Abstract
The existence of unconditional bases of reproducing kernels in the Fock-type spaces F φ 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 F φ . Thus, a criterion for the existence of unconditional bases cannot be given only in terms of the growth of the weight function.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 51, No. 4, pp. 50–61, 2017
Original Russian Text Copyright © by K. P. Isaev and R. S. Yulmukhametov
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Isaev, K.P., Yulmukhametov, R.S. On unconditional bases of reproducing kernels in Fock-type spaces. Funct Anal Its Appl 51, 283–292 (2017). https://doi.org/10.1007/s10688-017-0194-z
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DOI: https://doi.org/10.1007/s10688-017-0194-z