A GENERALIZATION OF A LEVITIN AND PARNOVSKI UNIVERSAL INEQUALITY FOR EIGENVALUES

Said Ilias (1) , Makhoul Ola (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

In this paper, we derive "universal" inequalities for the sums of eigenvalues of the Hodge de Rham Laplacian on Euclidean closed Submanifolds and of eigenvalues of the Kohn Laplacian on the Heisenberg group. These inequalities generalize the Levitin-Parnovski inequality obtained for the sums of eigenvalues of the Dirichlet Laplacian of a bounded Euclidean domain. New Reilly and Asada inequalities are also obtained.

Mots clés: eigenvalues; Hodge de Rham Laplacian; Universal inequalities; Submanifolds; Reilly inequality

Domaines: Théorie spectrale [math.SP]

Said Ilias, Makhoul Ola. A GENERALIZATION OF A LEVITIN AND PARNOVSKI UNIVERSAL INEQUALITY FOR EIGENVALUES. 2009. ⟨hal-00542688⟩