THE HURWITZ THEOREM FOR BESSEL FUNCTIONS AND ITS CONSEQUENCES FOR ANTIBOUND STATES

MICHAEL S P EASTHAM

mandh@chesilhay.fsnet.co.uk

Department of Computer Science
Cardiff University
PO Box 916, Cardiff CF24 3XF, UK

The Hurwitz theorem states (inter alia) that the Bessel function has no zeros for real and . We derive a number of consequences for the Dirichlet and Neumann antibound states concerning the Bessel and hypergeometric equations, in which the potential has only exponential decay at infinity. Little is known about the distribution of resonances and antibound states for this decay, and a number of conjectures are suggested, supported by computational considerations.

EPSRC Gregynog Workshop, 21-26 July 2002