On the stability in Ambarzumian theorems. (30th January 2015)

• Record Type: Journal Article
• Authors: Horváth, Miklós
• Is Part Of: Inverse problems. Volume 31:Number 2(2015:Feb.)
• Publication Date: 2015-01-30
• Subjects: inverse spectral problems -- Ambarzumian theorem -- spectral function asymptotics; Primary 35J25 -- Secondary 35J10 Key words and phrases: inverse eigenvalue problem -- stability; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/2/025008
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We provide extensions of the classical Ambarzumian theorem for bounded C 3 domains of any dimension. The simple proof is based on classical spectral function asymptotics. We prove a stability property by showing that if the perturbation of the eigenvalues of the zero potential is small in some sense then the L 2 -norm of the potential is also small. The problem is motivated by connections to a number of applications.