Real Analytic Version of Lévy’s Theorem

Autores/as

  • A. El Kinani Université Mohammed V, Ecole Normale Supérieure de Rabat, B.P. 5118, 10105 Rabat (Morocco)
  • L. Bouchikhi Université Mohammed V, Ecole Normale Supérieure de Rabat, B.P. 5118, 10105 Rabat (Morocco)

DOI:

https://doi.org/10.17398/

Palabras clave:

Fourier series, Lévy’s theorem, weight function, weihgted algebra, commutative Banach algebra, Hermitian Banach algebra, Gelfand space, functional calculus, real analytic function, harmonic function

Resumen

We obtain real analytic version of the classical theorem of Lévy on absolutely convergent power series. Whence, as a consequence, its harmonic version.

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Referencias

M. Akkar, A. El Kinani, M. Oudadess, Calculus fonctionnels harmonique et analytique réel, Ann. Sci. Math. Québec 12 (2) (1988), 151 – 169.

S.J. Bhatt, H.V. Dedania, Beurling algebra analogues of the classical theorems of Wiener and Lévy on absolutely convergent Fourier series, Proc. Indian Acad. Sci. Math. Sci. 113 (2) (2003), 179 – 182.

A. El Kinani, A version of Wiener’s and Lévy’s theorems, Rend. Circ. Mat. Palermo (2) 57 (3) (2008), 343 – 352.

A. El Kinani, L. Bouchikhi, A weighted algebra analogues of Wiener’s and Lévy’s theorems, Rend. Circ. Mat. Palermo (2) 61 (3) (2012), 331 – 341.

A. El Kinani, L. Bouchikhi, Wiener’s and Levy’s theorems for some weighted power series, Rend. Circ. Mat. Palermo (to appear).

I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] 9(51) (1941), 3 – 24.

P. Lévy, Sur la convergence absolue des séries de Fourier, Compositio Math. 1 (1935), 1 – 14.

S. Mazur, Sur les anneaux linéaires, C. R. Acad. Sci. Paris 207 (1938), 1025 – 1027.

V. Ptàk, Banach algebras with involution, Manuscripta Math. 6 (1972), 245 – 290.

N. Wiener, Tauberian theorems, Ann. of Math. (2) 33 (1) (1932), 1 – 100.

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Publicado

2015-12-01

Número

Sección

Banach Spaces

Cómo citar

Real Analytic Version of Lévy’s Theorem. (2015). Extracta Mathematicae, 30(2), 153-159. https://doi.org/10.17398/