no. 2
Resolvent expansions and continuity of the scattering matrix at embedded thresholds: the case of quantum waveguides
[Expansions de résolventes et continuité de la matrice de diffusion aux seuils immergés: le cas des guides d'onde quantiques]
Bulletin de la Société Mathématique de France, Tome 144 (2016) no. 2, pp. 251-277

We present an inversion formula which can be used to obtain resolvent expansions near embedded thresholds. As an application, we prove for a class of quantum waveguides the absence of accumulation of eigenvalues and the continuity of the scattering matrix at all thresholds.

Nous présentons une formule d'inversion qui peut être utilisée pour obtenir des expansions de résolventes à proximité de seuils immergés. Comme application, nous démontrons pour une classe de guides d'onde quantiques l'absence d'accumulation de valeurs propres et la continuité de la matrice de diffusion en chaque seuil.

Publié le :
DOI : 10.24033/bsmf.2713
Classification : 47A10, 81U35, 35J10
Keywords: Thresholds, resolvent expansions, scattering matrix, quantum waveguides.
Mots-clés : Seuils, expansions de résolventes, matrice de diffusion, guides d'onde quantiques. 
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     author = {Richard, S. and de Aldecoa, R. Tiedra},
     title = {Resolvent expansions and continuity of the scattering matrix at embedded thresholds: the case of quantum waveguides},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {251--277},
     year = {2016},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {144},
     number = {2},
     doi = {10.24033/bsmf.2713},
     mrnumber = {3499081},
     zbl = {1372.47004},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/bsmf.2713/}
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Richard, S.; de Aldecoa, R. Tiedra. Resolvent expansions and continuity of the scattering matrix at embedded thresholds: the case of quantum waveguides. Bulletin de la Société Mathématique de France, Tome 144 (2016) no. 2, pp. 251-277. doi: 10.24033/bsmf.2713

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