Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions
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- by Jim Agler and John E. McCarthy PDF
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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
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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
- MR Author ID: 271733
- ORCID: 0000-0003-0036-7606
- 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 - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 1379-1411
- MSC (2010): Primary 32A70, 46E22
- DOI: https://doi.org/10.1090/S0002-9947-2013-05952-1
- MathSciNet review: 3145735