Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables

• Дата: 2019
• Автори: Bandura, A., Skaskiv, O.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут прикладної математики і механіки НАН України 2019
• Назва видання: Український математичний вісник
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/169438
• 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.

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.