Geodesic
On unconditional bases of reproducing kernels in Fock-type spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 50-61 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2017},
     volume = {51},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a4/}
}
TY  - JOUR
AU  - K. P. Isaev
AU  - R. S. Yulmukhametov
TI  - On unconditional bases of reproducing kernels in Fock-type spaces
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2017
SP  - 50
EP  - 61
VL  - 51
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a4/
LA  - ru
ID  - FAA_2017_51_4_a4
ER  - 
%0 Journal Article
%A K. P. Isaev
%A R. S. Yulmukhametov
%T On unconditional bases of reproducing kernels in Fock-type spaces
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2017
%P 50-61
%V 51
%N 4
%U http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a4/
%G ru
%F FAA_2017_51_4_a4
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/

[1] N. Aronszajn, “Theory of reproducing kernels”, Trans. Amer. Math. Soc., 68:3 (1950), 337–404 | DOI | MR | Zbl

[2] S. V. Hru$\rm \check s$$ \check c$ev, N. K. Nikolżskii, B. S. Pavlov, “Unconditional bases of exponentials and of reproductional kernels”, Complex Analysis and Spectral Theory, Lecture Notes in Math., 864, 1981, 214–335 | DOI | MR | Zbl

[3] A. Borichev, Yu. Lyubarskii, “Riesz bases of reproducing kernels in Fock type spaces”, J. Inst. Math. Jussieu, 9:3 (2010), 449–461 | DOI | MR | Zbl

[4] A. Baranov, Yu. Belov, A. Borichev, “Fock type spaces with Riesz bases of reproducing kernels and de Branges spaces”, Studia Math., 236:2 (2017), 127–142 | DOI | MR | Zbl

[5] R. S. Yulmukhametov, “Asimptoticheskaya approksimatsiya subgarmonicheskikh funktsii”, Sib. matem. zhurn., 26:4 (1985), 159–175 | MR | Zbl

[6] K. P. Isaev, R. S. Yulmukhametov, “Bezuslovnye bazisy iz vosproizvodyaschikh yader v gilbertovykh prostranstvakh tselykh funktsii”, Ufimsk. matem. zhurn., 5:3 (2013), 67–77 | MR

[7] R. A. Bashmakov, K. P. Isaev, R. S. Yulmukhametov, “O geometricheskikh kharakteristikakh vypuklykh funktsii i integralax Laplasa”, Ufimsk. matem. zhurn., 2:1 (2010), 3–16 | MR | Zbl