English

Non-Linear Eigenvalues and Analytic Hypoellipticity

Analysis of PDEs 2007-05-23 v3 Spectral Theory

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.

Keywords

Cite

@article{arxiv.math/0211308,
  title  = {Non-Linear Eigenvalues and Analytic Hypoellipticity},
  author = {Sagun Chanillo and Bernard Helffer and Ari Laptev},
  journal= {arXiv preprint arXiv:math/0211308},
  year   = {2007}
}

Comments

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