Nous considérons un problème spectral inverse pour des équations de Sturm–Liouville sur l'intervalle unité avec une singularité explicite , . Un tel problème survient après décomposition de l'opérateur de Schrödinger à potentiel radial agissant sur la boule unité de . Notre but est la paramétrisation globale des potentiels par des données spectrales, notées et des constantes de normalisation, notées . Pour et 1, il est déjà connu que forme un système de coordonnées globales sur . Nous étendons cela à tout entier positif a. Un résultat similaire est obtenu pour un opérateur de type AKNS singulier.
We consider an inverse spectral problem for singular Sturm–Liouville equations on the unit interval with explicit singularity , . This problem arises by splitting of the Schrödinger operator with radial potential acting on the unit ball of . Our goal is the global parametrization of potentials by spectral data noted by , and some norming constants noted by . For and 1, was already known to be a global coordinate system on . We extend this to any non-negative integer a. Similar result is obtained for singular AKNS operator.
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@article{CRMATH_2005__340_9_671_0, author = {Serier, Fr\'ed\'eric}, title = {Inverse spectral problem for singular {AKNS} and {Schr\"odinger} operators on $ [0,1]$}, journal = {Comptes Rendus. Math\'ematique}, pages = {671--676}, publisher = {Elsevier}, volume = {340}, number = {9}, year = {2005}, doi = {10.1016/j.crma.2005.03.025}, language = {en}, url = {http://www.numdam.org./articles/10.1016/j.crma.2005.03.025/} }
TY - JOUR AU - Serier, Frédéric TI - Inverse spectral problem for singular AKNS and Schrödinger operators on $ [0,1]$ JO - Comptes Rendus. Mathématique PY - 2005 SP - 671 EP - 676 VL - 340 IS - 9 PB - Elsevier UR - http://www.numdam.org./articles/10.1016/j.crma.2005.03.025/ DO - 10.1016/j.crma.2005.03.025 LA - en ID - CRMATH_2005__340_9_671_0 ER -
%0 Journal Article %A Serier, Frédéric %T Inverse spectral problem for singular AKNS and Schrödinger operators on $ [0,1]$ %J Comptes Rendus. Mathématique %D 2005 %P 671-676 %V 340 %N 9 %I Elsevier %U http://www.numdam.org./articles/10.1016/j.crma.2005.03.025/ %R 10.1016/j.crma.2005.03.025 %G en %F CRMATH_2005__340_9_671_0
Serier, Frédéric. Inverse spectral problem for singular AKNS and Schrödinger operators on $ [0,1]$. Comptes Rendus. Mathématique, Tome 340 (2005) no. 9, pp. 671-676. doi : 10.1016/j.crma.2005.03.025. http://www.numdam.org./articles/10.1016/j.crma.2005.03.025/
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