The Newman–Shapiro problem

The Newman–Shapiro problem

We give a negative answer to the Newman–Shapiro problem on weighted approximation for entire functions formulated in 1966 and motivated by the theory of operators on the Fock space. There exists a function in the Fock space such that its exponential multiples do not approximate some entire multiples...

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Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2023-01, Vol.25 (4), p.1227-1251
Hauptverfasser: Belov, Yurii, Borichev, Alexander
Format: Artikel
Sprache:eng
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Zusammenfassung:We give a negative answer to the Newman–Shapiro problem on weighted approximation for entire functions formulated in 1966 and motivated by the theory of operators on the Fock space. There exists a function in the Fock space such that its exponential multiples do not approximate some entire multiples in the space. Furthermore, we establish several positive results under different restrictions on the function in question.
ISSN:1435-9855
1435-9863
DOI:10.4171/jems/1209