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A complex-variable proof of the Wiener tauberian theorem

Jean Esterlé — 1980

Annales de l'institut Fourier

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 | t | for Re t 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.

Sur quelques extensions au cadre banachique de la notion d'opérateur de Hilbert-Schmidt

Said Amana AbdillahJean EsterleBernhard H. Haak — 2015

Studia Mathematica

In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operator: p-summing operators, γ-summing or γ-radonifying operators, weakly* 1-nuclear operators and classes of operators defined via factorization properties. We introduce the class PS₂(E;F) of pre-Hilbert-Schmidt operators as the class of all operators u: E → F such that w ∘ u ∘ v is Hilbert-Schmidt for every bounded operator v: H₁ → E and every bounded operator w: F → H₂, where H₁ and...

Boundary values of analytic semigroups and associated norm estimates

Isabelle ChalendarJean EsterleJonathan R. Partington — 2010

Banach Center Publications

The theory of quasimultipliers in Banach algebras is developed in order to provide a mechanism for defining the boundary values of analytic semigroups on a sector in the complex plane. Then, some methods are presented for deriving lower estimates for operators defined in terms of quasinilpotent semigroups using techniques from the theory of complex analysis.

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