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Non-homogeneous directional equations: Slice solutions belonging to functions of bounded $L$ -index in the unit ball

Andriy Bandura; Tetyana Salo; Oleh Skaskiv — 2024

Mathematica Bohemica

For a given direction $𝐛 \in ℂ^{n} ∖ {0}$ we study non-homogeneous directional linear higher-order equations whose all coefficients belong to a class of joint continuous functions which are holomorphic on intersection of all directional slices with a unit ball. Conditions are established providing boundedness of $L$ -index in the direction with a positive continuous function $L$ satisfying some behavior conditions in the unit ball. The provided conditions concern every solution belonging to the same class of functions...

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Non-homogeneous directional equations: Slice solutions belonging to functions of bounded L -index in the unit ball

Non-homogeneous directional equations: Slice solutions belonging to functions of bounded $L$ -index in the unit ball