On the moment problems

1997 ◽  
Vol 35 (1) ◽  
pp. 85-90 ◽  
Author(s):  
Gwo Dong Lin
Keyword(s):  
Moment Problems ◽  
The Moment

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.

scholarly journals New Results on Markov Moment Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Octav Olteanu
Keyword(s):  
Moment Problem ◽  
Sufficient Conditions ◽  
Linear Operators ◽  
Moment Problems ◽  
Finite Dimensional ◽  
Integrable Functions ◽  
Truncated Moment Problem ◽  
Markov Moment ◽  
The Moment ◽  
Necessary And Sufficient

The present work deals with the existence of the solutions of some Markov moment problems. Necessary conditions, as well as necessary and sufficient conditions, are discussed. One recalls the background containing applications of extension results of linear operators with two constraints to the moment problem and approximation by polynomials on unbounded closed finite-dimensional subsets. Two domain spaces are considered: spaces of absolute integrable functions and spaces of analytic functions. Operator valued moment problems are solved in the latter case. In this paper, there is a section that contains new results, making the connection to some other topics: bang-bang principle, truncated moment problem, weak compactness, and convergence. Finally, a general independent statement with respect to polynomials is discussed.

scholarly journals MAXIMUM ENTROPY FOR REDUCED MOMENT PROBLEMS

2000 ◽  
Vol 10 (07) ◽  
pp. 1001-1025 ◽  
Author(s):  
MICHAEL JUNK
Keyword(s):  
Maximum Entropy ◽  
Wide Class ◽  
Moment Problem ◽  
Entropy Solution ◽  
Unbounded Domains ◽  
Entropy Solutions ◽  
Moment Problems ◽  
Precise Condition ◽  
The Moment

The existence of maximum entropy solutions for a wide class of reduced moment problems on arbitrary open subsets of ℝd is considered. In particular, new results for the case of unbounded domains are obtained. A precise condition is presented under which solvability of the moment problem implies existence of a maximum entropy solution.

scholarly journals On the Truncated Multidimensional Moment Problems in Cn

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Sergey Zagorodnyuk
Keyword(s):  
Integral Representation ◽  
Finite Subset ◽  
Moment Problem ◽  
Complex Numbers ◽  
Moment Problems ◽  
Linear Functionals ◽  
Truncated Moment Problem ◽  
The Moment ◽  
Multidimensional Moment Problem ◽  
Multidimensional Moment Problems

We consider the problem of finding a (non-negative) measure μ on B(Cn) such that ∫Cnzkdμ(z)=sk, ∀k∈K. Here, K is an arbitrary finite subset of Z+n, which contains (0,…,0), and sk are prescribed complex numbers (we use the usual notations for multi-indices). There are two possible interpretations of this problem. Firstly, one may consider this problem as an extension of the truncated multidimensional moment problem on Rn, where the support of the measure μ is allowed to lie in Cn. Secondly, the moment problem is a particular case of the truncated moment problem in Cn, with special truncations. We give simple conditions for the solvability of the above moment problem. As a corollary, we have an integral representation with a non-negative measure for linear functionals on some linear subspaces of polynomials.

ON THE SOLVABILITY OF MAXIMUM ENTROPY MOMENT PROBLEMS IN TEXTURE ANALYSIS

2012 ◽  
Vol 22 (12) ◽  
pp. 1250043 ◽  
Author(s):  
MICHAEL JUNK ◽  
JOHANNES BUDDAY ◽  
THOMAS BÖHLKE
Keyword(s):  
Distribution Function ◽  
Maximum Entropy ◽  
Orientation Distribution ◽  
Moment Problems ◽  
Topological Groups ◽  
Crystallite Orientation ◽  
Locally Compact ◽  
Texture Coefficients ◽  
Moment Functions ◽  
The Moment

The estimation of the crystallite orientation distribution function based on the leading texture coefficients can be rephrased as a maximum entropy moment problem. In this paper, we prove the solvability of these moment problems under quite general assumptions on the moment functions which carries over to general locally compact and σ-compact Hausdorff topological groups.

Consistency of Moment Systems

1995 ◽  
Vol 47 (5) ◽  
pp. 995-1006 ◽  
Author(s):  
A. S. Lewis
Keyword(s):  
Fixed Point ◽  
Large Deviations ◽  
Recent Work ◽  
Upper Bound ◽  
Optimization Problems ◽  
Analytic Approach ◽  
Moment Problems ◽  
Probabilistic Interpretation ◽  
Large Deviations Theory ◽  
The Moment

AbstractAn important question in the study of moment problems is to determine when a fixed point in ℝn lies in the moment cone of vectors , with μ a nonnegative measure. In associated optimization problems it is also important to be able to distinguish between the interior and boundary of the moment cone. Recent work of Dachuna-Castelle, Gamboa and Gassiat derived elegant computational characterizations for these problems, and for related questions with an upper bound on μ. Their technique involves a probabilistic interpretation and large deviations theory. In this paper a purely convex analytic approach is used, giving a more direct understanding of the underlying duality, and allowing the relaxation of their assumptions.

scholarly journals The Stieltjes condition and multidimensional $${\mathcal {K}}$$-moment problems

2021 ◽  
Author(s):  
Konrad Schmüdgen
Keyword(s):  
Moment Problem ◽  
Moment Problems ◽  
Solvability Theorem ◽  
The Moment

AbstractWe prove a solvability theorem for the Stieltjes problem on $$\mathbb {R}^d$$ R d which is based on the multivariate Stieltjes condition $$\sum _{n=1}^\infty L(x_j^{n})^{-1/(2n)} =+\infty $$ ∑ n = 1 ∞ L ( x j n ) - 1 / ( 2 n ) = + ∞ , $$j=1,\dots ,d.$$ j = 1 , ⋯ , d . This result is applied to derive a new solvability theorem for the moment problem on unbounded semi-algebraic subsets of $$\mathbb {R}^d$$ R d .

scholarly journals OTT Regulation a way of combating cybercrimes

2018 ◽  
Vol 331 ◽  
pp. 395-406
Author(s):  
Veronica Mocanu
Keyword(s):  
Communication Network ◽  
Quality Standards ◽  
Rapid Expansion ◽  
The Internet ◽  
Moment Problems ◽  
Internet Applications ◽  
The Past ◽  
Legal Perspective ◽  
New Challenges ◽  
The Moment

In the past decade we have witnessed a rapid expansion of the Internet gadgets, Internet services and internet applications. This revolutionary communication network has significantly changed the way people live, communicate, and conduct business. However, from legal perspective all of these new challenges remain under covered, things that frequently could generate harm, abuses and cybercrimes. Therefore, by this research, it is proposed to discuss the main risks, which are generated by using of uncontrolled OTT and present perspectives of regulations. The article includes topics such as description of OTT regulations practices used for the moment, problems generated by chaotic regulations of OTT, perspective that we have to take, need for licensing and certification of new internet applications and services, setting of quality standards, and proposes for involvement in development.

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