# On a uniqueness theorem of E. B. Vul

## TL;DR

This paper revisits a uniqueness theorem related to the cosine transform in spectral theory and applies it to prove a Bernstein approximation theorem with non-symmetric weights using elementary methods.

## Contribution

It connects a classical uniqueness theorem to a new application in approximation theory, providing a simpler proof of Volberg's theorem.

## Key findings

- A new proof of Volberg's Bernstein approximation theorem.
- Extension of the uniqueness theorem to non-symmetric weights.
- Simplification of existing proofs using elementary methods.

## Abstract

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.