On resonances generated by conic diffraction
Annales de l'Institut Fourier, Volume 70 (2020) no. 4, pp. 1715-1752.

We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenly spaced along a curve of the form

λ logλ=-ν;

here ν=(n-1)/2L 0 where n is the dimension and L 0 is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve

λ logλ=-Λ

for a fixed Λ>ν.

On décrit les résonances les plus proches de l’axe réel qui sont créées, sur une variété à bouts euclidiens, par diffraction sur des singularités coniques. Ces résonances sont, asymptotiquement, régulièrement distribuées le long d’une courbe logarithmique. On montre ensuite que, sous cette courbe, il y a une région logarithmique qui ne contient aucune autre résonance de la forme

λ logλ=-ν;

ici ; ν=(n-1)/2L 0 n est la dimension et L 0 la longueur de la plus longue géodésique reliant deux points coniques.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3355
Classification: 58J50,  58J47,  78A45
Keywords: Diffraction, conic singularities, wave propagation, scattering, resonances.
Hillairet, Luc 1; Wunsch, Jared 2

1 Institut Denis Poisson CNRS-Université d’Orléans rue de Chartres BP 6759, 45067 Orléans cedex 2 (France)
2 Department of Mathematics Northwestern University 2033 Sheridan Road Evanston IL 60208-2730 (USA)
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Hillairet, Luc; Wunsch, Jared. On resonances generated by conic diffraction. Annales de l'Institut Fourier, Volume 70 (2020) no. 4, pp. 1715-1752. doi : 10.5802/aif.3355. https://aif.centre-mersenne.org/articles/10.5802/aif.3355/

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