Eigenfunctions

We study the large eigenvalue limit for the eigenfunctions of the Laplacian, on a compact manifold of negative curvature – in fact, we only assume that the geodesic flow has the Anosov property. In the semi-classical limit, we prove that the Wigner measures associated to eigenfunctions have positive metric entropy. In particular, they cannot concentrate entirely on closed geodesics. 1. Introduction, statement of results We consider a compact Riemannian manifold M of dimension d ≥ 2, and assume that the geodesic flow (g t )t∈R , acting on the unit tangent bundle of M , has a “chaotic”...

43p dontetvui 17-01-2013 51 7   Download

THE FIRST EIGENVALUE OF p-LAPLACIAN SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS D. A. KANDILAKIS, M. MAGIROPOULOS, AND N. B. ZOGRAPHOPOULOS Received 12 October 2004 and in revised form 21 January 2005 We study the properties of the positive principal eigenvalue and the corresponding eigenspaces of two quasilinear elliptic systems under nonlinear boundary conditions. We prove that this eigenvalue is simple, unique up to positive eigenfunctions for both systems, and isolated for one of them. 1. Introduction Let Ω be an unbounded domain in RN , N ≥ 2, with a noncompact and smooth boundary ∂Ω.

15p sting12 10-03-2012 51 4   Download

EIGENSTRUCTURE OF NONSELFADJOINT COMPLEX DISCRETE VECTOR STURM-LIOUVILLE PROBLEMS ´ RAFAEL J. VILLANUEVA AND LUCAS JODAR Received 15 March 2004 and in revised form 5 June 2004 We present a study of complex discrete vector Sturm-Liouville problems, where coefficients of the difference equation are complex numbers and the strongly coupled boundary conditions are nonselfadjoint. Moreover, eigenstructure, orthogonality, and eigenfunctions expansion are studied. Finally, an example is given. 1.

15p sting12 10-03-2012 46 4   Download