On generalized moment matrices

Author:
Ruiming Zhang

Journal:
Proc. Amer. Math. Soc. **141** (2013), 2589-2595

MSC (2000):
Primary 15A09; Secondary 33D45

Published electronically:
April 8, 2013

MathSciNet review:
3056548

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Abstract | References | Similar Articles | Additional Information

Abstract: In this work we provide a method to compute the determinants and inverses of the generalized moment matrices. Using this method we also give lower bounds for the smallest eigenvalue of such matrices.

**1.**George E. Andrews, Richard Askey, and Ranjan Roy,*Special functions*, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, Cambridge, 1999. MR**1688958****2.**Christian Berg, Yang Chen, and Mourad E. H. Ismail,*Small eigenvalues of large Hankel matrices: the indeterminate case*, Math. Scand.**91**(2002), no. 1, 67–81. MR**1917682****3.**Mourad E. H. Ismail, Continuous and Discrete Orthogonal Polynomials. Cambridge University Press, Cambridge, 2005.**4.**Roelof Koekoek and René F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue,`http://fa.its.tudelft.nl/~koekoek/askey/`.**5.**Gábor Szegő,*Orthogonal polynomials*, 4th ed., American Mathematical Society, Providence, R.I., 1975. American Mathematical Society, Colloquium Publications, Vol. XXIII. MR**0372517****6.**Wikipedia, http://en.wikipedia.org/wiki/Hilbert_matrix.**7.**James A. Wilson,*Orthogonal functions from Gram determinants*, SIAM J. Math. Anal.**22**(1991), no. 4, 1147–1155. MR**1112071**, 10.1137/0522074

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Additional Information

**Ruiming Zhang**

Affiliation:
The Institute of Applied Mathematics, College of Science, Northwest A&F University, Yangling, Shaanxi 712100, People’s Republic of China

Email:
ruimingzhang@yahoo.com

DOI:
https://doi.org/10.1090/S0002-9939-2013-11782-X

Keywords:
Orthogonal polynomials,
generalized moment matrices,
determinants,
inverse matrices,
smallest eigenvalue

Received by editor(s):
October 28, 2011

Published electronically:
April 8, 2013

Additional Notes:
This work was partially supported by Northwest A&F University

Communicated by:
Sergei K. Suslov

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.