06-342 Sergei Avdonin, Victor Mikhaylov and Alexei Rybkin

The boundary control approach to the Titchmarsh-Weyl $m-$function. I. The response operator and the $A-$amplitude (317K, pdf) Nov 23, 06

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Abstract. We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the $A-$amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl $m-$function associated with the Schr\"{o}dinger operator $H=-\partial _{x}^{2}+q\left( x\right) $ on $L_{2}\left( 0,\infty \right) $ with Dirichlet boundary condition at $x=0.$

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