On the boundary control approach to inverse spectral and scattering theory for Schrödinger operators

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February 2009, 3(1): 139-149. doi: 10.3934/ipi.2009.3.139

On the boundary control approach to inverse spectral and scattering theory for Schrödinger operators

1.	Department of Math. and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99709, United States

Received April 2008 Revised January 2009 Published February 2009

Abstract
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We link boundary control theory and inverse spectral theory for the Schrödinger operator $H=-\partial _{x}^{2}+q( x) $ on $L^{2}( 0,\infty) $ with Dirichlet boundary condition at $x=0.$ This provides a shortcut to some results on inverse spectral theory due to Simon, Gesztesy-Simon and Remling. The approach also has a clear physical interpritation in terms of boundary control theory for the wave equation.

Keywords: Titchmarsh-Weyl $m$-function., boundary control, inverse spectral theory, Schrödinger operator.

Mathematics Subject Classification: Primary 34L25, 34L40, 35L20, 49N4.

Citation: Alexei Rybkin. On the boundary control approach to inverse spectral and scattering theory for Schrödinger operators. Inverse Problems & Imaging, 2009, 3 (1) : 139-149. doi: 10.3934/ipi.2009.3.139

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