1-D Schrödinger operator on a star graph with nondefinite weight function
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911071646777344 |
|---|---|
| author | Leguizamón, Edison Trunk, Carsten Wilson, Mitsuru Winklmeier, Monika |
| author_facet | Leguizamón, Edison Trunk, Carsten Wilson, Mitsuru Winklmeier, Monika |
| contents | On a star graph $G$ with $n = n_+ + n_-$ edges of unit length, we study the operator $-\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_+$ and $\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_-$ edges equipped with Dirichlet boundary conditions at the outer vertices and a Kirchhoff condition at the central vertex. We study the spectral properties of the corresponding indefinite Kirchhoff Laplacian on $G$ and we show that it is similar to a selfadjoint operator in the Hilbert space $L^2(G)$ and that its eigenfunctions form a Riesz basis. Furthermore, we give a complete description of the point spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 1-D Schrödinger operator on a star graph with nondefinite weight function Leguizamón, Edison Trunk, Carsten Wilson, Mitsuru Winklmeier, Monika Spectral Theory 47A10, 47A75, 34B45 On a star graph $G$ with $n = n_+ + n_-$ edges of unit length, we study the operator $-\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_+$ and $\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_-$ edges equipped with Dirichlet boundary conditions at the outer vertices and a Kirchhoff condition at the central vertex. We study the spectral properties of the corresponding indefinite Kirchhoff Laplacian on $G$ and we show that it is similar to a selfadjoint operator in the Hilbert space $L^2(G)$ and that its eigenfunctions form a Riesz basis. Furthermore, we give a complete description of the point spectrum. |
| title | 1-D Schrödinger operator on a star graph with nondefinite weight function |
| topic | Spectral Theory 47A10, 47A75, 34B45 |
| url | https://arxiv.org/abs/2505.22901 |