Some generalizations of the classical moment problem

2002 ◽  
Vol 44 (3) ◽  
pp. 255-289 ◽  
Author(s):  
Yurij M. Berezansky
Keyword(s):  
Moment Problem ◽  
Classical Moment Problem

On Polynomial Maximum Entropy Method for Classical Moment Problem

2015 ◽  
Vol 8 (1) ◽  
pp. 117-127
Author(s):  
Jiu Ding ◽  
Noah H. Rhee ◽  
Chenhua Zhang
Keyword(s):  
Maximum Entropy ◽  
Moment Problem ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Moment Problems ◽  
Monomial Basis ◽  
Ill Conditioning ◽  
Legendre Moment ◽  
Hausdorff Moment Problem ◽  
Classical Moment Problem

AbstractThe maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis {1,x,x2,...,xn}. The maximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in. In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in and present the maximum entropy method for the Legendre moment problem. We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments, respectively, and utilizing the corresponding maximum entropy method.

scholarly journals Multipeakons and the Classical Moment Problem

2000 ◽  
Vol 154 (2) ◽  
pp. 229-257 ◽  
Author(s):  
Richard Beals ◽  
David H. Sattinger ◽  
Jacek Szmigielski
Keyword(s):  
Moment Problem ◽  
Classical Moment Problem

scholarly journals Finite Toda lattice and classical moment problem

2020 ◽  
Vol 11 (1) ◽  
pp. 25-29
Author(s):  
A.S. Mikhaylov ◽  
V.S. Mikhaylov
Keyword(s):  
Moment Problem ◽  
Toda Lattice ◽  
Classical Moment Problem

scholarly journals Irreducible Representations of Deformed Oscillator Algebra and q-Special Functions

1997 ◽  
Vol 12 (01) ◽  
pp. 153-158 ◽  
Author(s):  
E. V. Damaskinsky ◽  
P. P. Kulish
Keyword(s):  
Moment Problem ◽  
Special Functions ◽  
Hermite Polynomials ◽  
Irreducible Representations ◽  
Oscillator Algebra ◽  
Exponential Functions ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra ◽  
Classical Moment Problem

Different generators of a deformed oscillator algebra give rise to one-parameter families of q-exponential functions and q-Hermite polynomials. Connections of the Stieltjes and Hamburger classical moment problem with the corresponding resolution of unity are also pointed out.

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