| Title:
|
Maximum modulus in a bidisc of analytic functions of bounded ${\bf L}$-index and an analogue of Hayman's theorem (English) |
| Author:
|
Bandura, Andriy |
| Author:
|
Petrechko, Nataliia |
| Author:
|
Skaskiv, Oleh |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
339-354 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We generalize some criteria of boundedness of $\mathbf {L}$-index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p+1)$th partial derivative by lower order partial derivatives (analogue of Hayman's theorem). (English) |
| Keyword:
|
analytic function |
| Keyword:
|
bidisc |
| Keyword:
|
bounded ${\mathbf L}$-index in joint variables |
| Keyword:
|
maximum modulus |
| Keyword:
|
partial derivative |
| Keyword:
|
Cauchy's integral formula |
| MSC:
|
30D60 |
| MSC:
|
32A10 |
| MSC:
|
32A17 |
| MSC:
|
32A30 |
| idZBL:
|
Zbl 06997370 |
| idMR:
|
MR3895260 |
| DOI:
|
10.21136/MB.2017.0110-16 |
| . |
| Date available:
|
2018-11-29T09:22:08Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147473 |
| . |
| Reference:
|
[1] Bandura, A.: New criteria of boundedness of L-index in joint variables for entire functions.Mat. Visn. Nauk. Tov. Im. Shevchenka 13 (2016), 58-67 Ukrainian. Zbl 06742099 |
| Reference:
|
[2] Bandura, A. I., Bordulyak, M. T., Skaskiv, O. B.: Sufficient conditions of boundedness of L-index in joint variables.Mat. Stud. 45 (2016), 12-26. Zbl 1353.30030, MR 3561322, 10.15330/ms.45.1.12-26 |
| Reference:
|
[3] Bandura, A. I., Skaskiv, O. B.: Entire Functions of Several Variables of Bounded Index.Chyslo, Lviv (2015). Zbl 1342.32001, MR 3725018 |
| Reference:
|
[4] Bandura, A. I., Skaskiv, O. B.: Analytic in the unit ball functions of bounded $L$-index in direction.Avaible at https://arxiv.org/abs/1501.04166. MR 3702166 |
| Reference:
|
[5] Bandura, A. I., Petrechko, N. V., Skaskiv, O. B.: Analytic functions in a polydisc of bounded L-index in joint variables.Mat. Stud. 46 (2016), 72-80. Zbl 1373.30043, MR 3649050, 10.15330/ms.46.1.72-80 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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[11] Lepson, B.: Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index.Entire Funct. and Relat. Parts of Anal., La Jolla, Calif. 1966 Proc. Sympos. Pure Math. 11, AMS, Providence, Rhode Island (1968), 298-307. Zbl 0199.12902, MR 0237788 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
