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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 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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