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## moment problems and orthogonal polynomials (1989)

Venue: | Transactions of the American Mathematical Society |

Citations: | 3 - 0 self |

### Citations

283 |
The Problem of Moments,
- Shohat, Tamarkin
- 1943
(Show Context)
Citation Context ...iteria expressed in terms of the coefficients in (1.1) for deciding the determinacy or indeterminacy of the Hamburger moment problem. Probably the best known criterion of this type is due to Carleman =-=[4; 14]-=-. Carleman's theorem says that the moment problem is determined if (1.6) £C/2 = ~- Our approach is based upon use of chain sequences and as such limits our results to cases where the spectrum is restr... |

275 |
Analytic Theory of Continued Fractions.
- Wall
- 1948
(Show Context)
Citation Context ...rion given by Wouk is that the Hamburger moment problem is determined if X^ñ'/4 = °° and if the related Jacobi matrix is positive. Wall and Wetzel's quadratic form characterization of chain sequences =-=[16]-=- shows that positivity of the Jacobi matrix implies that again, {an(-M)} is a chain sequence (after a reflection) so that once again the spectrum is contained in a half-line. Wouk obtains these criter... |

73 |
Recurrence relations, continued fractions, and orthogonal polynomials,”
- Askey, Ismail
- 1984
(Show Context)
Citation Context ...als for which, in many cases, our methods (and all others that we are aware of) fail to yield conclusions. Askey and Ismail have recently studied intensively several classes of orthogonal polynomials =-=[3]-=-. This important work analyzes, among others, the orthogonal polynomials whose monic form satisfies (1.1) with (6.1) cn+x=aq~", Xn+x=(l-q")(b-cq"~X)qX~2" , 0 < \q\ < 1, where either (i) 0 < q < 1, b >... |

51 |
Some hypergeometric orthogonal polynomials. -
- Wilson
- 1980
(Show Context)
Citation Context ... of orthogonal polynomials [11, p. 638]. In fact, this limiting case turns out to be a special limiting case of Wilson's 47"3 orthogonal polynomials and Wilson has given their orthogonality relations =-=[17]-=-. Specifically, in this case we have cn+x =2(2« + l)2, Xn+X =4«2(4«2-l) 2 2 _1 that an = « (4« - 1) > 1/4. The determinacy of the associated Hamburger moment problems cannot be determined by the theor... |

28 | Some orthogonal q-polynomials - Al-Salam, Carlitz - 1965 |

18 |
Sur les équations intégrales singulières à noyau réel et symetrique, Almqvist and Wiksell
- Carleman
- 1923
(Show Context)
Citation Context ...iteria expressed in terms of the coefficients in (1.1) for deciding the determinacy or indeterminacy of the Hamburger moment problem. Probably the best known criterion of this type is due to Carleman =-=[4; 14]-=-. Carleman's theorem says that the moment problem is determined if (1.6) £C/2 = ~- Our approach is based upon use of chain sequences and as such limits our results to cases where the spectrum is restr... |

13 |
Chain sequences and orthogonal polynomials,
- Chihara
- 1962
(Show Context)
Citation Context ...rect some annoying misprints that appeared in [6]. We will use the notation (2-1) an(x) = -/-tt^-r, a„=a(0). " (c„ - x)(cn+x - x) » "v A major role played by the sequence {«„(x)}^, fundamental result =-=[5; 8]-=-: is explained by the following License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-useHAMBURGER MOMENT PROBLEMS AND ORTHOGONAL POLYNOMIALS 191 Theo... |

10 |
On the numerators of the convergents of the Stieltjes continued fractions
- Sherman
- 1993
(Show Context)
Citation Context ... polynomials of order j " (the polynomials corresponding to the recurrence coefficients c]n = c , XJn = a .) and conclude that the corresponding Hamburger moment problem is indeterminate. But Sherman =-=[13]-=- has noted that if the Hamburger moment problem for (1.1) is determined, so is the moment problem for the corresponding numerator polynomials (of (2.15)); hence by induction, the moment problem for th... |

5 | The Classical Moment Problem - Ahiezer - 1965 |

2 | Difference equations and - Wouk - 1953 |

1 | polynomials whose distributions have finite point spectra - Orthogonal - 1980 |

1 |
properties of orthogonal polynomials on unbounded sets
- Spectral
(Show Context)
Citation Context ... must have L < \ . If L < ¿, then {an} is an eventual chain sequence and (2.2) is automatically satisfied. However, if L= \, then each of the three extremes, cr = -oo, |cr| < oo, cr = oo, is possible =-=[11]-=- so we will have to impose the additional hypothesis (2.2)(ii) explicitly. We continue to use the notation of §2, so that {«i*}^0 denotes the minimal parameter sequence of the chain sequence {a[ (c)} ... |

1 |
The limit circle case for a positive-definite J-fraction
- Dennis, Wall
(Show Context)
Citation Context ...based upon use of chain sequences and as such limits our results to cases where the spectrum is restricted to a half-line. Thus our results are more limited than those of Carleman and Dennis and Wall =-=[12]-=- (see also §5) which predict determinacy of the Hamburger moment problem without assuming any bounds on the spectrum. On the other hand, our theorems are applicable to many cases for which the aforeme... |