Abstract
We describe some radial Fock type spaces which possess Riesz bases of normalized reproducing kernels, the spaces \(\mathcal F_{\varphi }\) of entire functions f such that \(fe^{-\varphi }\in L_2(\mathbb C)\), where \(\varphi (z) = \varphi (|z|)\) is a radial subharmonic function. We prove that \(\mathcal F_{\varphi }\) has Riesz basis of normalized reproducing kernels for sufficiently regular \(\psi (r)=\varphi (e^r)\) such that \(\psi ''(r)\) is bounded above.
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The research was supported by the grant of Russian Science Foundation (project no. 21-11-00168)
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Isaev, K.P., Yulmukhametov, R.S. Riesz bases of normalized reproducing kernels in Fock type spaces. Anal.Math.Phys. 12, 11 (2022). https://doi.org/10.1007/s13324-021-00623-z
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DOI: https://doi.org/10.1007/s13324-021-00623-z