Beurling algebra

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In mathematics, a Beurling algebra, introduced by Arne Beurling (1949), is the algebra of periodic functions with Fourier series

$f(x)=\sum a_ne^{inx}$

such that the majorants

$c_k=\sup_{|n|\ge k} a_n$

of the Fourier coefficients a_n are summable. In other words

$\sum_{k\ge 0} c_k<\infty.$

It is closely related to the Wiener algebra.

[edit] References

Belinsky, E.S. & Liflyand, E.R. (2001), “Beurling algebra”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104
Beurling, Arne (1949), “On the spectral synthesis of bounded functions”, Acta Math. 81: 225–238, MR 0027891, DOI 10.1007/BF02395018

Categories: Fourier series

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