moment problem


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moment problem

[′mō·mənt ‚präb·ləm]
(statistics)
The problem of finding a distribution whose moments have specified values, or of determining whether such a distribution exists.
References in periodicals archive ?
Generally, this problem is distinguished between the three types for the monovariate case: the Hausdorff moment problem with the PSD supported on the closed interval [a, b], where [a, b] are the lower and upper limits of the domain of PSD; the Stieltjes moment problem with the PSD supported on [0, +[infinity]); and the Hamburger moment problem with the PSD supported on (-[infinity], +[infinity]) [8].
To state what the generalized moment problem is about, let ([OMEGA], F, P) be a probability space and let (S, B, m) be a measure space, with m a finite or sigma-finite measure.
Here is the setting of a reasonably general moment problem. Given moments [[mu].sub.1], ...
Among their topics are the moment problem, the Kato-Friedrichs operator, the integral operator of a moment matrix, and boundedness and spectral properties.
of Saskatchewan and elsewhere, this provides an elementary introduction and includes such subjects as the moment problem and applications to polynomial optimization.
[5] Jacob Stordal Christiansen, The moment problem associated with the q-Laguerre polynomials, Constr.
The text covers the Stieltjes integral, fundamental formulas, the moment problem, absolutely and completely monotonic functions, Tauberian theorems, the bilateral Laplace transform, inversion and representation problems for the Laplace transform, and the Stieltjes transform.
Lessons here include such topics as the matrix moment problem, Hausdorff and q-Hausdorff
, of orthogonal polynomials in one variable corresponds to the determinate or indeterminate moment problem. If a polynomial family corresponds to the determinate moment problem, then there exists only one positive orthogonality measure [mu] for these polynomials and they constitute a complete orthogonal set in the Hilbert space [L.sup.2] ([mu]).
Specific topics include Young-Fenchel transformation and some new characteristics of Banach spaces, an example of the boundary of topologically inverted elements, sums and products of bad functions, disc algebra and a moment problem, the stability of logmodularity for uniform algebras, regularity and amenability conditions for uniform algebras, closed suns of marginal subspaces of Banach function space, surjections on the algebras of continuous functions which preserve peripheral spectrum, asymptotics of Toeplitz determinants generated by functions with Fourier coefficients in weighted Orlicz sequence classes, spectral isometries, examples of Banach spaces that are not Banach algebras, and a spectra of algebras of analytic functions and polynomials on Banach space.
ATZMON, A moment problem for positive measures on the unit disc, Pacific J.