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).

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.

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.

Solutions of the Al-Salam–Chihara and allied moment problems

2019 ◽  
Vol 18 (02) ◽  
pp. 185-210 ◽  
Author(s):  
Mourad E. H. Ismail
Keyword(s):  
Moment Problem ◽  
Sufficient Conditions ◽  
Infinite Family ◽  
Weight Functions ◽  
Moment Problems ◽  
Order Operator ◽  
Absolutely Continuous ◽  
Rodrigues Formula ◽  
Wilson Operator ◽  
The Moment

We study the moment problem associated with the Al-Salam–Chihara polynomials in some detail providing raising (creation) and lowering (annihilation) operators, Rodrigues formula, and a second-order operator equation involving the Askey–Wilson operator. A new infinite family of weight functions is also given. Sufficient conditions for functions to be weight functions for the [Formula: see text]-Hermite, [Formula: see text]-Laguerre and Stieltjes–Wigert polynomials are established and used to give new infinite families of absolutely continuous orthogonality measures for each of these polynomials.

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