1. References

In mathematics, the term Beurling algebra is used for different algebras introduced by {{harvs|txt=yes|first=Arne|last=Beurling|authorlink=Arne Beurling|year=1949}}, usually it is an algebra of periodic functions with Fourier series

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

of the Fourier coefficients a_n are summable. In other words

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

• {{springer|id=B/b130120|first=E.S.|last= Belinsky|first2=E.R.|last2= Liflyand}}
• {{citation|mr=0027891|first=Arne |last=Beurling|title= On the spectral synthesis of bounded functions|journal= Acta Math. |volume= 81 |year=1949|issue=1|pages= 225–238

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