Analytic Continuations of Fourier and Stieltjes Transforms and Generalized Moments of Probability Measures

Takahiro Hasebe ()
Additional contact information
Takahiro Hasebe: Kyoto University

Journal of Theoretical Probability, 2012, vol. 25, issue 3, 756-770

Abstract: Abstract We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two ways to generalize moments accordingly to Fourier and Stieltjes transforms; however these two turn out to coincide. As applications, we give short proofs of the convergence of probability measures to Cauchy distributions with respect to tensor, free, Boolean and monotone convolutions.

Keywords: Fourier transform; Stieltjes transform; Cauchy distribution; Non-commutative probability theory; Paley–Wiener theorem; 60B10; 30D20; 46L53; 46L54 (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-011-0344-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:25:y:2012:i:3:d:10.1007_s10959-011-0344-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-011-0344-9

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().