scholarly journals A Family of Heat Functions as Solutions of Indeterminate Moment Problems

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Ricardo Gómez ◽  
Marcos López-García
Keyword(s):  
Heat Equation ◽  
Moment Problems ◽  
Indeterminate Moment Problems ◽  
Log Normal

We construct a family of functions satisfying the heat equation and show how they can be used to generate solutions to indeterminate moment problems. The following cases are considered: log-normal, generalized Stieltjes-Wigert, andq-Laguerre.

scholarly journals A question by T. S. Chihara about shell polynomials and indeterminate moment problems

2011 ◽  
Vol 163 (10) ◽  
pp. 1449-1464
Author(s):  
Christian Berg ◽  
Jacob Stordal Christiansen
Keyword(s):  
Moment Problems ◽  
Indeterminate Moment Problems

scholarly journals Small eigenvalues of large Hankel matrices: The indeterminate case

2002 ◽  
Vol 91 (1) ◽  
pp. 67 ◽  
Author(s):  
Christian Berg ◽  
Yang Chen ◽  
Mourad E. H. Ismail
Keyword(s):  
Lower Bound ◽  
Positive Constant ◽  
Moment Problems ◽  
Hankel Matrices ◽  
Orthonormal Polynomials ◽  
Indeterminate Moment Problems ◽  
Explicit Lower Bound ◽  
Indeterminate Case ◽  
Bounded Below ◽  
Small Eigenvalues

In this paper we characterize the indeterminate case by the eigenvalues of the Hankel matrices being bounded below by a strictly positive constant. An explicit lower bound is given in terms of the orthonormal polynomials and we find expressions for this lower bound in a number of indeterminate moment problems.

scholarly journals GAP FORMATION PROBABILITY OF THE α-ENSEMBLE

1995 ◽  
Vol 09 (10) ◽  
pp. 1205-1225 ◽  
Author(s):  
YANG CHEN ◽  
KASPER JUEL ERIKSEN
Keyword(s):  
Orthogonal Polynomials ◽  
Continuum Approximation ◽  
Moment Problems ◽  
Gap Formation ◽  
Hermitian Matrices ◽  
Formation Probability ◽  
Indeterminate Moment Problems ◽  
The Continuum

In this paper we employ the continuum approximation of Dyson to determine the asymptotic gap formation probability in the spectrum of N×N Hermitian matrices associated with orthogonal polynomials that are solutions of indeterminate moment problems. We have shown that the probability, Eβ[J], that an interval J is free of eigenvalues is [Formula: see text] where [Formula: see text]

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