In this paper we prove that the Turán inequality in quaternionic setting holds for all polynomials of degree n≤ 2 and for some particular subclasses of polynomials of arbitrary degree n≥ 3. It is important to note that the proofs of Turán’s inequality in the complex case do not work in the quaternionic setting for n≥ 3 , however we are lead to make the intriguing conjecture that the Turán inequality still holds for all quaternionic polynomials of arbitrary degree n≥ 3.
On the Turán Inequality for Quaternionic Polynomials
Sabadini I.
2019-01-01
Abstract
In this paper we prove that the Turán inequality in quaternionic setting holds for all polynomials of degree n≤ 2 and for some particular subclasses of polynomials of arbitrary degree n≥ 3. It is important to note that the proofs of Turán’s inequality in the complex case do not work in the quaternionic setting for n≥ 3 , however we are lead to make the intriguing conjecture that the Turán inequality still holds for all quaternionic polynomials of arbitrary degree n≥ 3.File in questo prodotto:
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