Karamata's theorem for regularized Cauchy transforms

Matthias Langer, Harald Woracek

Research output: Contribution to journalArticlepeer-review

9 Downloads (Pure)


We prove Abelian and Tauberian theorems for regularized Cauchy transforms of positive Borel measures on the real line whose distribution functions grow at most polynomially at infinity. In particular, we relate the asymptotics of the distribution functions to the asymptotics of the regularized Cauchy transform.

Original languageEnglish
Pages (from-to)1-61
Number of pages61
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Early online date26 Jan 2024
Publication statusE-pub ahead of print - 26 Jan 2024


  • regularised Cauchy transform
  • Tauberian theorem
  • Abelian theorem
  • regularly varying function
  • Grommer-Hamburger theorem


Dive into the research topics of 'Karamata's theorem for regularized Cauchy transforms'. Together they form a unique fingerprint.

Cite this