Eigenvalue Inequalities for Klein-Gordon Operators

Research Horizons Seminar
Tuesday, October 21, 2008 - 13:00
1 hour (actually 50 minutes)
Skiles 255
School of Mathematics, Georgia Tech
We consider the pseudodifferential operators H_{m,\Omega} associated by the prescriptions of quantum mechanics to the Klein-Gordon Hamiltonian when restricted to a compact domain \Omega in {\mathbb R}^d. When the mass m is 0 the operator H_{0,\Omega} coincides with the generator of the Cauchy stochastic process with a killing condition on \partial \Omega. (The operator H_{0,\Omega} is sometimes called the fractional Laplacian with power 1/2.) We prove several universal inequalities for the eigenvalues (joint work with Evans Harrell).