Sextic Moment Problems on 3 Parallel Lines

Yoo, Seonguk

doi:10.4134/bkms.b160102

Cited by 12 publications

(15 citation statements)

References 7 publications

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“…Observe that the spectral measure E(δ) in relation (24) can have jumps at points (x, y) with x ∈ {λ , λ }, y ∈ { λ , λ }. The measure support is contained in this set of four points.…”

Section: Propositionmentioning

confidence: 99%

“…Step 2. Calculate the (atomic) solution of the moment problem by formula (24). Observe that the solution can have atoms at points (x, y), where x is an eigenvalue of M , y is an eigenvalue of M .…”

Section: Algorithm 2 (The Construction Of a Solution Of The Moment Prmentioning

confidence: 99%

“…A general approach for this moment problem was given by Curto and Fialkow in their books [4] and [5]. These books entailed a series of papers by a group of mathematicians, see recent papers [6], [22], [24] and references therein. This approach includes an extension of the matrix of prescribed moments with the same rank.…”

Section: Introductionmentioning

confidence: 99%

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The operator approach to the truncated multidimensional moment problem

Zagorodnyuk

2019

Concrete Operators

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We study the truncated multidimensional moment problem with a general type of truncations. The operator approach to the moment problem is presented. The case where the associated operators form a commuting self-adjoint tuple is characterized in terms of the given moments. The case of the dimensional stability is characterized in terms of the prescribed moments as well. Some sufficient conditions for the solvability of the moment problem are presented. A construction of the corresponding solution is described by algorithms. Numerical examples of the construction are provided.

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Section: Propositionmentioning

confidence: 99%

Section: Algorithm 2 (The Construction Of a Solution Of The Moment Prmentioning

confidence: 99%

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The operator approach to the truncated multidimensional moment problem

Zagorodnyuk

2019

Concrete Operators

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“…Other approaches to truncated moment problems can be found in [4], [5], [13], [16], [9], [8]. Recent results can be also found in [14], [7].…”

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confidence: 99%

On the truncated multidimensional moment problems in $\mathbb{C}^n$

Zagorodnyuk

2021

Preprint

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We consider the problem of finding a (non-negative) measureHere K is an arbitrary finite subset of Z n + , which contains (0, ..., 0), and s k are prescribed complex numbers (we use the usual notations for multi-indices). There are two possible interpretations of this problem. At first, one may consider this problem as an extension of the truncated multidimensional moment problem on R n , where the support of the measure µ is allowed to lie in C n . Secondly, the moment problem is a particular case of the truncated moment problem in C n , 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.

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“…A general approach for this moment problem was given by Curto and Fialkow in their books [6] and [7]. These books entailed a series of papers by a group of mathematicians, see recent papers [8], [20], [18] and references therein. This approach includes an extension of the matrix of prescribed moments with the same rank.…”

mentioning

confidence: 99%

On the truncated two-dimensional moment problem

Zagorodnyuk¹

2018

Adv. Oper. Theory

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Moment problems form a classical and fruitful domain of the mathematical analysis. From their origins in 19-th centure (the Stieltjes moment problem) there appeared many variations of these problems which became classical: Hamburger, Hausdorff and trigonometric moment problems, matrix and operator moment problems, multidimensional moment problems, see classicalThe multidimensional moment problem (both the full and the truncated versions) turned out to be much more complicated than its one-dimensional prototype [4], [11]. An operator-theoretical interpretation of the multidimensional moment problem was given by Fuglede in [9]. It should be noticed that the operator approach to moment problems was introduced by Naimark in 1940-1943 and then developed by many authors, see historical notes in [26]. Elegant conditions for the solvability of the multidimensional moment problem in the case of the support on semi-algebraic sets were given by Schmüdgen in [15], [16]. Another conditions for the solvability of the multidimensional moment problem, using an extension of the moment sequence, were given by Putinar and Vasilescu, see [14], [19]. Developing the idea of Putinar and Vasilescu, we presented another conditions for the solvability of the two-dimensional moment problem and proposed an algorithm (which essentially consists of solving of linear equations) for a construction of the solutions set [24]. An analytic parametrization for all solutions of the twodimensional moment problem in a strip was given in [25]. Another approach to multidimensional and complex moment problems (including truncated problems), using extension arguments for * -semigroups, has been developed by Cichoń, Stochel and Szafraniec, see [5] and references therein. Still another approach for the two-dimensional moment problem was proposed by Ovcharenko in [12], [13].In this paper we shall be focused on the truncated two-dimensional moment problem. A general approach for this moment problem was given by Curto and Fialkow in their books [6] and [7]. These books entailed a series of papers by a group of mathematicians, see recent papers [8], [20], [18] and references therein. This approach includes an extension of the matrix of prescribed moments with the same rank. While positive extensions are easy

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Sextic Moment Problems on 3 Parallel Lines

Cited by 12 publications

References 7 publications

The operator approach to the truncated multidimensional moment problem

The operator approach to the truncated multidimensional moment problem

On the truncated multidimensional moment problems in $\mathbb{C}^n$

On the truncated two-dimensional moment problem

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