We prove that the Fock space 
with a nonradial weight φ has an unconditional basis of reproducing kernels if and only if such a basis exists for the Fock space 
with a certain radial weight υ determined by φ.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. Seip, “Density theorems for sampling and interpolation in the Bargmann–Fock space. I,” J. Reine Angew. Math. 429, 91–106 (1992).
K. Seip and R. Wallsten, “Density theorems for sampling and interpolation in the Bargmann–Fock space. II,” J. Reine Angew. Math. 429, 107–113 (1992).
A. Borichev, R. Dhuez, and K. Kellay, “Sampling and interpolation in large Bergman and Fock spaces,” J. Funct. Anal. 242, No. 2, 563–606 (2007).
A. Borichev and Yu. Lyubarskii, “Riesz bases of reproducing kernels in Fock type spaces,” J. Inst. Math. Jussieu 9, No. 3, 449–461 (2010).
A. Baranov, Yu. Belov, and A. Borichev, “Fock type spaces with Riesz bases of reproducing kernels and de Branges spaces,” Stud. Math. 236, No. 2, 127–142 (2017).
K. P. Isaev, A. V. Lutsenko, and R. S. Yulmukhametov, “Necessary condition for the existence of unconditional bases of reproducing kernels for Hilbert spaces of entire functions,” J. Math. Sci. 257, No. 5, 662–671 (2021).
K. P. Isaev and R. S. Yulmukhametov, “On a sufficient condition for the existence of unconditional bases of reproducing kernels in Hilbert spaces of entire functions,” Lobachevskii J. Math. 42, No. 6, 1154–1165 (2021).
K. P. Isaev and R. S. Yulmukhametov, “Equivalent conditions for the existence of unconditional bases of reproducing kernels in spaces of entire functions,” Probl. Anal. Issues Anal. 10, No. 3, 41–52 (2021).
K. P. Isaev and R. S. Yulmukhametov, “Riesz bases of normalized reproducing kernels in Fock type spaces,” Anal. Math. Phys. 12, No. 1, Paper No. 11 (2022).
K. P. Isaev, K. V. Trunov, and R. S. Yulmukhametov, “Equivalent norms in Hilbert spaces with unconditional bases of reproducing kernels,” J. Math. Sci. 250, No. 2, 310–321 (2020).
K. P. Isaev, A. V. Lutsenko, and R. S. Yulmukhametov, “Unconditional bases in weakly weighted spaces of entire functions,” St. Petersbg. Math. J. 30, No. 2, 253–262 (2019).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Problemy Matematicheskogo Analiza 113, 2022, pp. 37-43.
Rights and permissions
About this article
Cite this article
Isaev, K.P., Lutsenko, A.V. & Yulmukhametov, R.S. Unconditional Bases of Reproducing Kernels for Fock Spaces with Nonradial Weights. J Math Sci 260, 748–755 (2022). https://doi.org/10.1007/s10958-022-05725-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-022-05725-y