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Journal of the London Mathematical Society 2003 68(2):383-401; doi:10.1112/S0024610703004654
© 2003 by London Mathematical Society
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© The London Mathematical Society

On the Inverse Resonance Problem

B. M. Brown, I. Knowles and R. Weikard

Department of Computer Science, University of Wales Cardiff CF2 3XF, malcolm.brown{at}cs.cf.ac.uk
Department of Mathematics, University of Alabama Birmingham, AL 35294-1170, USA, iwk{at}math.uab.edu
Department of Mathematics, University of Alabama Birmingham, AL 35294-1170, USA, rudi{at}math.uab.edu

Received 7 May 2002. Revision received 17 December 2002.

A new technique is presented which gives conditions under which perturbations of certain base potentials are uniquely determined from the location of eigenvalues and resonances in the context of a Schrödinger operator on a half line. The method extends to complex-valued potentials and certain potentials whose first moment is not integrable.


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