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- Title
BOUNDEDNESS OF THE L-INDEX IN A DIRECTION OF THE SUM AND PRODUCT OF SLICE HOLOMORPHIC FUNCTIONS IN THE UNIT BALL.
- Authors
BAKSA, V. P.; BANDURA, A. I.; SALO, T. M.
- Abstract
Let b ∈ Cn \ {0} be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice {z0 + tb: t ∈ C} with the unit ball Bn = {z ∈ Cn: |z| := √|z|21 + . . . + |zn|² < 1} for any z0 ∈ Bn. For this class of functions there is considered the concept of boundedness of L-index in the direction b, where L: Bn → R+ is a positive continuous function such that L(z) > β|b|/1-|z| and β > 1 is some constant. There are presented sufficient conditions that the sum of slice holomorphic functions of bounded L-index in direction belong this class. This class of slice holomorphic functions is closed under the operation of multiplication.
- Subjects
HOLOMORPHIC functions; MATHEMATICAL constants; UNIT ball (Mathematics); MULTIPLICATION; MATHEMATICAL variables
- Publication
Matematychni Studii, 2022, Vol 57, Issue 2, p216
- ISSN
1027-4634
- Publication type
Article
- DOI
10.30970/ms.57.2.216-224