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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.00284 |
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| _version_ | 1866909729893122048 |
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| author | Makino, Tetu |
| author_facet | Makino, Tetu |
| contents | The generator $\mathbf{L}$ of the linearized evolution equation of adiabatic oscillations of a gaseous star, ELASO, is a second order integro-differential operator and is realized as a self-adjoint operator in the Hilbert space of square integrable unknown functions with weight, which is the density distribution of the compactly supported background. Eigenvalues and eigenfunctions of the operator $\mathbf{L}$ have been investigated in practical point of view of eigenmode expansion of oscillations. But it should be examined whether continuous spectra are absent in the spectrum of $\mathbf{L}$ or not. In order to discuss this question, the existence of essential spectra in a closely related evolution problem is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the essential spectrum of adiabatic stellar oscillations Makino, Tetu Analysis of PDEs The generator $\mathbf{L}$ of the linearized evolution equation of adiabatic oscillations of a gaseous star, ELASO, is a second order integro-differential operator and is realized as a self-adjoint operator in the Hilbert space of square integrable unknown functions with weight, which is the density distribution of the compactly supported background. Eigenvalues and eigenfunctions of the operator $\mathbf{L}$ have been investigated in practical point of view of eigenmode expansion of oscillations. But it should be examined whether continuous spectra are absent in the spectrum of $\mathbf{L}$ or not. In order to discuss this question, the existence of essential spectra in a closely related evolution problem is established. |
| title | On the essential spectrum of adiabatic stellar oscillations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.00284 |