2012/03/13 by Alberto Ibort, A. Ibort, Ibort, A. +5
Economics, Econometrics and Finance · Mathematics · #44A60 #46G25 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Stochastic processes and financial applications #math.FA #msc:44A60 #msc:46G25
paper · pdf · doi:10.48550/arxiv.1203.2967
arxiv created 2012/03/13 · openalex publication_date 2012/03/13 · arxiv updated 2012/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a multi-index sequence μk, k = (k1,..., kn) ∈ ℕ0n, necessary and sufficient conditions are given for the existence of a regular Borel polymeasure γ on the unit interval I= [0,1] such that μk = ∫In t1k1⊗ ... ⊗ tnkn γ. This problem will be called the weak multilinear Hausdorff problem of moments for μk. 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 μ on [0,1] such that Lμ(f1,..., fn) = ∫I f1(t) ... fn(t) μ(dt) where Lμ is the n-linear moment functional on the space of continuous functions on the unit interval defined by the sequence μk. 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.