Open AccessRight-Sided Invertibility of Binomial Functional Operators and Graded Dichotomy
Author(s) -
А. Б. Антоневич
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-2-208-236
Subject(s) - mathematics , binomial (polynomial) , invertible matrix , homogeneous , pure mathematics , binomial theorem , property (philosophy) , binomial coefficient , discrete mathematics , combinatorics , statistics , philosophy , epistemology
In this paper, we consider the right-sided invertibility problem for binomial functional operators. It is known that such operators are invertible iff there exists dichotomy of solutions of the homogeneous equation. New property of solutions of the homogeneous equation named graded dichotomy is introduced and it is proved that right-sided invertibility of binomial functional operators is equivalent to existence of graded dichotomy.