We recall a uniqueness theorem of E. B. Vul pertaining to a version of the cosine transform originating in spectral theory. Then we point out an application to the Bernstein approximation problem with non-symmetric weights: a theorem of Volberg is proved by elementary means.
- Bernstein approximation problem
- Completeness of polynomials
- Cosine transform
- Non-symmetric weights
- Quasianalytic classes