# An operator-valued moment problem

@inproceedings{Lemnete1991AnOM, title={An operator-valued moment problem}, author={Luminiţa Lemnete}, year={1991} }

We link Carey's exponential representation of the determining function of a perturbation pair with the moment problem. We prove that an operator sequence represents the moments of a phase operator if and only if there is another positively defined sequence of operators satisfying a boundedness condition. INTRODUCTION The L-moment problem consists in characterizing the moment sequence (1) ~~~~~An = |tnf (t) dt, n Ez N of a measurable function f (with prescribed support in R) which satisfies O…

## 12 Citations

### Application of the operator phase shift in the $L$-problem of moments

- Mathematics
- 1995

This note studies more deeply the results obtained in an earlier paper of the author (An operator-valued moment problem, Proc. Amer. Math. Soc. 112 (1991)). It gives a similar condition for the…

### SOME NEW ASPECTS OF THE L-MOMENT PROBLEM

- Mathematics
- 2010

This note is devoted to the L-moment problem. The L-moment problem consists of characterising the sequence of moments an = ∫ Rt nf(t)dt, n ∈ N of a real measurable function f (with prescribed…

### MARKOV-TYPE AND OPERATOR-VALUED MULTIDIMENSIONAL MOMENT PROBLEMS, WITH SOME APPLICATIONS

- Mathematics
- 2007

In Section 2 we prove a general result which gives sufficient conditions for the existence of a solution for a Markov-type moment problem in the space Lν(T ) (the implication (b)⇒ (a) of Theorem…

### OPERATOR-VALUED TRIGONOMETRIC MOMENT AND L-MOMENT PROBLEMS

- Mathematics
- 2010

The present note is related to some finite dimensional complex matrix valued moment problem. Results about the so-called “k-complex moment problem” and “L-moment problem” will be published [8], [11].…

### On the Moment Problem and Related Problems

- MathematicsMathematics
- 2021

Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence (yj)j∈ℕn of real numbers and a closed…

### On Markov Moment Problem and Related Results

- MathematicsSymmetry
- 2021

New results and theorems on the vector-valued Markov moment problem are proved by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result.

### On truncated and full classical Markov moment problems

- Mathematics
- 2021

Abstract Giving necessary and sufficient conditions for the existence of solutions of truncated and full classical Markov moment problems in terms of the given (or measured) moments, in Lp,μ (S) (1 ≤…

### EXTENSION OF LINEAR OPERATORS, DISTANCED CONVEX SETS AND THE MOMENT PROBLEM

- Mathematics
- 2004

One applies an extension theorem of linear operators ((10, Theorem 5, p. 969)) to the classical moment problem in spaces of continuous functions on a compact interval and in spaces of analytic…

### From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications

- MathematicsMathematics
- 2020

The aim of this review paper is to recall known solutions for two Markov moment problems, which can be formulated as Hahn–Banach extension theorems, in order to emphasize their relationship with the…

### Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications

- Mathematics
- 2020

This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under…

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