On identities for derivative operators
DOI:
https://doi.org/10.5604/01.3001.0013.7230Słowa kluczowe:
derivative operators, polynomial inequalitiesAbstrakt
Let X be a commutative algebra with unity e and let D be a derivative on X that means the Leibniz rule is satised: D(f g) = D(f) g +f D(g). If D(k) is k-th iteration of D then we prove that the following identity holds for any positive integer k:
As an application we prove a sharp version of Bernstein’s inequality for trigonometric polynomials.
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Prawa autorskie (c) 2019 Państwowa Wyższa Szkoła Zawodowa w Tarnowie & Autorzy
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