Integral inequalities for self-reciprocal polynomials |
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| Authors: | Horst Alzer |
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| Affiliation: | (1) Abt. Math. III Univ. Ulm, Ulm, Germany |
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| Abstract: | Let n ≥ 1 be an integer and let P n be the class of polynomials P of degree at most n satisfying z n P(1/z) = P(z) for all z ∈ C. Moreover, let r be an integer with 1 ≤ r ≤ n. Then we have for all P ∈ P n : | $
alpha _n (r)int_0^{2pi } {|P(e^{it} )|^2 dt} leqslant int_0^{2pi } {|P^r (e^{it} )|^2 dt} leqslant beta _n (r)int_0^{2pi } {|P(e^{it} )|^2 dt}
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alpha _n (r)int_0^{2pi } {|P(e^{it} )|^2 dt} leqslant int_0^{2pi } {|P^r (e^{it} )|^2 dt} leqslant beta _n (r)int_0^{2pi } {|P(e^{it} )|^2 dt}
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