Riesz-haviland criterion for incomplete data. (English) Zbl 1214.30020

Summary: The aim of this paper is to analyze a “support-free” version of the Riesz-Haviland theorem proved recently by the present authors, which characterizes truncations of the complex moment problem via positivity condition on appropriate families of polynomials in \(z\) and \(\tilde z\). The attention is focused on modifications of the positivity condition as well as the assumption on admissible truncations. The former results in truncations for which the corresponding “support-free” Riesz-Haviland condition locates a representing measure on the distinguished subset of the complex plane, while the latter effects a non-integral variant of the Riesz-Haviland theorem.


30E05 Moment problems and interpolation problems in the complex plane
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