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Journal of the London Mathematical Society 2002 65(3):624-638; doi:10.1112/S0024610702003216
© 2002 by London Mathematical Society
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© The London Mathematical Society

Antibound States and Exponentially Decaying Sturm–Liouville Potentials

M. S. P. Eastham

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

Received 14 June 2001.

We consider the Sturm–Liouville equation

y''(x)+{{lambda}–q(x)}y(x)=0 (0≤x<{infty}) (1.1)

with a boundary condition at x = 0 which can be either the Dirichlet condition

y(0)=0 (1.2)

or the Neumann condition

y'(0)=0 (1.3)

As usual, {lambda} is the complex spectral parameter with 0 ≤ arg {lambda} < 2{pi}, and the potential q is real-valued and locally integrable in [0, {infty}).


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