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
Recommended Citation
Vindas, J., & Estrada, R. (2008). A tauberian theorem for distributional point values. Archiv der Mathematik, 91 (3), 247-253. https://doi.org/10.1007/s00013-008-2683-z
COinS