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We describe all solutions of the matrix Hamburger moment problem in a general case (no conditions besides solvability are assumed). We use the fundamental results of A.V. Shtraus on the generalized resolvents of symmetric operators. All…

Classical Analysis and ODEs · Mathematics 2009-10-21 Sergey M. Zagorodnyuk

The Stieltjes-Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference…

Classical Analysis and ODEs · Mathematics 2010-11-03 Jacob S. Christiansen , Erik Koelink

In this paper, we study some existence and uniqueness results for systems of differential equations in which each of equations of the system involves a different Stieltjes derivative. Specifically, we show that this problems can only have…

Classical Analysis and ODEs · Mathematics 2025-01-14 Ignacio Márquez Albés , F. Adrián F. Tojo

For an N-extremal solution $\mu$ to an indeterminate moment problem it is known by a theorem of M. Riesz that the measure $(1+x^2)^{-1}d\mu(x)$ is determinate. For $0<\alpha<1$ we show by contradiction that there exist indeterminate…

Functional Analysis · Mathematics 2026-03-30 Christian Berg , Ryszard Szwarc

We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well-known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger's results a…

Functional Analysis · Mathematics 2023-10-09 Pier Luigi Novi Inverardi , Aldo Tagliani , Jordan M. Stoyanov

Applying the method of moments to the chemical master equation (CME) appearing in stochastic chemical kinetics often leads to the so-called closure problem. Recently, several authors showed that this problem can be partially overcome using…

Probability · Mathematics 2018-08-24 Garrett R. Dowdy , Paul I. Barton

We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein-Stieltjes string. We offer three methods of recovering unknown parameters:…

Analysis of PDEs · Mathematics 2025-05-12 Alexander Mikhaylov , Victor Mikhaylov

The Stieltjes (or sometimes called the Cauchy) transform is a fundamental object associated with probability measures, corresponding to the generating function of the moments. In certain applications such as free probability it is essential…

Numerical Analysis · Mathematics 2024-10-22 James Chen , Sheehan Olver

A class of Stieltjes functions of finite type is introduced. These satisfy Widder's conditions on the successive derivatives up to some finite order, and are not necessarily smooth. We show that such functions have a unique integral…

Classical Analysis and ODEs · Mathematics 2016-04-19 Lennart Bondesson , Thomas Simon

An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…

Optimization and Control · Mathematics 2021-07-09 Frank E. Curtis , Daniel P. Robinson , Baoyu Zhou

Let d\mu(t) be a probability measure on [0,+\infty) such that its moments are finite. Then the Cauchy-Stieltjes transform S of d\mu(t) is a Stieltjes function, which admits an expansion into a Stieltjes continued fraction. In the present…

Classical Analysis and ODEs · Mathematics 2012-12-06 Maxim Derevyagin

This paper is devoted to the study of general (Laurent) polynomial modifications of moment functionals on the unit circle, i.e., associated with hermitian Toeplitz matrices. We present a new approach which allows us to study polynomial…

Classical Analysis and ODEs · Mathematics 2009-08-19 M. J. Cantero , L. Moral , L. Velazquez

Material response of real, passive, linear, time-invariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions -- a special class of analytic…

Optimization and Control · Mathematics 2022-03-25 Yury Grabovsky

The main goal of this paper is to reconsider a phenomenon which was treated in earlier work of the authors' on several truncated matricial moment problems. Using a special kind of Schur complement we obtain a more transparent insight into…

Classical Analysis and ODEs · Mathematics 2017-12-20 Bernd Fritzsche , Bernd Kirstein , Conrad Mädler

The paper has two relatively distinct but connected goals; the first is to define the notion of Pad\'e\ approximation of Weyl-Stiltjes transforms on an arbitrary compact Riemann surface of higher genus. The data consists of a contour in the…

Exactly Solvable and Integrable Systems · Physics 2021-08-10 Marco Bertola

In this paper, we study the truncated matrix moment problem in one variable through recursive matrix extensions. \ We give necessary and sufficient conditions for a recursive matrix extension of finite data to be a matrix moment sequence in…

Functional Analysis · Mathematics 2024-01-02 R. Curto , A. Ech-charyfy , K. Idrissi , E. H. Zerouali

Computing the permanent of a non-negative matrix is a computationally challenging, \#P-complete problem with wide-ranging applications. We introduce a novel permanental analogue of Schur's determinant formula, leveraging a newly defined…

Discrete Mathematics · Computer Science 2025-09-11 Aditi Laddha , Madhusudhan Reddy Pittu

In the standard theory of delay equations, the fundamental solution does not 'live' in the state space. To eliminate this age-old anomaly, we enlarge the state space. As a consequence, we lose the strong continuity of the solution operators…

Dynamical Systems · Mathematics 2021-03-22 Odo Diekmann , Sjoerd Verduyn Lunel

Preliminary results of our investigations on solving indefinite qua\-dra\-tic programs by dynamical systems are given. First, dynamical systems corresponding to two fundamental DC programming algorithms to deal with indefinite quadratic…

Optimization and Control · Mathematics 2025-04-01 Massimo Pappalardo , Nguyen Nang Thieu , Nguyen Dong Yen

This German paper discusses certain aspects of the non-degenerate case of truncated matricial moment problems on the intervals [$\alpha$,$\infty$) and (-$\infty$,\alpha] for any real number $\alpha$.

Classical Analysis and ODEs · Mathematics 2017-03-21 Benjamin Jeschke