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Abstract:

Abstract. Let D and ∂D denote the open unit disk and the unit circle of the complex plane, respectively. We denote the set of all polynomials of degree at most n with real coefficients by Pn. We denote the set of all polynomials of degree at most n with complex coefficients by Pc n. We define the truncation operator Sn for polynomials Pn ∈Pc n of the form by (1.1) Sn(Pn)(z):= Pn(z):= nX j=0 nX j=0 ajz j, aj ∈ C, eajz j, eaj: = (aj/|aj|)min{|aj|, 1}. We define the norms of the truncation operators by and �Sn � real maxz∈∂D |Sn(Pn)(z)| ∞,∂D: = sup Pn∈Pn maxz∈∂D |Pn(z)| �Sn � comp ∞,∂D: = sup

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