On an Application of the Lax-Phillips Scattering Approach in the Theory of Singular Perturbations
For a singular perturbation $A = A_0 + \sum^n_{i, j=1}t_{ij} \langle \psi_j, \cdot \rangle \psi_i,\quad n \leq \infty$ of a positive self-adjoint operator $A_0$ with Lebesgue spectrum, the spectral analysis of the corresponding self-adjoint operator realizations $A_T$ is carried out and the scatteri...
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| Datum: | 2005 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2005
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3634 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | For a singular perturbation $A = A_0 + \sum^n_{i, j=1}t_{ij} \langle \psi_j, \cdot \rangle \psi_i,\quad n \leq \infty$ of a positive self-adjoint operator $A_0$
with Lebesgue spectrum, the spectral analysis of the corresponding self-adjoint operator realizations $A_T$ is carried out and the scattering matrix $\mathfrak{S}_{(A_T, A_0)}(\delta)$ is calculated in terms of parameters $t_{ij}$ under some additional restrictions on singular elements $\psi_{j}$ that provides the possibility of application of the Lax -Phillips approach in the scattering theory. |
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