The boundary control approach to the Titchmarsh-Weyl $m-$function
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913865902587904 |
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| author | Avdonin, S. A. Mikhaylov, V. S. Rybkin, A. V. |
| author_facet | Avdonin, S. A. Mikhaylov, V. S. Rybkin, A. V. |
| contents | 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 Schrödinger operator $H=-\partial _{x}^{2}+q\left( x\right) $ on $L_{2}\left( 0,\infty \right) $ with Dirichlet boundary condition at $x=0.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23332 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The boundary control approach to the Titchmarsh-Weyl $m-$function Avdonin, S. A. Mikhaylov, V. S. Rybkin, A. V. Analysis of PDEs Spectral Theory 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 Schrödinger operator $H=-\partial _{x}^{2}+q\left( x\right) $ on $L_{2}\left( 0,\infty \right) $ with Dirichlet boundary condition at $x=0.$ |
| title | The boundary control approach to the Titchmarsh-Weyl $m-$function |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2505.23332 |