Bernstein-type Inequalities for Bicomplex Polynomials
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Description
This paper considers the well-known Bernstein and Erdős–Lax inequalities in the case of bicomplex polynomials. We shall prove that the validity of these inequalities depends on the norm in use and we consider the cases of the Euclidean, Lie, dual Lie and hyperbolic-valued norms. In particular, we show that in the case of the Euclidean norm the inequalities holds keeping the same relation with the degree of the polynomial that holds in the classical complex case, but we have to enlarge the radius of the ball. In the case of the dual Lie norm both the relation with the degree and the radius of the ball have to be changed. Finally, we prove that the exact analogs of the two inequalities hold when considering the Lie norm and the hyperbolic-valued norm. In the case of these two norms we also show the validity of the maximum modulus principle for bicomplex holomorphic functions.
ISBN
978-3-319-62362-7
Publication Date
9-2017
Publisher
Springer
City
Cham, Switzerland
Keywords
Bicomplex and hyperbolic numbers, polynomials, Bernstein inequality, Erdős–Lax inequality
Disciplines
Analysis | Numerical Analysis and Computation | Other Mathematics
Recommended Citation
Sabadini I., Vajiac A., Vajiac M.B. (2017) Bernstein-type Inequalities for Bicomplex Polynomials. In: Colombo F., Sabadini I., Struppa D., Vajiac M. (eds) Advances in Complex Analysis and Operator Theory. Trends in Mathematics. Birkhäuser, Cham
Copyright
Springer
Comments
In Fabrizio Colombo, Irene Sabadini, Daniele Sgtruppa, and Mihaela Vajiac (Eds.), Advances in Complex Analysis and Operator Theory. Trends in Mathematics.
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