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Journal articles on the topic 'Truncated moment problem'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Jung, Il Bong, Eungil Ko, Chunji Li, and Sang Soo Park. "Embry truncated complex moment problem." Linear Algebra and its Applications 375 (December 2003): 95–114. http://dx.doi.org/10.1016/s0024-3795(03)00617-7.

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2

Curto, Raúl E., Lawrence A. Fialkow, and H. Michael Möller. "The Extremal Truncated Moment Problem." Integral Equations and Operator Theory 60, no. 2 (January 25, 2008): 177–200. http://dx.doi.org/10.1007/s00020-008-1557-x.

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3

Olteanu, Octav. "On the Moment Problem and Related Problems." Mathematics 9, no. 18 (September 17, 2021): 2289. http://dx.doi.org/10.3390/math9182289.

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Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence (yj)j∈ℕn of real numbers and a closed subset F⊆ℝn, n∈{1,2,…}, find a positive regular Borel measure μ on F such that ∫Ftjdμ=yj, j∈ℕn. This is the full moment problem. The existence, uniqueness, and construction of the unknown solution μ are the focus of attention. The numbers yj, j∈ℕn are called the moments of the measure μ. When a sandwich condition on the solution is required, we have a Markov moment problem. Secondly, we study the existence and uniqueness of the solutions to some full Markov moment problems. If the moments yj are self-adjoint operators, we have an operator-valued moment problem. Related results are the subject of attention. The truncated moment problem is also discussed, constituting the third aim of this work.

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4

Curto, Raúl, and Lawrence A. Fialkow. "The truncated complex $K$-moment problem." Transactions of the American Mathematical Society 352, no. 6 (February 28, 2000): 2825–55. http://dx.doi.org/10.1090/s0002-9947-00-02472-7.

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5

Zagorodnyuk, Sergey M. "The truncated matrix Hausdorff moment problem." Methods and Applications of Analysis 19, no. 1 (2012): 21–42. http://dx.doi.org/10.4310/maa.2012.v19.n1.a2.

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6

Infusino, M., T. Kuna, J. L. Lebowitz, and E. R. Speer. "The truncated moment problem on N0." Journal of Mathematical Analysis and Applications 452, no. 1 (August 2017): 443–68. http://dx.doi.org/10.1016/j.jmaa.2017.02.060.

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7

Kovalyov, Ivan. "A truncated indefinite Stieltjes moment problem." Journal of Mathematical Sciences 224, no. 4 (June 7, 2017): 509–29. http://dx.doi.org/10.1007/s10958-017-3432-2.

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8

Zagorodnyuk, Sergey M. "The operator approach to the truncated multidimensional moment problem." Concrete Operators 6, no. 1 (February 1, 2019): 1–19. http://dx.doi.org/10.1515/conop-2019-0001.

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Abstract 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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9

Zagorodnyuk, Sergey. "On the truncated two-dimensional moment problem." Advances in Operator Theory 3, no. 2 (April 2018): 388–99. http://dx.doi.org/10.15352/aot.1708-1212.

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10

Idrissi, K., and E. H. Zerouali. "Charges solve the truncated complex moment problem." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 04 (December 2018): 1850027. http://dx.doi.org/10.1142/s0219025718500273.

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Let [Formula: see text], with [Formula: see text] and [Formula: see text], be a given complex-valued sequence. The complex moment problem (respectively, the general complex moment problem) associated with [Formula: see text] consists in determining necessary and sufficient conditions for the existence of a positive Borel measure (respectively, a charge) [Formula: see text] on [Formula: see text] such that [Formula: see text] In this paper, we investigate the notion of recursiveness in the two variable case. We obtain several useful results that we use to deduce new necessary and sufficient conditions for the truncated complex moment problem to admit a solution. In particular, we show that the general complex moment problem always has a solution. A concrete construction of the solution and an illustrating example are also given.

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11

di Dio, Philipp J., and Konrad Schmüdgen. "The multidimensional truncated moment problem: Carathéodory numbers." Journal of Mathematical Analysis and Applications 461, no. 2 (May 2018): 1606–38. http://dx.doi.org/10.1016/j.jmaa.2017.12.021.

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12

Curto, Ra�l E., and Lawrence A. Fialkow. "Solution of the Truncated Parabolic Moment Problem." Integral Equations and Operator Theory 50, no. 2 (October 2004): 169–96. http://dx.doi.org/10.1007/s00020-003-1275-3.

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13

Curto, Raúl E., and Lawrence A. Fialkow. "Solution of the Truncated Hyperbolic Moment Problem." Integral Equations and Operator Theory 52, no. 2 (June 2005): 181–218. http://dx.doi.org/10.1007/s00020-004-1340-6.

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14

Curto, Raúl E., Lawrence A. Fialkow, and H. Michael Möller. "Addendum to “The Extremal Truncated Moment Problem”." Integral Equations and Operator Theory 61, no. 1 (April 18, 2008): 147–48. http://dx.doi.org/10.1007/s00020-008-1591-8.

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15

Adamyan, Vadim M., and Igor M. Tkachenko. "Stieltjes Truncated Moment Problem with Point Constraints." PAMM 3, no. 1 (December 2003): 438–39. http://dx.doi.org/10.1002/pamm.200310490.

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16

BEN TAHER, R., M. RACHIDI, and E. H. ZEROUALI. "RECURSIVE SUBNORMAL COMPLETION AND THE TRUNCATED MOMENT PROBLEM." Bulletin of the London Mathematical Society 33, no. 4 (July 2001): 425–32. http://dx.doi.org/10.1017/s0024609301008116.

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The aim of this paper is to study properties of sequences that are recursively defined by a linear equation and their applications to the truncated moment problem in connection with the problem of subnormal completion of the truncated weighted shifts. Special cases are considered and some classical results due to Stampfli, Curto and Fialkow are recovered using elementary techniques.

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17

Duran, Antonio J., and Pedro Lopez-Rodriguez. "Density Questions for the Truncated Matrix Moment Problem." Canadian Journal of Mathematics 49, no. 4 (August 1, 1997): 708–21. http://dx.doi.org/10.4153/cjm-1997-034-5.

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AbstractFor a truncated matrix moment problem, we describe in detail the set of positive definite matrices of measures μ in V2n (this is the set of solutions of the problem of degree 2n) for which the polynomials up to degree n are dense in the corresponding space L2(μ). These matrices of measures are exactly the extremal measures of the set Vn.

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18

Chung, Kun-Jen, and Matthew J. Sobel. "Linear programming solutions of the truncated moment problem." Computers & Operations Research 18, no. 5 (January 1991): 477–85. http://dx.doi.org/10.1016/0305-0548(91)90024-l.

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19

Li, X., and A. Sri Ranga. "Szegő polynomials and the truncated trigonometric moment problem." Ramanujan Journal 12, no. 3 (December 2006): 461–72. http://dx.doi.org/10.1007/s11139-006-0155-2.

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20

Osaka, Hiroyuki, Sergei Silvestrov, and Jun Tomiyama. "Monotone operator functions, gaps and power moment problem." MATHEMATICA SCANDINAVICA 100, no. 1 (March 1, 2007): 161. http://dx.doi.org/10.7146/math.scand.a-15019.

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The article is devoted to investigation of the classes of functions belonging to the gaps between classes $P_{n+1}(I)$ and $P_{n}(I)$ of matrix monotone functions for full matrix algebras of successive dimensions. In this paper we address the problem of characterizing polynomials belonging to the gaps $P_{n}(I) \setminus P_{n+1}(I)$ for bounded intervals $I$. We show that solution of this problem is closely linked to solution of truncated moment problems, Hankel matrices and Hankel extensions. Namely, we show that using the solutions to truncated moment problems we can construct continuum many polynomials in the gaps. We also provide via several examples some first insights into the further problem of description of polynomials in the gaps that are not coming from the truncated moment problem. Also, in this article, we deepen further in another way into the structure of the classes of matrix monotone functions and of the gaps between them by considering the problem of position in the gaps of certain interesting subclasses of matrix monotone functions that appeared in connection to interpolation of spaces and in a proof of the Löwner theorem on integral representation of operator monotone functions.

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21

Zagorodnyuk, S. M. "Nevanlinna formula for the truncated matrix trigonometric moment problem." Ukrainian Mathematical Journal 64, no. 8 (January 2013): 1199–214. http://dx.doi.org/10.1007/s11253-013-0710-0.

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22

Fialkow, Lawrence, and Jiawang Nie. "The truncated moment problem via homogenization and flat extensions." Journal of Functional Analysis 263, no. 6 (September 2012): 1682–700. http://dx.doi.org/10.1016/j.jfa.2012.06.004.

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23

Nie, Jiawang. "The $${\mathcal {A}}$$ A -Truncated $$K$$ K -Moment Problem." Foundations of Computational Mathematics 14, no. 6 (October 9, 2014): 1243–76. http://dx.doi.org/10.1007/s10208-014-9225-9.

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24

Olteanu, Octav. "New Results on Markov Moment Problem." International Journal of Analysis 2013 (February 3, 2013): 1–17. http://dx.doi.org/10.1155/2013/901318.

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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.

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25

Curto, Raúl E., and Lawrence A. Fialkow. "Solution of the truncated complex moment problem for flat data." Memoirs of the American Mathematical Society 119, no. 568 (1996): 0. http://dx.doi.org/10.1090/memo/0568.

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26

Choque-Rivero, Abdon E. "Dyukarev–Stieltjes parameters of the truncated Hausdorff matrix moment problem." Boletín de la Sociedad Matemática Mexicana 23, no. 2 (January 5, 2016): 891–918. http://dx.doi.org/10.1007/s40590-015-0083-5.

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27

Gabardo, Jean-Pierre. "Tight Frames of Polynomials and the Truncated Trigonometric Moment Problem." Journal of Fourier Analysis and Applications 1, no. 3 (August 1994): 249–79. http://dx.doi.org/10.1007/s00041-001-4012-9.

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28

Blekherman, G., and J. B. Lasserre. "The truncated K-moment problem for closure of open sets." Journal of Functional Analysis 263, no. 11 (December 2012): 3604–16. http://dx.doi.org/10.1016/j.jfa.2012.09.001.

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29

di Dio, Philipp J., and Konrad Schmüdgen. "The multidimensional truncated moment problem: Atoms, determinacy, and core variety." Journal of Functional Analysis 274, no. 11 (June 2018): 3124–48. http://dx.doi.org/10.1016/j.jfa.2017.11.013.

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30

Zellinger, Werner, and Bernhard A. Moser. "On the truncated Hausdorff moment problem under Sobolev regularity conditions." Applied Mathematics and Computation 400 (July 2021): 126057. http://dx.doi.org/10.1016/j.amc.2021.126057.

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31

Athanassoulis, G. A., and P. N. Gavriliadis. "The truncated Hausdorff moment problem solved by using kernel density functions." Probabilistic Engineering Mechanics 17, no. 3 (July 2002): 273–91. http://dx.doi.org/10.1016/s0266-8920(02)00012-7.

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32

Fialkow, Lawrence A. "Solution of the truncated moment problem with variety $y = x^{3}$." Transactions of the American Mathematical Society 363, no. 06 (June 1, 2011): 3133. http://dx.doi.org/10.1090/s0002-9947-2011-05262-1.

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33

Arlinskiĭ, Yury. "Truncated Hamburger moment problem for an operator measure with compact support." Mathematische Nachrichten 285, no. 14-15 (April 11, 2012): 1677–95. http://dx.doi.org/10.1002/mana.201200028.

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34

Lasarow, Andreas. "On maximal weight solutions in a truncated trigonometric matrix moment problem." Functiones et Approximatio Commentarii Mathematici 43, no. 2 (December 2010): 117–28. http://dx.doi.org/10.7169/facm/1291903393.

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35

Fialkow, Lawrence A. "The core variety of a multisequence in the truncated moment problem." Journal of Mathematical Analysis and Applications 456, no. 2 (December 2017): 946–69. http://dx.doi.org/10.1016/j.jmaa.2017.07.041.

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36

Moroder, Tobias, Keyl Michael, and Lütkenhaus Norbert. "Truncated \mathfrak{su}(2) moment problem for spin and polarization states." Journal of Physics A: Mathematical and Theoretical 41, no. 27 (June 12, 2008): 275302. http://dx.doi.org/10.1088/1751-8113/41/27/275302.

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37

Gavriliadis, P. N., and G. A. Athanassoulis. "The truncated Stieltjes moment problem solved by using kernel density functions." Journal of Computational and Applied Mathematics 236, no. 17 (November 2012): 4193–213. http://dx.doi.org/10.1016/j.cam.2012.05.015.

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38

Kimsey, David P. "On a minimal solution for the indefinite multidimensional truncated moment problem." Journal of Mathematical Analysis and Applications 500, no. 1 (August 2021): 125091. http://dx.doi.org/10.1016/j.jmaa.2021.125091.

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39

Choque-Rivero, A. E. "Relations between the orthogonal matrix polynomials on [a, b], Dyukarev-Stieltjes parameters, and Schur complements." Special Matrices 5, no. 1 (December 20, 2017): 303–18. http://dx.doi.org/10.1515/spma-2017-0023.

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Abstract We obtain explicit interrelations between new Dyukarev-Stieltjes matrix parameters and orthogonal matrix polynomials on a finite interval [a, b], as well as the Schur complements of the block Hankel matrices constructed through the moments of the truncated Hausdorff matrix moment (THMM) problem in the nondegenerate case. Extremal solutions of the THMM problem are described with the help of matrix continued fractions.

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40

Olteanu, Octav. "On Markov Moment Problem and Related Results." Symmetry 13, no. 6 (June 1, 2021): 986. http://dx.doi.org/10.3390/sym13060986.

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We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result. The domain is the Banach lattice of continuous real-valued functions on a compact subset or an Lν1 space, where ν is a positive moment determinate measure on a closed unbounded set. The existence and uniqueness of the operator solution are proved. Our solutions satisfy the interpolation moment conditions and are between two given linear operators on the positive cone of the domain space. The norm controlling of the solution is emphasized. The most part of the results are stated and proved in terms of quadratic forms. This type of result represents the first aim of the paper. Secondly, we construct a polynomial solution for a truncated multidimensional moment problem.

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41

Fritzsche, Bernd, Bernd Kirstein, Conrad Mädler, and Torsten Schröder. "On the truncated matricial Stieltjes moment problem M[[α,∞);(sj)j=0m,≤]." Linear Algebra and its Applications 544 (May 2018): 30–114. http://dx.doi.org/10.1016/j.laa.2018.01.004.

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42

Kim, Yong Jung, and Wei-Ming Ni. "Higher Order Approximations in the Heat Equation and the Truncated Moment Problem." SIAM Journal on Mathematical Analysis 40, no. 6 (January 2009): 2241–61. http://dx.doi.org/10.1137/08071778x.

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43

Curto, Raúl E., and Lawrence A. Fialkow. "An analogue of the Riesz–Haviland theorem for the truncated moment problem." Journal of Functional Analysis 255, no. 10 (November 2008): 2709–31. http://dx.doi.org/10.1016/j.jfa.2008.09.003.

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44

Chidume, C. E., M. Rachidi, and E. H. Zerouali. "Solving the General Truncated Moment Problem by the r-Generalized Fibonacci Sequences Method." Journal of Mathematical Analysis and Applications 256, no. 2 (April 2001): 625–35. http://dx.doi.org/10.1006/jmaa.2000.7332.

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45

di Dio, Philipp J. "The multidimensional truncated moment problem: Gaussian and log-normal mixtures, their Carathéodory numbers, and set of atoms." Proceedings of the American Mathematical Society 147, no. 7 (March 21, 2019): 3021–38. http://dx.doi.org/10.1090/proc/14499.

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46

KHINE, YU YU, DENNIS B. CREAMER, and STEVEN FINETTE. "ACOUSTIC PROPAGATION IN AN UNCERTAIN WAVEGUIDE ENVIRONMENT USING STOCHASTIC BASIS EXPANSIONS." Journal of Computational Acoustics 18, no. 04 (December 2010): 397–441. http://dx.doi.org/10.1142/s0218396x10004255.

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A generalization of acoustic propagation in an uncertain ocean waveguide environment is described using a probabilistic formulation in terms of stochastic basis expansions. The problem is studied in the context of wave propagation in random media, where environmental uncertainty and its interaction with the acoustic field are described by stochastic, rather than deterministic parameters and fields. This representation, constructed explicitly in terms of Karhunen-Loève (KL) and polynomial chaos (PC) expansions, leads to coupled differential equations for the expansion coefficients from which the stochastic acoustic field can be obtained as a random process. The equations are solved in the narrow-angle parabolic approximation using a split-step method to compute moments of the random acoustic field at any point in the waveguide. Results are compared with Monte-Carlo computations of the acoustic field in the same environment to study the convergence of the truncated stochastic basis expansion representing the acoustic field. The rate of convergence of the truncated chaos expansion was found to be dependent on the particular moment computed. For the first and second moments corresponding to the mean field and the field intensity, convergence was achieved rapidly, only requiring low order expansions. Another second moment, the acoustic spatial coherence, converged more slowly due to the relative phase information that, in this formulation, is described by polynomial approximation. While stochastic basis expansions show promise for the development of compact representations of the acoustic field in the presence of environmental uncertainty, accelerated convergence schemes will be needed to allow for practical applications.

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47

Choque Rivero, Abdon Eddy. "On Dyukarev's resolvent matrix for a truncated Stieltjes matrix moment problem under the view of orthogonal matrix polynomials." Linear Algebra and its Applications 474 (June 2015): 44–109. http://dx.doi.org/10.1016/j.laa.2015.01.027.

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48

Kimsey, David P., and Hugo J. Woerdeman. "The truncated matrix-valued $K$-moment problem on $\mathbb {R}^d$, $\mathbb {C}^d$, and $\mathbb {T}^d$." Transactions of the American Mathematical Society 365, no. 10 (May 16, 2013): 5393–430. http://dx.doi.org/10.1090/s0002-9947-2013-05812-6.

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49

Ivanov, V. P. "Information dualism of the problem of optimum terminal control of dynamic object." Informatization and communication, no. 2 (February 16, 2021): 85–90. http://dx.doi.org/10.34219/2078-8320-2021-12-2-85-90.

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The article deals with the problem of synthesis of terminal control. A functional, a nonlinear mathematical model of a dynamic object, restrictions on the maximum permissible values of control are given. The control law is synthesized. The following statement is proved: the synthesis of the optimal control is carried out using the entire initial mathematical model of the dynamical object, but to calculate the control at any particular moment of time, it is possible to use a reduced (truncated) model, which simplifies the computational algorithms. Thus, there is an informational dualism of the manage- ment task. The approach is an extension of the principle of information redefinition of Yu.B. Germeier to the area of optimal terminal control.

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50

Bakery, Awad A., Wael Zakaria, and OM Kalthum S. K. Mohamed. "A New Double Truncated Generalized Gamma Model with Some Applications." Journal of Mathematics 2021 (August 16, 2021): 1–27. http://dx.doi.org/10.1155/2021/5500631.

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The generalized Gamma model has been applied in a variety of research fields, including reliability engineering and lifetime analysis. Indeed, we know that, from the above, it is unbounded. Data have a bounded service area in a variety of applications. A new five-parameter bounded generalized Gamma model, the bounded Weibull model with four parameters, the bounded Gamma model with four parameters, the bounded generalized Gaussian model with three parameters, the bounded exponential model with three parameters, and the bounded Rayleigh model with two parameters, is presented in this paper as a special case. This approach to the problem, which utilizes a bounded support area, allows for a great deal of versatility in fitting various shapes of observed data. Numerous properties of the proposed distribution have been deduced, including explicit expressions for the moments, quantiles, mode, moment generating function, mean variance, mean residual lifespan, and entropies, skewness, kurtosis, hazard function, survival function, r th order statistic, and median distributions. The delivery has hazard frequencies that are monotonically increasing or declining, bathtub-shaped, or upside-down bathtub-shaped. We use the Newton Raphson approach to approximate model parameters that increase the log-likelihood function and some of the parameters have a closed iterative structure. Six actual data sets and six simulated data sets were tested to demonstrate how the proposed model works in reality. We illustrate why the Model is more stable and less affected by sample size. Additionally, the suggested model for wavelet histogram fitting of images and sounds is very accurate.

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