An inverse problem for weighted Paley–Wiener spaces *The work is supported by Russian Science Foundation Grant 14-21-00035 (theorem 1) and by Russian Science Foundation Grant 14-41-00010 (theorem 2). (21st September 2016)

• Record Type: Journal Article
• Authors: Bessonov, R V; Romanov, R V
• Is Part Of: Inverse problems. Volume 32:Number 11(2016:Nov.)
• Publication Date: 2016-09-21
• Subjects: canonical Hamiltonian system -- Dirac system -- inverse problem -- de Branges space -- truncated toeplitz operator; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/11/115007
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Let μ be a measure on the real line R such that ∫ R d μ ( t ) 1 + t 2 < ∞ and let a > 0 . Assume that the norms ∥ f ∥ L 2 ( R ) and ∥ f ∥ L 2 ( μ ) are comparable for functions f in the Paley–Wiener space PW a and that PW a is dense in L 2 ( μ ) . We reconstruct the canonical Hamiltonian system JX ′ = z  X such that μ is the spectral measure for this system.