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- Title
Approximation on unbounded subsets and the moment problem.
- Authors
Olteanu, Octav
- Abstract
We apply L1 approximation to characterize existence of the solutions of the multidimensional moment problems in terms of quadratic mappings, similarly to the one-dimensional case. To this end, we approximate any nonnegative continuous compactly supported function by sums of tensor products of positive polynomials in each separate variable. On the other hand, an application of an earlier result concerning Markov moment problems related to distanced convex subsets is discussed. Finally, we deduce an application of an abstract moment problem to a concrete Markov moment problem. The Hahn-Banach principle and its generalizations play an important role along this work.
- Subjects
APPROXIMATION theory; MATHEMATICAL bounds; MOMENT problems (Mathematics); EXISTENCE theorems; TENSOR products; CONVEX domains
- Publication
Applied Sciences, 2014, Vol 16, p99
- ISSN
1454-5101
- Publication type
Article