Positivity 5: 51–63, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands. Limit Behaviour of Convolution Products of Probability Measures 1 2 WOLFHARD HANSEN and IVAN NETUKA Universität Bielefeld, Fakultät für Mathematik, Postfach 100 131, 33501 Bielefeld, Germany. E-mail: firstname.lastname@example.org. Mathematical Institute, Charles University, Sokolovská 83, 186 75 Praha, Czech Republic. E-mail: email@example.com. ( Corresponding author) (Received 18 May 1999; accepted 7 November 1999) AMS subject classiﬁcations: 60B10; 28A33 Key words: Convergence of probability measures, convolution 1. Introduction For r> 0let m denote normalized Lebesgue measure on the ball B.0;r/ with centre at the origin and radius r . The following question asked by Choquet (see , p. 478) on the occasion of the International Conference on Potential Theory (1994, Kouty, Czech Republic) was the starting point of our investigations of the limit behaviour of successive convolutions of probability measures: Let f be a con- tinuous real function on R and let r ;r ;r ;::: be strictly positive real numbers. 1 2 3 Under what conditions on f and the sequence .r / does .f m m m / n r r r 1 2 n converge to a harmonic function? An answer to this question
Positivity – Springer Journals
Published: Oct 3, 2004
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
All the latest content is available, no embargo periods.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud