The Moment Problem on Compact Semi-Algebraic Sets

2017 ◽  
pp. 283-313
Author(s):  
Konrad Schmüdgen
Keyword(s):  
Moment Problem ◽  
Algebraic Sets ◽  
The Moment

scholarly journals The moment problem on curves with bumps

2020 ◽  
Author(s):  
David P. Kimsey ◽  
Mihai Putinar
Keyword(s):  
Moment Problem ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Infinite Matrix ◽  
Power Moment ◽  
Closed Set ◽  
Algebraic Sets ◽  
Power Moments ◽  
The Moment ◽  
Power Moment Problem

Abstract The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher dimensions there are no non-negativity criteria for the power moments of a measure to be supported by a prescribed closed set. We combine two well studied fortunate situations, specifically a class of curves in two dimensions classified by Scheiderer and Plaumann, and compact, basic semi-algebraic sets, with the aim at enlarging the realm of geometric shapes on which the power moment problem is accessible and solvable by non-negativity certificates.

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 On the moment problem for a finite interval

1932 ◽  
Vol 38 (4) ◽  
pp. 269-271 ◽  
Author(s):  
T. H. Hildebrandt
Keyword(s):  
Moment Problem ◽  
Finite Interval ◽  
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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