naa a22 4500 510811205 CHVBK 20180411083443.0 cr unu---uuuuu 180411e20131201xx s 000 0 eng 10.1134/S0081543813080130 doi (NATIONALLICENCE)springer-10.1134/S0081543813080130 Uniform stability of the inverse Sturm-Liouville problem with respect to the spectral function in the scale of Sobolev spaces [Elektronische Daten] [A. Savchuk, A. Shkalikov] We consider the inverse problem of recovering the potential for the Sturm-Liouville operator Ly = −y″ + q(x)y on the interval [0, π] from the spectrum of the Dirichlet problem and norming constants (from the spectral function). For a fixed θ ≥ 0, with this problem we associate a map F: W 2 θ → l D θ , F(σ) = {s k } 1 ∞ , where W 2 θ = W 2 θ [0, π] is the Sobolev space, σ = ∫ q is a primitive of the potential q ∈ W 2 θ − 1 , and l D θ is a specially constructed finite-dimensional extension of the weighted space l 2 θ ; this extension contains the regularized spectral data s = {s k } 1 ∞ for the problem of recovering the potential from the spectral function. The main result consists in proving both lower and upper uniform estimates for the norm of the difference ‖σ − σ 1‖ θ in terms of the l D θ norm of the difference of the regularized spectral data ‖s − s1‖ θ . The result is new even for the classical case q ∈ L 2, which corresponds to the case θ = 1. Pleiades Publishing, Ltd., 2013 Savchuk A. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut Shkalikov A. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 283/1(2013-12-01), 181-196 0081-5438 283:1<181 2013 283 11501 https://doi.org/10.1134/S0081543813080130 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813080130 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Savchuk A. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut NATIONALLICENCE 700 1- Shkalikov A. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 283/1(2013-12-01), 181-196 0081-5438 283:1<181 2013 283 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer