1 research outputs found
Weighted exponential approximation and non-classical orthogonal spectral measures
A long-standing open problem in harmonic analysis is: given a non-negative
measure on , find the infimal width of frequencies needed to
approximate any function in . 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.Comment: footnote 4 is corrected; some changes are made in the proof of
Theorem 2.1