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

Andriy Bandura; Tetyana Salo; Oleh Skaskiv

Mathematica Bohemica (2024)

  • Volume: 149, Issue: 2, page 247-260
  • ISSN: 0862-7959

Abstract

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For a given direction 𝐛 ∈ 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 as the coefficients of the equation. Our considerations use some estimates involving a directional logarithmic derivative and distribution of zeros on all directional slices in the unit ball.

How to cite

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Bandura, Andriy, Salo, Tetyana, and Skaskiv, Oleh. "Non-homogeneous directional equations: Slice solutions belonging to functions of bounded $L$-index in the unit ball." Mathematica Bohemica 149.2 (2024): 247-260. <http://eudml.org/doc/299432>.

@article{Bandura2024,
abstract = {For a given direction $\{\bf b\}\in \mathbb \{C\}^n\setminus \lbrace \{\bf 0\}\rbrace $ 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 as the coefficients of the equation. Our considerations use some estimates involving a directional logarithmic derivative and distribution of zeros on all directional slices in the unit ball.},
author = {Bandura, Andriy, Salo, Tetyana, Skaskiv, Oleh},
journal = {Mathematica Bohemica},
keywords = {bounded index; bounded $L$-index in direction; slice function; holomorphic function; directional differential equation; bounded $l$-index; directional derivative; unit ball},
language = {eng},
number = {2},
pages = {247-260},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non-homogeneous directional equations: Slice solutions belonging to functions of bounded $L$-index in the unit ball},
url = {http://eudml.org/doc/299432},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Bandura, Andriy
AU - Salo, Tetyana
AU - Skaskiv, Oleh
TI - Non-homogeneous directional equations: Slice solutions belonging to functions of bounded $L$-index in the unit ball
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 2
SP - 247
EP - 260
AB - For a given direction ${\bf b}\in \mathbb {C}^n\setminus \lbrace {\bf 0}\rbrace $ 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 as the coefficients of the equation. Our considerations use some estimates involving a directional logarithmic derivative and distribution of zeros on all directional slices in the unit ball.
LA - eng
KW - bounded index; bounded $L$-index in direction; slice function; holomorphic function; directional differential equation; bounded $l$-index; directional derivative; unit ball
UR - http://eudml.org/doc/299432
ER -

References

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