The spectral problem for a class of highly oscillatory Fredholm integral operators
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Bibliographic record
Abstract
Let be a linear, complex-symmetric Fredholm integral operator with highly oscillatory kernel K0(x, y)eiω|x–y|. We study the spectral problem for large ω, showing that the spectrum consists of infinitely many discrete (complex) eigenvalues and give a precise description of the way in which they converge to the origin. In addition, we investigate the asymptotic properties of the solutions f = f(x;ω) to the associated Fredholm integral equation f = μf + a as ω→∞, thus refining a classical result by Ursell. Possible extensions of these results to highly oscillatory Fredholm integral operators with more general highly oscillating kernels are also discussed.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
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| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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