On degenerate Hamburger moment problem and extensions of nonnegative Hankel block matrices

1996 ◽  
Vol 25 (3) ◽  
pp. 253-276 ◽  
Author(s):  
Vladimir Bolotnikov
Keyword(s):  
Moment Problem ◽  
Hamburger Moment Problem ◽  
Block Matrices

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.

scholarly journals An extended Hamburger moment problem

1985 ◽  
Vol 28 (2) ◽  
pp. 167-183 ◽  
Author(s):  
Olav Njåstad
Keyword(s):  
Distribution Function ◽  
Moment Problem ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Moment Problems ◽  
Real Numbers ◽  
Orthogonal Functions ◽  
Hamburger Moment Problem ◽  
Hankel Determinants ◽  
Necessary And Sufficient

The classical Hamburger moment problem can be formulated as follows: Given a sequence {cn:n=0,1,2,…} of real numbers, find necessary and sufficient conditions for the existence of a distribution function ψ (i.e. a bounded, real-valued, non-decreasing function) on (– ∞,∞) with infinitely many points of increase, such that , n = 0,1,2, … This problem was posed and solved by Hamburger [5] in 1921. The corresponding problem for functions ψ on the interval [0,∞) had already been treated by Stieltjes [15] in 1894. The characterizations were in terms of positivity of Hankel determinants associated with the sequence {cn}, and the original proofs rested on the theory of continued fractions. Much work has since been done on questions connected with these problems, using orthogonal functions and extension of positive definite functionals associated with the sequence. Accounts of the classical moment problems with later developments can be found in [1,4,14]. Good modern accounts of the theory of orthogonal polynomials can be found in [2,3].

Analytic functions associated with strong Hamburger moment problems

2009 ◽  
Vol 52 (1) ◽  
pp. 181-187 ◽  
Author(s):  
Olav Njåstad
Keyword(s):  
Moment Problem ◽  
Analytic Functions ◽  
Moment Problems ◽  
Hamburger Moment Problem ◽  
Growth Properties

AbstractWe complete the investigation of growth properties of analytic functions connected with the Nevanlinna parametrization of the solutions of an indeterminate strong Hamburger moment problem.

Hamburger moment problem for powers and products of random variables

2014 ◽  
Vol 154 ◽  
pp. 166-177 ◽  
Author(s):  
Jordan Stoyanov ◽  
Gwo Dong Lin ◽  
Anirban DasGupta
Keyword(s):  
Moment Problem ◽  
Random Variables ◽  
Hamburger Moment Problem ◽  
Products Of Random Variables
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