Geodesic
On unconditional bases of reproducing kernels in Fock-type spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 50-61

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The existence of unconditional bases of reproducing kernels in the Fock-type spaces $\mathcal F_{\varphi }$ with radial weights $\varphi $ is studied. It is shown that there exist functions $\varphi (r)$ of arbitrarily slow growth for which $\ln r=o(\varphi (r))$ as $r\to\infty$ and there are no unconditional bases of reproducing kernels in the space $\mathcal F_{\varphi }$. Thus, a criterion for the existence of unconditional bases cannot be given only in terms of the growth of the weight function.
Keywords: Hilbert spaces, entire functions, unconditional bases, Riesz bases, reproducing kernels. 
@article{FAA_2017_51_4_a4,
     author = {K. P. Isaev and R. S. Yulmukhametov},
     title = {On unconditional bases of reproducing kernels in {Fock-type} spaces},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {50--61},
     publisher = {mathdoc},
     volume = {51},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a4/}
}
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K. P. Isaev; R. S. Yulmukhametov. On unconditional bases of reproducing kernels in Fock-type spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 50-61. http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a4/