Two extremal problems for trigonometric polynomials with a prescribed number of harmonics (Q1174019)

The author presents some further results in connection with the problem of determining the asymptotic behaviour (as \(N \to \infty)\) of \(\inf \biggl\| \bigl( \sum^ N_{k=1} e^{ij_ kx} \bigr) \biggr\|_{L_ q}\), where the derivative of order \(\alpha \geq 0\) is understood in the sense of Weyl and the infimum is taken over all possible sets of distinct integers \(\{j_ 1,\ldots,j_ N\}\).