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- W2017435146 abstract "Given a multi-index sequence $$mu _mathbf{k }$$ , $$mathbf k = (k_1, ldots , k_n) in mathbb N _0^n$$ , necessary and sufficient conditions are given for the existence of a regular Borel polymeasure $$gamma $$ on the unit interval $$I= [0,1]$$ such that $$mu _mathbf{k } = int _{I^n} t_1^{k_1}otimes cdots otimes t_n^{k_n} , gamma $$ . This problem will be called the weak multilinear Hausdorff problemof moments for $$mu _mathbf{k }$$ . Comparison with classical results will allow us to relate the weak multilinear Hausdorff problem with the multivariate Hausdorff problem. A solution to the strong multilinear Hausdorff problem of moments will be provided by exhibiting necessary and sufficient conditions for the existence of a Radon measure $$mu $$ on $$[0,1]$$ such that $$L_mu (f_1,ldots , f_n) = int _{I} f_1(t) cdots f_n(t) , mu (dt)$$ where $$L_mu $$ is the $$n$$ -linear moment functional on the space of continuous functions on the unit interval defined by the sequence $$mu _mathbf{k }$$ . Finally the previous results will be used to provide a characterization of a class of weakly harmonizable stochastic processes with bimeasures supported on compact sets." @default.
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- W2017435146 date "2013-04-19" @default.
- W2017435146 modified "2023-10-16" @default.
- W2017435146 title "On the multilinear Hausdorff problem of moments" @default.
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- W2017435146 doi "https://doi.org/10.1007/s13163-013-0123-5" @default.
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