Abstract
We show that an interpolating sequence for the weighted Banach space of analytic functions on the unit ball of a Hilbert space is hyperbolically separated. In the case of the so-called standard weights, a sufficient condition for a sequence to be linear interpolating is given in terms of Carleson type measures. Other conditions to be linearly interpolating are provided as well. Our results apply to the space of Bloch functions of such unit ball.
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Acknowledgements
This paper was completed during the 2016 fall semester while Mikael Lindström was visiting Universidad de Valencia whose hospitality is gratefully acknowledged with special thanks to Pablo Galindo. We warmly thank the referees for their very careful reading and the suggestions provided.
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O. Blasco: partially supported by MTM2014-53009-P. P. Galindo: partially supported by MTM2014-53241-P. M. Lindström: partially supported by MTM2014-53241-P and the Academy of Finland project 296718. A. Miralles: partially supported by MTM2014-53241-P, P1-1B2014-35 and AICO/2016/030.
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Blasco, O., Galindo, P., Lindström, M. et al. Interpolating sequences for weighted spaces of analytic functions on the unit ball of a Hilbert space. Rev Mat Complut 32, 115–139 (2019). https://doi.org/10.1007/s13163-018-0271-8
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DOI: https://doi.org/10.1007/s13163-018-0271-8
Keywords
- Interpolating sequence
- Hyperbolically separated
- Bloch function in the ball
- Infinite dimensional holomorphy
- Weighted space of analytic functions