Title

A tauberian theorem for distributional point values

Document Type

Article

Publication Date

9-1-2008

Abstract

We give a tauberian theorem for boundary values of analytic functions. We prove that if f ∈ D′ (a, b) is the distributional limit of the analytic function F defined in a region of the form (a, b) × (0, R), if F (x 0 + iy)→ γ as y → 0+, and if f is distributionally bounded at x = x0, then f (x0) = γ distributionally. As a consequence of our tauberian theorem, we obtain a new proof of a tauberian theorem of Hardy and Littlewood. © 2008 Birkhaeuser.

Publication Source (Journal or Book title)

Archiv der Mathematik

First Page

247

Last Page

253

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