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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| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Назва видання: | Український математичний вісник |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/169438 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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| id |
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irk-123456789-1694382020-06-14T01:26:44Z Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables Bandura, A. Skaskiv, O. 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. 2019 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/169438 en Український математичний вісник Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bandura, A. Skaskiv, O. |
| spellingShingle |
Bandura, A. Skaskiv, O. Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables Український математичний вісник |
| author_facet |
Bandura, A. Skaskiv, O. |
| author_sort |
Bandura, A. |
| title |
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_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_sort |
some criteria of boundedness of the l-index in direction for slice holomorphic functions of several complex variables |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2019 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/169438 |
| 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. |
| series |
Український математичний вісник |
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2023-10-18T22:25:11Z |
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