# The spectral problem for a class of highly oscillatory Fredholm integral operators

@article{Brunner2010TheSP, title={The spectral problem for a class of highly oscillatory Fredholm integral operators}, author={Hermann Brunner and Arieh Iserles and Syvert P. N{\o}rsett}, journal={Ima Journal of Numerical Analysis}, year={2010}, volume={30}, pages={108-130} }

Let ℱ ω be a linear, complex-symmetric Fredholm integral operator with highly oscillatory kernel K o (x, y)e iω|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 ω f + a as ω → ∞, thus refining a…

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