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The moment problem associated with the Stieltjes-Wigert polynomials

Christiansen, Jacob Stordal LU (2003) In Journal of Mathematical Analysis and Applications 277(1). p.218-245
Abstract

We consider the indeterminate Stieltjes moment problem associated with the Stieltjes-Wigert polynomials. After a presentation of the well-known solutions, we study a transformation T of the set of solutions. All the classical solutions turn out to be fixed under this transformation but this is not the case for the so-called canonical solutions. Based on generating functions for the Stieltjes-Wigert polynomials, expressions for the entire functions A, B, C, and D from the Nevanlinna parametrization are obtained. We describe T (n) (μ) for n ∈ ε ℕ when μ = μ 0 is a particular... (More)

We consider the indeterminate Stieltjes moment problem associated with the Stieltjes-Wigert polynomials. After a presentation of the well-known solutions, we study a transformation T of the set of solutions. All the classical solutions turn out to be fixed under this transformation but this is not the case for the so-called canonical solutions. Based on generating functions for the Stieltjes-Wigert polynomials, expressions for the entire functions A, B, C, and D from the Nevanlinna parametrization are obtained. We describe T (n) (μ) for n ∈ ε ℕ when μ = μ 0 is a particular N-extremal solution and explain in detail what happens when n → ∞.

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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Indeterminate moment problem, Nevanlinna parametrization, Stieltjes-Wigert polynomials
in
Journal of Mathematical Analysis and Applications
volume
277
issue
1
pages
28 pages
publisher
Academic Press
external identifiers
  • scopus:0037283138
ISSN
0022-247X
DOI
10.1016/S0022-247X(02)00534-6
language
English
LU publication?
no
id
f3cbb91b-5ab4-454e-bce6-6c67fb59758d
date added to LUP
2025-07-11 11:43:46
date last changed
2025-10-14 13:19:11
@article{f3cbb91b-5ab4-454e-bce6-6c67fb59758d,
  abstract     = {{<p>                             We consider the indeterminate Stieltjes moment problem associated with the Stieltjes-Wigert polynomials. After a presentation of the well-known solutions, we study a transformation T of the set of solutions. All the classical solutions turn out to be fixed under this transformation but this is not the case for the so-called canonical solutions. Based on generating functions for the Stieltjes-Wigert polynomials, expressions for the entire functions A, B, C, and D from the Nevanlinna parametrization are obtained. We describe T                             <sup>(n)</sup>                              (μ) for n ∈ ε ℕ when μ = μ                             <sub>0</sub>                              is a particular N-extremal solution and explain in detail what happens when n → ∞.</p>}},
  author       = {{Christiansen, Jacob Stordal}},
  issn         = {{0022-247X}},
  keywords     = {{Indeterminate moment problem; Nevanlinna parametrization; Stieltjes-Wigert polynomials}},
  language     = {{eng}},
  month        = {{01}},
  number       = {{1}},
  pages        = {{218--245}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Mathematical Analysis and Applications}},
  title        = {{The moment problem associated with the Stieltjes-Wigert polynomials}},
  url          = {{http://dx.doi.org/10.1016/S0022-247X(02)00534-6}},
  doi          = {{10.1016/S0022-247X(02)00534-6}},
  volume       = {{277}},
  year         = {{2003}},
}