A Characterization and a Class of Distribution Functions for the Stieltjes-Wigert Polynomials

1970 ◽  
Vol 13 (4) ◽  
pp. 529-532 ◽  
Author(s):  
T. S. Chihara
Keyword(s):  
Orthogonal Polynomials ◽  
Moment Problem ◽  
Recurrence Formula ◽  
Distribution Functions ◽  
Moment Sequence ◽  
The Moment ◽  
Image Position ◽  
Stieltjes Moment Sequence

In his classic memoir on the moment problem that bears his name, Stieltjes [2] exhibited1as an example of an indeterminate (Stieltjes) moment sequence.Stieltjes also obtained the corresponding S-fraction and thus implicitly obtained the three-term recurrence formula satisfied by the corresponding orthogonal polynomials.

scholarly journals Uniqueness criterion for a moment problem

1974 ◽  
Vol 18 (3) ◽  
pp. 303-305 ◽  
Author(s):  
A. Lenard
Keyword(s):  
Explicit Formula ◽  
Moment Problem ◽  
Uniqueness Criterion ◽  
The Moment ◽  
Image Position

In an article that appeared some years ago in this journal, Takács [1] gave a uniqueness criterion for the solution of the moment problem where the Br are given numbers and the Pk are sought, Pk ≧ 0, σkPk = 1. Takács showed that if Br < ∞ for all r and then the solution is unique. In addition, he gave an explicit formula for the solution in this case where q is any number satisfying q ≧ 0 and q > p2 — 1.

scholarly journals Unique solvability of the strong Hamburger moment problem

1986 ◽  
Vol 40 (1) ◽  
pp. 5-19 ◽  
Author(s):  
Olav Njåstad ◽  
W. J. Thron
Keyword(s):  
Distribution Function ◽  
Orthogonal Polynomials ◽  
Unique Solution ◽  
Unique Solvability ◽  
Moment Problem ◽  
Limit Point ◽  
Double Sequence ◽  
Hamburger Moment Problem ◽  
Limit Point Case ◽  
The Moment

AbstractMethods from the theory of orthogonal polynomials are extended to L-polynomials . By this means the authors and W. B. Jones (J. Math. Anal. Appl. 98 (1984), 528–554) solved the strong Hamburger moment problem, that is, given a double sequence , to find a distribution function ψ(t), non-decreasing, with an infinitenumber of points of increase and bounded on −∞ < t < ∞, such that for all integers . In this article further menthods such as analogues of the Lioville-Ostrogradski formula and of the Christoffel-Darboux formula are developed to investigated When the moment porblem has a unique solution. This will be the case if and only if a sequence of nested disks associated with the sequence has only a point as its intersection (the so called limit point case).

scholarly journals AVERAGING OF AN INCREASING NUMBER OF MOMENT CONDITION ESTIMATORS

2014 ◽  
Vol 32 (1) ◽  
pp. 30-70 ◽  
Author(s):  
Xiaohong Chen ◽  
David T. Jacho-Chávez ◽  
Oliver Linton
Keyword(s):  
Moment Condition ◽  
Moment Conditions ◽  
Parameter Heterogeneity ◽  
Class Of Estimators ◽  
Optimal Weighting ◽  
The Mean ◽  
The Moment ◽  
Image Position ◽  
Nonlinear Estimators ◽  
Available Information

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of$\sqrt n$-consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.

The moment problem on perfect hypergroups

2016 ◽  
Vol 29 (2) ◽  
pp. 232-236
Author(s):  
A. S. Okb El Bab ◽  
Hossam A. Ghany
Keyword(s):  
Moment Problem ◽  
The Moment

scholarly journals Applied Optimization and Approximation

2014 ◽  
Vol 3 (4) ◽  
pp. 37-48
Author(s):  
Octav Olteanu
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Linear Function ◽  
Polynomial Approximation ◽  
Moment Problem ◽  
Quadratic Forms ◽  
Two Dimensional ◽  
Several Variables ◽  
Applied Optimization ◽  
The Moment

The present work deals with optimization in kinematics, generalizing previous results of the author. A second theme is maximizing the constrained gain linear function and minimizing the constrained cost function. Elementary notions of optimal control are considered as well. Finally, polynomial approximation results on unbounded subsets in several variables are applied to the moment problem. The existence of the solution of a two dimensional moment problem is characterized in terms of quadratic forms.

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