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arXiv · 2505.23332

The boundary control approach to the Titchmarsh-Weyl $m-$function

S. A. Avdonin·V. S. Mikhaylov·A. V. Rybkin
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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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S. A. Avdonin, V. S. Mikhaylov, A. V. Rybkin. 2025-05-29. The boundary control approach to the Titchmarsh-Weyl $m-$function. https://doi.org/10.1007/s00220-007-0315-2

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