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## Absolutely Convergent Fourier Series. An Improvement of the Beurling-Helson Theorem

Functional Analysis and Its Applications. 2012. Vol. 46. No. 2. P. 121-132.

We obtain a partial solution of the problem on the growth of the norms of exponential functions with a continuous phase in the Wiener algebra. The problem was posed by J.-P. Kahane at the International Congress of Mathematicians in Stockholm in 1962. He conjectured that (for a nonlinear phase) one can not achieve the growth slower than the logarithm of the frequency. Though the conjecture is still not confirmed, the author obtained first nontrivial results.