On generalized moment matrices

Zhang, Ruiming

doi:10.1090/S0002-9939-2013-11782-X

On generalized moment matrices
HTML articles powered by AMS MathViewer

by Ruiming Zhang PDF

Proc. Amer. Math. Soc. 141 (2013), 2589-2595 Request permission

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.

References

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, DOI 10.1017/CBO9781107325937
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, DOI 10.7146/math.scand.a-14379
Mourad E. H. Ismail, Continuous and Discrete Orthogonal Polynomials. Cambridge University Press, Cambridge, 2005.
Roelof Koekoek and René F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, http://fa.its.tudelft.nl/~koekoek/askey/.
Gábor Szegő, Orthogonal polynomials, 4th ed., American Mathematical Society Colloquium Publications, Vol. XXIII, American Mathematical Society, Providence, R.I., 1975. MR 0372517
Wikipedia, http://en.wikipedia.org/wiki/Hilbert_matrix.
James A. Wilson, Orthogonal functions from Gram determinants, SIAM J. Math. Anal. 22 (1991), no. 4, 1147–1155. MR 1112071, DOI 10.1137/0522074