematics · #math.AP #math.SP #msc:35J70 #msc:35J10
published as J. Functional Analysis, 209(2), 2004, 425-443 · 22 pages, theorem 4.3 in new version is improved from m>18(old) to m>5(new) Proofs simplified considerably and typos fixed
arxiv created 2002/12/07 · arxiv updated 2009/11/30
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.