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

Alexei Rybkin

doi:10.3934/ipi.2009.3.139

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2009, Volume 3, Issue 1: 139-149. Doi: 10.3934/ipi.2009.3.139

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

Alexei Rybkin^1,

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

Received: April 2008

Revised: January 2009

Published: February 2009

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Abstract

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.

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Mathematics Subject Classification: Primary 34L25, 34L40, 35L20, 49N45.

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