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Interpolation Sequences of Pavlov–Korevaar–Dixon and Generalizations
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Journal Article
Interpolation Sequences of Pavlov–Korevaar–Dixon and Generalizations
2025
Overview
Interpolation sequences in the Pavlov–Korevaar–Dixon sense and their generalizations are studied. The relationship between Macintyre sequences, convergence class, and interpolation sequences is discussed. Interpolation sequences have the property that the corresponding systems of powers (exponential systems) form strongly incomplete and strongly free (minimal) systems. The issues of interpolation of sequences of natural numbers, as well as symmetric sequences of integers, have been studied to some extent in the works of J. Korevaar and M. Dixon. However, they generally failed to characterize them, but limited themselves to considering particular examples (Pavlov and Kovari sequences). Later, B. Berndtsson succeeded in proving the interpolation criterion for sequences of natural numbers. R.A. Gaisin proved a similar criterion for arbitrary positive sequences in a broader class of entire functions defined by the majorant of the convergence class. Later, he also proved the corresponding criterion for symmetric sequences of real numbers. In this article, the Pavlov–Korevaar–Dixon type interpolation criterion for arbitrary real nodes is proved.
Publisher
Pleiades Publishing,Springer Nature B.V
