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Beurling algebra

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In mathematics, the term Beurling algebra is used for different algebras introduced by Arne Beurling (1949), usually it is an algebra of periodic functions with Fourier series

Example We may consider the algebra of those functions f where the majorants

of the Fourier coefficients an are summable. In other words

Example We may consider a weight function w on such that

in which case is a unitary commutative Banach algebra.

These algebras are closely related to the Wiener algebra.

References

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  • Belinsky, E.S.; Liflyand, E.R. (2001) [1994], "Beurling algebra", Encyclopedia of Mathematics, EMS Press
  • Beurling, Arne (1949), "On the spectral synthesis of bounded functions", Acta Math., 81 (1): 225–238, doi:10.1007/BF02395018, MR 0027891