Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions


Authors: Jim Agler and John E. McCarthy
Journal: Trans. Amer. Math. Soc. 366 (2014), 1379-1411
MSC (2010): Primary 32A70, 46E22
Published electronically: September 19, 2013
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A Pick function of $ d$ variables is a holomorphic map from $ \Pi ^d$ to $ \Pi $, where $ \Pi $ is the upper halfplane. Some Pick functions of one variable have an asymptotic expansion at infinity, a power series $ \sum _{n=1}^\infty \rho _n z^{-n}$ with real numbers $ \rho _n$ that gives an asymptotic expansion on non-tangential approach regions to infinity. In 1921 H. Hamburger characterized which sequences $ \{ \rho _n\} $ can occur. We give an extension of Hamburger's results to Pick functions of two variables.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 32A70, 46E22

Retrieve articles in all journals with MSC (2010): 32A70, 46E22


Additional Information

Jim Agler
Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093

John E. McCarthy
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05952-1
PII: S 0002-9947(2013)05952-1
Received by editor(s): January 17, 2012
Published electronically: September 19, 2013
Additional Notes: The first author was partially supported by National Science Foundation Grants DMS 0801259 and DMS 1068830
The second author was partially supported by National Science Foundation Grants DMS 0966845 and DMS 1300280
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.