Spectral Theory of the Infinite Block Jacobi Type Normal Matrices, Orthogonal Polynomials on a Complex Domain, and the Complex Moment Problem

2009 ◽  
pp. 37-50
Author(s):  
Yu.M. Berezansky
Keyword(s):  
Orthogonal Polynomials ◽  
Spectral Theory ◽  
Moment Problem ◽  
Complex Domain ◽  
Normal Matrices

A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators

2011 ◽  
Vol 3 (2) ◽  
pp. 204-218 ◽  
Author(s):  
Jiu Ding ◽  
Noah H. Rhee
Keyword(s):  
Orthogonal Polynomials ◽  
Maximum Entropy ◽  
Moment Problem ◽  
Chebyshev Polynomials ◽  
Numerical Experiments ◽  
Maximum Entropy Method ◽  
Chaotic Map ◽  
Entropy Method ◽  
The Stability ◽  
Stability Consideration

AbstractLet S: [0, 1]→[0, 1] be a chaotic map and let f* be a stationary density of the Frobenius-Perron operator PS: L1→L1 associated with S. We develop a numerical algorithm for approximating f*, using the maximum entropy approach to an under-determined moment problem and the Chebyshev polynomials for the stability consideration. Numerical experiments show considerable improvements to both the original maximum entropy method and the discrete maximum entropy method.

Spectral theory of orthogonal polynomials of several variables

1991 ◽  
Vol 43 (10) ◽  
pp. 1334-1337 ◽  
Author(s):  
M. I. Gekhtman ◽  
A. A. Kalyuzhnyi
Keyword(s):  
Orthogonal Polynomials ◽  
Spectral Theory ◽  
Several Variables

scholarly journals Unique solvability of the strong Hamburger moment problem

1986 ◽  
Vol 40 (1) ◽  
pp. 5-19 ◽  
Author(s):  
Olav Njåstad ◽  
W. J. Thron
Keyword(s):  
Distribution Function ◽  
Orthogonal Polynomials ◽  
Unique Solution ◽  
Unique Solvability ◽  
Moment Problem ◽  
Limit Point ◽  
Double Sequence ◽  
Hamburger Moment Problem ◽  
Limit Point Case ◽  
The Moment

AbstractMethods from the theory of orthogonal polynomials are extended to L-polynomials . By this means the authors and W. B. Jones (J. Math. Anal. Appl. 98 (1984), 528–554) solved the strong Hamburger moment problem, that is, given a double sequence , to find a distribution function ψ(t), non-decreasing, with an infinitenumber of points of increase and bounded on −∞ < t < ∞, such that for all integers . In this article further menthods such as analogues of the Lioville-Ostrogradski formula and of the Christoffel-Darboux formula are developed to investigated When the moment porblem has a unique solution. This will be the case if and only if a sequence of nested disks associated with the sequence has only a point as its intersection (the so called limit point case).

scholarly journals On the completely indeterminate case for block Jacobi matrices

2017 ◽  
Vol 4 (1) ◽  
pp. 48-57
Author(s):  
Andrey Osipov
Keyword(s):  
Orthogonal Polynomials ◽  
Moment Problem ◽  
Jacobi Matrices ◽  
Hamburger Moment Problem ◽  
Block Matrices ◽  
Deficiency Indices ◽  
Jacobi Operators ◽  
Indeterminate Case

Abstract We consider the infinite Jacobi block matrices in the completely indeterminate case, i. e. such that the deficiency indices of the corresponding Jacobi operators are maximal. For such matrices, some criteria of complete indeterminacy are established. These criteria are similar to several known criteria of indeterminacy of the Hamburger moment problem in terms of the corresponding scalar Jacobi matrices and the related systems of orthogonal polynomials.

A Characterization and a Class of Distribution Functions for the Stieltjes-Wigert Polynomials

1970 ◽  
Vol 13 (4) ◽  
pp. 529-532 ◽  
Author(s):  
T. S. Chihara
Keyword(s):  
Orthogonal Polynomials ◽  
Moment Problem ◽  
Recurrence Formula ◽  
Distribution Functions ◽  
Moment Sequence ◽  
The Moment ◽  
Image Position ◽  
Stieltjes Moment Sequence

In his classic memoir on the moment problem that bears his name, Stieltjes [2] exhibited1as an example of an indeterminate (Stieltjes) moment sequence.Stieltjes also obtained the corresponding S-fraction and thus implicitly obtained the three-term recurrence formula satisfied by the corresponding orthogonal polynomials.

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