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1. CJM 2006 (vol 58 pp. 249)
Convergence of Fourier--PadÃ© Approximants for Stieltjes Functions We prove convergence of diagonal multipoint Pad\'e approximants of
Stieltjes-type functions when a certain moment problem is
determinate. This is used for the study of the convergence of
Fourier--Pad\'e and nonlinear Fourier--Pad\'e approximants for such
type of functions.
Keywords:rational approximation, multipoint PadÃ© approximants, Fourier--PadÃ© approximants, moment problem Categories:41A20, 41A21, 44A60 |
2. CJM 2005 (vol 57 pp. 941)
Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers We introduce some non-linear transformations from the set of
Hausdorff moment sequences into itself; among
them is the one defined by
the formula:
$T((a_n)_n)=1/(a_0+\dots +a_n)$. We give some examples of
Hausdorff moment sequences arising from the transformations and
provide the corresponding measures: one of these sequences is the
reciprocal of the harmonic numbers $(1+1/2+\dots +1/(n+1))^{-1}$.
Categories:44A60, 40B05 |
3. CJM 1997 (vol 49 pp. 708)
Density questions for the truncated matrix moment problem For a truncated matrix moment problem, we describe in detail
the set of positive definite matrices of measures $\mu$ in $V_{2n}$ (this is
the set of solutions of the problem of degree $2n$) for which the polynomials
up to degree $n$ are dense in the corresponding space ${\cal L}^2(\mu)$.
These matrices of measures are exactly the extremal measures of the set $V_n$.
Categories:42C05, 44A60 |