Geodesic
Zeros of Functions in Weighted Spaces with Mixed Norm
Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 279-294 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the spaces of analytic functions $f$ in the unit disk with mixed norm and measure satisfying the $\Delta_2$-condition, sharp necessary conditions on subsequences of zeros $\{z_{n_k}(f)\}$ of the function $f$ are obtained in terms of subsequences of numbers $\{n_k\}$. These conditions can be used to define, in the spaces with mixed norm, subsets of functions with certain extremal properties; these subsets provide answers to a number of questions about the zero sets of the spaces under consideration and, in particular, about weighted Bergman spaces.
Keywords: weighted space with mixed norm, weighted Bergman space, distribution of moduli of zeros, zero set of a function, Hardy space. 
@article{MZM_2013_94_2_a10,
     author = {E. A. Sevast'yanov and A. A. Dolgoborodov},
     title = {Zeros of {Functions} in {Weighted} {Spaces} with {Mixed} {Norm}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {279--294},
     year = {2013},
     volume = {94},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a10/}
}
TY  - JOUR
AU  - E. A. Sevast'yanov
AU  - A. A. Dolgoborodov
TI  - Zeros of Functions in Weighted Spaces with Mixed Norm
JO  - Matematičeskie zametki
PY  - 2013
SP  - 279
EP  - 294
VL  - 94
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a10/
LA  - ru
ID  - MZM_2013_94_2_a10
ER  - 
%0 Journal Article
%A E. A. Sevast'yanov
%A A. A. Dolgoborodov
%T Zeros of Functions in Weighted Spaces with Mixed Norm
%J Matematičeskie zametki
%D 2013
%P 279-294
%V 94
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a10/
%G ru
%F MZM_2013_94_2_a10
E. A. Sevast'yanov; A. A. Dolgoborodov. Zeros of Functions in Weighted Spaces with Mixed Norm. Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 279-294. http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a10/

[1] S. V. Shvedenko, “Klassy Khardi i svyazannye s nimi prostranstva analiticheskikh funktsii v edinichnom kruge, polikruge i share”, Itogi nauki i tekhn. Ser. Mat. anal., 23, VINITI, M., 1985, 3–124 | MR | Zbl

[2] L. N. Biryukov, “Raspredelenie nulei funktsii iz klassov $A_{p,-1,l}$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2005, no. 5, 13–20 | MR | Zbl

[3] E. A. Sevastyanov, A. A. Dolgoborodov, “O raspredelenii nulei funktsii iz prostranstv Bergmana s vesom”, Matem. zametki, 86:1 (2009), 95–109 | DOI | MR | Zbl

[4] E. A. Sevastyanov, A. A. Dolgoborodov, “Pismo v redaktsiyu”, Matem. zametki, 94:2 (2013), 317–320

[5] A. A. Dolgoborodov, “O nulyakh funktsii iz prostranstv Bergmana i nekotorykh blizkikh k nim prostranstv”, Matem. zametki, 88:2 (2010), 201–216 | DOI | MR | Zbl

[6] C. Horowitz, “Zeros of functions in the Bergman spaces”, Duke Math. J., 41:4 (1974), 693–710 | DOI | MR | Zbl

[7] H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman Spaces, Grad. Texts in Math., 199, Springer-Verlag, New York, 2000 | MR | Zbl

[8] A. M. Sedletskii, “O probleme Myuntsa–Sasa”, Matem. zametki, 39:1 (1986), 97–107 | MR | Zbl

[9] A. M. Sedletskii, “O nulyakh analiticheskikh funktsii klassov $A^p_{\alpha}$”, Aktualnye voprosy teorii funktsii, Izd-vo RGU, Rostov-na-Donu, 1987, 24–29