A Laplace transform of irregular growth

Jan Wiegerinck

A Laplace transform of irregular growth

Complex Variables 2026-04-15 v3

Authors: Jan Wiegerinck

Abstract

We give an example of a Laplace transform $\int_\gamma e^{\zeta z} d\mu(\zeta)$ that does not have regular growth. This answers a question in Hayman's List

Keywords

Laplace transform irregular growth complex analysis entire function growth order

Cite

@article{arxiv.2511.00275,
  title  = {A Laplace transform of irregular growth},
  author = {Jan Wiegerinck},
  journal= {arXiv preprint arXiv:2511.00275},
  year   = {2026}
}

Comments

5 pages. Section 2 was expanded to improve readability and some inaccuracies have been corrected. The proof in Section 3 has been expanded a bit In the final version only the introduction has been changed slightly

A Laplace transform of irregular growth

Abstract

Keywords

Cite

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