### Citations

248 |
The classical moment problem.
- Akhiezer
- 1965
(Show Context)
Citation Context ...tements on the size and location of the support of µ. 4 KRISTINE EY In general, the representing measure of ϕ is not unique. In fact, there exist either exactly one or uncountably many solutions, cf. =-=[1, 10]-=-. But there always exists a solution µ, such that P[R] is dense in L2(R, µ). This kind of solution is called N-extremal. In that case, there exists a self-adjoint tridiagonal linear operator A : D(A) ... |

169 | Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions, - Berg, Christensen, et al. - 1984 |

148 | The classical moment problem as a self–adjoint finite difference operator.
- Simon
- 1998
(Show Context)
Citation Context ...tements on the size and location of the support of µ. 4 KRISTINE EY In general, the representing measure of ϕ is not unique. In fact, there exist either exactly one or uncountably many solutions, cf. =-=[1, 10]-=-. But there always exists a solution µ, such that P[R] is dense in L2(R, µ). This kind of solution is called N-extremal. In that case, there exists a self-adjoint tridiagonal linear operator A : D(A) ... |

103 |
Harmonic Analysis of Probability Measures on Hypergroups.
- Bloom, Heyer
- 1995
(Show Context)
Citation Context ...n the space of real bounded characters on (N0, ∗), which is homeomorphic to the set Ds := {x ∈ R : |Rn(x)| ≤ 1 ∀n ∈ N0} ⊆ [−1; 1]. For reference on hypergroups and the Bochner theorem see for example =-=[4, 7]-=-. The assumptions of this theorem are rather strong, just as the outcome. We are interested in the question, which assumptions are actually necessary in order to obtain single statements of the theore... |

56 |
Polynomials and Polynomial Inequalities,
- Borwein, Erdelyi
- 1995
(Show Context)
Citation Context ...me ε > 0. W.l.o.g. we assume [a; b] = [−2−ε; 2+ε]. Define Q(x) := 12P ((2 + ε)x). Since |P (x)| ≤ 2 for all x ∈ [−2 − ε; 2 + ε], we have |Q(x)| ≤ 1 for all x ∈ [−1; 1]. By Chebyshev’s inequality, cf. =-=[5]-=-, we have |Q(x)| ≤ |Tn(x)| for all x ∈ R\ [−1; 1]. But this is a contradiction, since the leading coefficient of Q equals (2+ε) n 2 , whereas the leading coefficient of Tn equals 2 n−1. It remains to ... |

24 |
Orthogonal polynomials and hypergroups
- Lasser
- 1983
(Show Context)
Citation Context ...n the space of real bounded characters on (N0, ∗), which is homeomorphic to the set Ds := {x ∈ R : |Rn(x)| ≤ 1 ∀n ∈ N0} ⊆ [−1; 1]. For reference on hypergroups and the Bochner theorem see for example =-=[4, 7]-=-. The assumptions of this theorem are rather strong, just as the outcome. We are interested in the question, which assumptions are actually necessary in order to obtain single statements of the theore... |

23 | Lectures on analysis. Vol. II: Representation theory. - Choquet - 1969 |

10 |
Convolution algebras which are not necessarily probability preserving. In: Applications of hypergroups and related measure algebras (Summer Research Conference
- Rösler
- 1993
(Show Context)
Citation Context ...We are interested in the question, which assumptions are actually necessary in order to obtain single statements of the theorem. A large step in this direction has already been made by Margit Rösler =-=[9]-=-. She was able to show that replacing assumption (1) by (2) m+n∑ k=|m−n| |g(m,n; k)| ≤ C ∀m,n ∈ N0, 2000 Mathematics Subject Classification. 43A62; 26C05; 26D05; 44A60; 11C08. Key words and phrases. p... |

8 | How to choose modified moments
- Beckermann, Bourreau
- 1998
(Show Context)
Citation Context ...t the theorem uncovers the fact that a function ϕ : N0 → C is positive definite if and only if ( ϕ(n) ) n∈N0 is a sequence of modified moments, which play an important role in numerical analysis, cf. =-=[2]-=-. Proof. Suppose ϕ is a positive definite function. By Choquet’s representation theorem, cf. [6, 34.9 Thm, 34.11 Lemma, p. 279f], it suffices to show that for any nonnegative polynomial Q ∈ P[R], i.e.... |

3 |
On the problem of modified moments
- Lasser
- 1984
(Show Context)
Citation Context ...quence with respect to( Pn ) n∈N0 if and only if there exists a µ ∈M+(R) with infinite support and ϕ(n) = ∫ R Pn dµ ∀n ∈ N0. Remark that this corollary is essentially equivalent to the main result of =-=[8]-=-. By dropping some of the assumptions for the polynomial sequence and the boundedness of ϕ, we loose an important property of the representing measure µ, namely the characterization of the support of ... |