Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables
We investigate the slice holomorphic functions of several complex variables that have a bounded L-index in some direction and are entire on every slice {z⁰ + tb : t ∈ C} for every z⁰ ∈ Cⁿ and for a given direction b ∈ Cⁿ \ {0}. For this class of functions, we prove some criteria of boundedness of th...
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| Published in: | Український математичний вісник |
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| Date: | 2019 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/169438 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables / A. Bandura, O. Skaskiv // Український математичний вісник. — 2019. — Т. 16, № 2. — С. 154-180. — Бібліогр.: 31 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862711463205928960 |
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| author | Bandura, A. Skaskiv, O. |
| author_facet | Bandura, A. Skaskiv, O. |
| citation_txt | Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables / A. Bandura, O. Skaskiv // Український математичний вісник. — 2019. — Т. 16, № 2. — С. 154-180. — Бібліогр.: 31 назв. — англ. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| description | We investigate the slice holomorphic functions of several complex variables that have a bounded L-index in some direction and are entire on every slice {z⁰ + tb : t ∈ C} for every z⁰ ∈ Cⁿ and for a given direction b ∈ Cⁿ \ {0}. For this class of functions, we prove some criteria of boundedness of the L-index in direction describing a local behavior of the maximum and minimum moduli of a slice holomorphic function and give estimates of the logarithmic derivative and the distribution of zeros. Moreover, we obtain analogs of the known Hayman theorem and logarithmic criteria. They are applicable to the analytic theory of differential equations. We also study the value distribution and prove the
existence theorem for those functions. It is shown that the bounded multiplicity of zeros for a slice holomorphic function F : Cⁿ → C is the necessary and sufficient condition for the existence of a positive continuous function L : Cⁿ → R₊ such that F has a bounded L-index in direction.
The authors are thankful to Professor S. Yu. Favorov (Kharkiv) for the formulation of interesting problem.
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| first_indexed | 2025-12-07T17:30:37Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-169438 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T17:30:37Z |
| publishDate | 2019 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bandura, A. Skaskiv, O. 2020-06-13T10:14:42Z 2020-06-13T10:14:42Z 2019 Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables / A. Bandura, O. Skaskiv // Український математичний вісник. — 2019. — Т. 16, № 2. — С. 154-180. — Бібліогр.: 31 назв. — англ. 1810-3200 2010 MSC. 32A10, 32A17, 32A37, 30H99, 30A05 https://nasplib.isofts.kiev.ua/handle/123456789/169438 We investigate the slice holomorphic functions of several complex variables that have a bounded L-index in some direction and are entire on every slice {z⁰ + tb : t ∈ C} for every z⁰ ∈ Cⁿ and for a given direction b ∈ Cⁿ \ {0}. For this class of functions, we prove some criteria of boundedness of the L-index in direction describing a local behavior of the maximum and minimum moduli of a slice holomorphic function and give estimates of the logarithmic derivative and the distribution of zeros. Moreover, we obtain analogs of the known Hayman theorem and logarithmic criteria. They are applicable to the analytic theory of differential equations. We also study the value distribution and prove the
 existence theorem for those functions. It is shown that the bounded multiplicity of zeros for a slice holomorphic function F : Cⁿ → C is the necessary and sufficient condition for the existence of a positive continuous function L : Cⁿ → R₊ such that F has a bounded L-index in direction. The authors are thankful to Professor S. Yu. Favorov (Kharkiv) for the formulation of interesting problem. en Інститут прикладної математики і механіки НАН України Український математичний вісник Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables Article published earlier |
| spellingShingle | Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables Bandura, A. Skaskiv, O. |
| title | Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables |
| title_full | Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables |
| title_fullStr | Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables |
| title_full_unstemmed | Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables |
| title_short | Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables |
| title_sort | some criteria of boundedness of the l-index in direction for slice holomorphic functions of several complex variables |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/169438 |
| work_keys_str_mv | AT banduraa somecriteriaofboundednessofthelindexindirectionforsliceholomorphicfunctionsofseveralcomplexvariables AT skaskivo somecriteriaofboundednessofthelindexindirectionforsliceholomorphicfunctionsofseveralcomplexvariables |