Some weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball
We partially reinforce some criteria of $L$-index boundedness in direction for functions analytic in the unit ball. These results describe local behavior of directional derivatives on the circle, estimates of maximum modulus, minimum modulus of analytic function, distribution of its zeros and modulu...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2019-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1503 |
| _version_ | 1818288220453994496 |
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| author | A.I. Bandura |
| author_facet | A.I. Bandura |
| author_sort | A.I. Bandura |
| collection | DOAJ |
| description | We partially reinforce some criteria of $L$-index boundedness in direction for functions analytic in the unit ball. These results describe local behavior of directional derivatives on the circle, estimates of maximum modulus, minimum modulus of analytic function, distribution of its zeros and modulus of directional logarithmic derivative of analytic function outside some exceptional set. Replacement of universal quantifier on existential quantifier gives new weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball. The results are also new for analytic functions in the unit disc. The logarithmic criterion has applications in analytic theory of differential equations. This is convenient to investigate index boundedness for entire solutions of linear differential equations. It is also apllicable to infinite products.
Auxiliary class of positive continuous functions in the unit ball (so-denoted $Q_{\mathbf{b}}(\mathbb{B}^n)$) is also considered. There are proved some characterizing properties of these functions. The properties describe local behavior of these functions in the polydisc neighborhood of every point from the unit ball. |
| first_indexed | 2024-12-13T01:52:55Z |
| format | Article |
| id | doaj.art-0b23083944b24cfba5ba851eac0a4e20 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-13T01:52:55Z |
| publishDate | 2019-06-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-0b23083944b24cfba5ba851eac0a4e202022-12-22T00:03:28ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102019-06-01111142510.15330/cmp.11.1.14-251503Some weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ballA.I. Bandura0Ivano-Frankivsk National Technical University of Oil and Gas, 15 Karpatska str., 76019, Ivano-Frankivsk, UkraineWe partially reinforce some criteria of $L$-index boundedness in direction for functions analytic in the unit ball. These results describe local behavior of directional derivatives on the circle, estimates of maximum modulus, minimum modulus of analytic function, distribution of its zeros and modulus of directional logarithmic derivative of analytic function outside some exceptional set. Replacement of universal quantifier on existential quantifier gives new weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball. The results are also new for analytic functions in the unit disc. The logarithmic criterion has applications in analytic theory of differential equations. This is convenient to investigate index boundedness for entire solutions of linear differential equations. It is also apllicable to infinite products. Auxiliary class of positive continuous functions in the unit ball (so-denoted $Q_{\mathbf{b}}(\mathbb{B}^n)$) is also considered. There are proved some characterizing properties of these functions. The properties describe local behavior of these functions in the polydisc neighborhood of every point from the unit ball.https://journals.pnu.edu.ua/index.php/cmp/article/view/1503bounded $l$-index in directionanalytic functionunit ballmaximum modulusdirectional derivativedistribution of zero |
| spellingShingle | A.I. Bandura Some weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball Karpatsʹkì Matematičnì Publìkacìï bounded $l$-index in direction analytic function unit ball maximum modulus directional derivative distribution of zero |
| title | Some weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball |
| title_full | Some weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball |
| title_fullStr | Some weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball |
| title_full_unstemmed | Some weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball |
| title_short | Some weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball |
| title_sort | some weaker sufficient conditions of l index boundedness in direction for functions analytic in the unit ball |
| topic | bounded $l$-index in direction analytic function unit ball maximum modulus directional derivative distribution of zero |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/1503 |
| work_keys_str_mv | AT aibandura someweakersufficientconditionsoflindexboundednessindirectionforfunctionsanalyticintheunitball |