Algebrability of the set of non-convergent Fourier series

• Autorzy: Richard M. Aron , David Pérez-García , Juan B. Seoane-Sepúlveda
• Języki publikacji: EN

Abstrakty

EN

We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.

Kategorie tematyczne

• 42A20: Convergence and absolute convergence of Fourier and trigonometric series
• 46E25: Rings and algebras of continuous, differentiable or analytic functions
• 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 175
• Numer: 1
• Strony: 83-90

Daty

wydano

2006

Twórcy

autor

Richard M. Aron

• Department of Mathematics, Kent State University, Kent, OH 44242, U.S.A.

autor

David Pérez-García

• Departamento de Matemática Aplicada, E.S.C.E.T. - Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain

autor

Juan B. Seoane-Sepúlveda

• Department of Mathematics, Kent State University, Kent, OH 44242. U.S.A.

Identyfikatory

DOI

10.4064/sm175-1-5