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.
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.
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Frédéric Serier 1
@article{CRMATH_2005__340_9_671_0, author = {Fr\'ed\'eric Serier}, 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}, }
Frédéric Serier. Inverse spectral problem for singular AKNS and Schrödinger operators on $ [0,1]$. Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 671-676. doi : 10.1016/j.crma.2005.03.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.03.025/
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