Sobolev mapping properties of the scattering transform for the Schr\'odinger equation

Autor:	Hryniv, Rostyslav O., Mykytyuk, Yaroslav V., Perry, Peter A.
Rok vydání:	2010
Předmět:	Mathematical Physics 34L25 (Primary) 34L40 47L10 81U40 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We consider the scattering transform for the Schr\"odinger equation with a singular potential and no bound states. Using the Riccati representation for real-valued potentials on the line, we obtain invertibility and Lipschitz continuity of the scattering transform between weighted and Sobolev spaces. Our approach exploits the connection between scattering theory for the Schr\"odinger equation and scattering theory for the ZS-AKNS system Comment: 15 pages, uses "conm-p-l.cls" class file
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1002.0540 Zobrazit plný text záznamu View this record from Arxiv