We characterize simply interpolating sequences (also known as onto interpolating sequences) for complete Pick spaces. We show that a sequence is simply interpolating if and only if it is strongly separated. This answers a question of Agler and McCarthy. Moreover, we show that in many important examples of complete Pick spaces, including weighted Dirichlet spaces on the unit disc and the Drury–Arveson space in finitely many variables, simple interpolation does not imply multiplier interpolation. In fact, in those spaces, we construct simply interpolating sequences that generate infinite measures, and uniformly separated sequences that are not multiplier interpolating.

Chalmoukis, N., Dayan, A., Hartz, M. (2024). Simply interpolating sequences in complete Pick spaces. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 377(5), 3261-3286 [10.1090/tran/9123].

Simply interpolating sequences in complete Pick spaces

Chalmoukis, N;
2024

Abstract

We characterize simply interpolating sequences (also known as onto interpolating sequences) for complete Pick spaces. We show that a sequence is simply interpolating if and only if it is strongly separated. This answers a question of Agler and McCarthy. Moreover, we show that in many important examples of complete Pick spaces, including weighted Dirichlet spaces on the unit disc and the Drury–Arveson space in finitely many variables, simple interpolation does not imply multiplier interpolation. In fact, in those spaces, we construct simply interpolating sequences that generate infinite measures, and uniformly separated sequences that are not multiplier interpolating.
Articolo in rivista - Articolo scientifico
complete Pick space; Feichtinger conjecture; Interpolating sequence; strong separation; uniformly minimal;
English
26-feb-2024
2024
377
5
3261
3286
none
Chalmoukis, N., Dayan, A., Hartz, M. (2024). Simply interpolating sequences in complete Pick spaces. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 377(5), 3261-3286 [10.1090/tran/9123].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/478479
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