Abstract
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. A new property of solutions of the homogeneous equation named graded dichotomy is introduced and it is proved that the right-sided invertibility of binomial functional operators is equivalent to the existence of graded dichotomy.
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In memory of Nikolai Dmitrievich Kopachevsky.
The results presented in this work were repeatedly reported at the Crimea Autumn Mathematical School, organized and directed by Nikolai Dmitrievich.
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 2, Dedicated to the memory of Professor N. D. Kopachevsky, 2021.
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Antonevich, A.B. Right-Sided Invertibility of Binomial Functional Operators and Graded Dichotomy. J Math Sci 278, 12–38 (2024). https://doi.org/10.1007/s10958-024-06903-w
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DOI: https://doi.org/10.1007/s10958-024-06903-w