Abstract
On truncated and full classical Markov moment problems
Highlights
The truncated moment problem is important in mathematics as well as in mathematical applications, because it involves only a finite number of moments, which are assumed to be known
This corresponds to real-life problems, where only a finite number of samples are available
In the case of onedimensional truncated moment problem, sometimes the solution can be found as a polynomial function, whose coefficients are determined by solving a Cramer system
Summary
The truncated moment problem is important in mathematics as well as in mathematical applications, because it involves only a finite number of moments (of limited order), which are assumed to be known (or given, or measurable). On the other hand, applying Theorem 2.1 once more, and using the notations and hypothesis on the finite absolute moments of the measure μ, the following result holds: Theorem 2.4. Let S ⊆ Rn be a closed unbounded subset, μ be a Borel regular M -determinate probability measure on S with finite absolute moments of all orders, (mk)k∈Nn0 be a given sequence of real numbers. We consider the construction of the solution h for the truncated moment problem related to the Theorem 2.7, in the space L2,μ ([0, ∞)) , dμ = exp (−t) dt.
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