Esterlè's proof of the tauberian theorem for Beurling algebras

H. G. Dales; W. K. Hayman

Displaying similar documents to “Esterlè's proof of the tauberian theorem for Beurling algebras”

A complex-variable proof of the Wiener tauberian theorem

Jean Esterlé (1980)

Annales de l'institut Fourier

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The fundamental semigroup $(a^{t})_{t > 0}$ of the heat equation for the real line has an analytic extension $(a^{t})_{Re t > 0}$ to the right-hand open half plane which satisfies $∥ a^{t} ∥ \leq \sqrt{| t |}$ for Re $t \geq 1$ . Using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane we show that the Wiener tauberian theorem for $L^{1} (R)$ follows from the above inequality.

Tauberian theorems for vector-valued Fourier and Laplace transforms

Ralph Chill (1998)

Studia Mathematica

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Let X be a Banach space and $f \in L_{l}^{1} o c (ℝ; X)$ be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.

Homogeneous algebras on the circle. I. Ideals of analytic functions

Colin Bennett, John E. Gilbert (1972)

Annales de l'institut Fourier

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Let $𝒜$ be a homogeneous algebra on the circle and $𝒜^{+}$ the closed subalgebra of $𝒜$ of functions having analytic extensions into the unit disk $D$ . This paper considers the structure of closed ideals of $𝒜^{+}$ under suitable restrictions on the synthesis properties of $𝒜$ . In particular, completely characterized are the closed ideals in $𝒜^{+}$ whose zero sets meet the circle in a countable set of points. These results contain some previous results of Kahane and Taylor-Williams obtained independently. ...

Asymptotic values and the growth of analytic functions in spiral domains.

James E. Brennan, Alexander L. Volberg (1993)

Publicacions Matemàtiques

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In this note we present a simple proof of a theorem of Hornblower which characterizes those functions analytic in the open unit disk having asymptotic values at a dense set in the boundary. Our method is based on a kind of ∂-mollification and may be of use in other problems as well.

On the growth of analytic semigroups along vertical lines

José Galé, Thomas Ransford (2000)

Studia Mathematica

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We construct two Banach algebras, one which contains analytic semigroups ${(a^{z})}_{R e z > 0}$ such that $| a^{1 + i y} | \to \infty$ arbitrarily slowly as $| y | \to \infty$ , the other which contains ones such that $| a^{1 + i y} | \to \infty$ arbitrarily fast

A failure of quantifier elimination.

Angus Macintyre, David Marker (1997)

Revista Matemática de la Universidad Complutense de Madrid

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We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.

On ideals generated by bounded analytic functions in the bidisc

Urban Cegrell (1993)

Bulletin de la Société Mathématique de France

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A value-distribution criterion for the class $L \log L$ and some related questions

M. Essen, D. F. Shea, C. S. Stanton (1985)

Annales de l'institut Fourier

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We give a necessary and sufficient condition for an analytic function in $H^{1}$ to have real part in class $L$ $log L$ . This condition contains the classical one of Zygmund; other variants are also given.