Weighted exponential approximation and non-classical orthogonal spectral measures - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Advances in Mathematics Année : 2011

Weighted exponential approximation and non-classical orthogonal spectral measures

Résumé

A long-standing open problem in harmonic analysis is: given a non-negative measure μ on ℝ, find the infimal width of frequencies needed to approximate any function in L2(μ). We consider this problem in the "perturbative regime", and characterize asymptotic smallness of perturbations of measures which do not change that infimal width. Then we apply this result to show that there are no local restrictions on the structure of orthogonal spectral measures of one-dimensional Schrodinger operators on a finite interval. This answers a question raised by V.A.Marchenko.

Dates et versions

hal-01257806 , version 1 (18-01-2016)

Identifiants

Citer

Alexander Borichev, Mikhail Sodin. Weighted exponential approximation and non-classical orthogonal spectral measures. Advances in Mathematics, 2011, 226 (3), ⟨10.1016/j.aim.2010.08.019⟩. ⟨hal-01257806⟩
57 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More