On self-reciprocal polynomials
A polynomial \(P(z)\) of degree \(n\) is said to be self-reciprocal when it satisfies \(z^nP(1/z)=P(z)\) for all complex \(z\). The authors' result can be stated most easily using as norm \(\| Q\| \) of a polynomial \(Q\) the \(L^2\) norm of \(Q(e^{it})\) on \([0,2\pi]\). Theorem: If \(P(z)\) is a self-reciprocal polynomial of degree at most \(n\) then \(n/2 \leq \| P'\| /\| P\| \leq n/ \sqrt 2 \). Both estimates are sharp.
scientific article; zbMATH DE number 1192589