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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2506.18914 |
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| _version_ | 1866918068903477248 |
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| author | Alexa, Anton |
| author_facet | Alexa, Anton |
| contents | We define a second-order differential operator $\hat{C}$ on the Hilbert space $L^2([-v_c, v_c])$, constructed from a smooth deformation function $C(v)$. The operator is considered on the Sobolev domain $H^2([-v_c, v_c]) \cap H^1_0([-v_c, v_c])$ with Dirichlet boundary conditions. We prove that $\hat{C}$ is essentially self-adjoint by verifying its symmetry and computing von Neumann deficiency indices, which vanish. All steps are carried out explicitly. This result ensures the mathematical consistency of the operator and enables future spectral analysis on compact intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18914 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Essential Self-Adjointness of the Geometric Deformation Operator on a Compact Interval Alexa, Anton Spectral Theory Functional Analysis 47A10, 47B25, 47E05, 58J50 We define a second-order differential operator $\hat{C}$ on the Hilbert space $L^2([-v_c, v_c])$, constructed from a smooth deformation function $C(v)$. The operator is considered on the Sobolev domain $H^2([-v_c, v_c]) \cap H^1_0([-v_c, v_c])$ with Dirichlet boundary conditions. We prove that $\hat{C}$ is essentially self-adjoint by verifying its symmetry and computing von Neumann deficiency indices, which vanish. All steps are carried out explicitly. This result ensures the mathematical consistency of the operator and enables future spectral analysis on compact intervals. |
| title | Essential Self-Adjointness of the Geometric Deformation Operator on a Compact Interval |
| topic | Spectral Theory Functional Analysis 47A10, 47B25, 47E05, 58J50 |
| url | https://arxiv.org/abs/2506.18914 |