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| Main Author: | |
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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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Table of 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.