Non?harmonic Gohberg's lemma, Gershgorin theory and heat equation on manifolds with boundary

We use Operator Ideals Theory and Gershgorin theory to obtain explicit information in terms of the symbol concerning spectrum pseudo-differential operators, on a smooth manifold ? with boundary ? , context non-harmonic analysis value problems introduced [29] model operator L. For symbols Hörmander class S 1 0 ( ¯ × I ) we provide version Gohberg's lemma, sufficient necessary condition ensure that corresponding is compact L 2 or Riesz p case Riemannian manifolds boundary. extend well known theorems about exact domain elliptic discuss some applications obtained results evolution equations.