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Multipeakons and the classical moment problem
 Adv. Math
"... to appear: Advances in Mathematics Dedicated to Professor GianCarlo Rota Classical results of Stieltjes are used to obtain explicit formulas for the peakonantipeakon solutions of the CamassaHolm equation. The closed form solution is expressed in terms of the orthogonal polynomials of the related c ..."
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Cited by 61 (12 self)
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classical moment problem. It is shown that collisions occur only in peakonantipeakon pairs, and the details of the collisions are analyzed using results from the moment problem. A sharp result on the steepening of the slope at the time of collision is given. Asymptotic formulas are given
On the polynomial moment problem
 Math. Research Letters
"... In this paper we treat the following ”polynomial moment problem”: for a complex polynomial P(z) and distinct a, b ∈ C such that P(a) = P(b) to describe polynomials q(z) such that ∫ b ..."
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Cited by 24 (10 self)
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In this paper we treat the following ”polynomial moment problem”: for a complex polynomial P(z) and distinct a, b ∈ C such that P(a) = P(b) to describe polynomials q(z) such that ∫ b
THE MATRIX MOMENT PROBLEM
, 2001
"... We expose the recent extensions to the matrix case of classical results in the theory of the moment problem: the theorem of Riesz, the parametrization of Nevanlinna and properties of the Nextremal matrices of measures. ..."
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Cited by 1 (0 self)
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We expose the recent extensions to the matrix case of classical results in the theory of the moment problem: the theorem of Riesz, the parametrization of Nevanlinna and properties of the Nextremal matrices of measures.
Solving the Truncated Moment Problem Solves the Full Moment Problem
, 1999
"... It is shown that the truncated multidimensional moment problem is more general than the full multidimensional moment problem. ..."
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Cited by 6 (0 self)
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It is shown that the truncated multidimensional moment problem is more general than the full multidimensional moment problem.
Recursiveness, positivity, and truncated moment problems
 Houston J. Math
"... Abstract. Using elementary techniques from linear algebra, we describe a recursire model for singular positive Hankel matrices. We then use this model to obtain necessary and sufficient conditions for existence or uniqueness of positive Borel measures which solve the truncated moment problems of Ha ..."
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Cited by 76 (19 self)
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Abstract. Using elementary techniques from linear algebra, we describe a recursire model for singular positive Hankel matrices. We then use this model to obtain necessary and sufficient conditions for existence or uniqueness of positive Borel measures which solve the truncated moment problems
Global Optimization with Polynomials and the Problem of Moments
 SIAM JOURNAL ON OPTIMIZATION
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear ma ..."
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Cited by 577 (48 self)
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We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear
moment problems and orthogonal polynomials
 Transactions of the American Mathematical Society
, 1989
"... Abstract. We consider a sequence of orthogonal polynomials given by the classical three term recurrence relation. We address the problem of deciding the determinacy or indeterminacy of the associated Hamburger moment problem on the basis of the behavior of the coefficients in the three term recurren ..."
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Cited by 3 (0 self)
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Abstract. We consider a sequence of orthogonal polynomials given by the classical three term recurrence relation. We address the problem of deciding the determinacy or indeterminacy of the associated Hamburger moment problem on the basis of the behavior of the coefficients in the three term
MARKOV MOMENT PROBLEM AND APPROXIMATION
, 2013
"... Copyright © 2014 O. Olteanu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract: In this paper, we start by recalling some poly ..."
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is well known. This method leads to characterization of the existence of the solution of the multidimensional Markov moment problem in terms of quadratic mappings. Two other applications related to the Markov moment problem are considered. Here the main ingredients of the proofs are extension of linear
SPECTRAL MEASURES AND MOMENT PROBLEMS
 SPECTRAL THEORY AND ITS APPLICATIONS THETA 2003, PAGES 173215
, 2003
"... In this expository paper we try to emphasize some connections between functional analysis, in particular operator theory, and moment problems. A central role in this discussion is played by the operatorvalued positive measures, in particular the spectral measures, which are mathematical objects r ..."
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In this expository paper we try to emphasize some connections between functional analysis, in particular operator theory, and moment problems. A central role in this discussion is played by the operatorvalued positive measures, in particular the spectral measures, which are mathematical objects
MAXIMUM ENTROPY FOR REDUCED MOMENT PROBLEMS
 MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES
"... The existence of maximum entropy solutions for a wide class of reduced moment problems on arbitrary open subsets of R d 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 exi ..."
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Cited by 29 (3 self)
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The existence of maximum entropy solutions for a wide class of reduced moment problems on arbitrary open subsets of R d 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
Results 1  10
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823,276