Email this article On unconditional bases of reproducing kernels in Fock-type spaces
- Authors: Isaev K.P.1,2, Yulmukhametov R.S.1
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Affiliations:
- Institute of Mathematics with Computer Center, Russian Academy of Sciences
- Bashkir State University
- Issue: Vol 51, No 4 (2017)
- Pages: 283-292
- Section: Article
- URL: https://journal-vniispk.ru/0016-2663/article/view/234361
- DOI: https://doi.org/10.1007/s10688-017-0194-z
- ID: 234361
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Abstract
The existence of unconditional bases of reproducing kernels in the Fock-type spaces Fφ with radial weights φ is studied. It is shown that there exist functions φ(r) of arbitrarily slow growth for which ln r = o(φ(r)) as r → ∞ and there are no unconditional bases of reproducing kernels in the space Fφ. Thus, a criterion for the existence of unconditional bases cannot be given only in terms of the growth of the weight function.
About the authors
K. P. Isaev
Institute of Mathematics with Computer Center, Russian Academy of Sciences; Bashkir State University
Author for correspondence.
Email: orbit81@list.ru
Russian Federation, Ufa; Ufa
R. S. Yulmukhametov
Institute of Mathematics with Computer Center, Russian Academy of Sciences
Email: orbit81@list.ru
Russian Federation, Ufa
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