Geodesic
A resolvent approach in the Fourier method for the wave equation: The non-selfadjoint case
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 7, pp. 1156-1167 Cet article a éte moissonné depuis la source Math-Net.Ru

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Under minimum smoothness requirements for the initial data, the Fourier method in the mixed problem for the wave equation with a complex potential is justified by using the Cauchy–Poincare technique for the contour integration of the resolvent of the eigenvalue problem. Generic boundary conditions are used; one of them contains first-order derivatives, while the other does not. In this case, even for the benchmark situation, the operator in the eigenvalue problem can have any number of generalized eigenfunctions. A substantial use is made of the technique for accelerating Fourier series due to A. N. Krylov. 
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     title = {A resolvent approach in the {Fourier} method for the wave equation: {The~non-selfadjoint} case},
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V. V. Kornev; A. P. Khromov. A resolvent approach in the Fourier method for the wave equation: The non-selfadjoint case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 7, pp. 1156-1167. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_7_a5/

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