Delvos, Franz-Jürgen; Knoche, Ludger Lacunary interpolation by antiperiodic trigonometric polynomials. (English) Zbl 0931.42003 BIT 39, No. 3, 439-450 (1999). Summary: The problem of lacunary trigonometric interpolation is investigated. Does a trigonometric polynomial \(T\) exist which satisfies \(T(x_k)= a_k\), \(D^mT(x_k)= b_k\), \(0\leq k\leq n-1\), where \(x_k= k\pi/n\) is a nodal set, \(a_k\) and \(b_k\) are prescribed complex numbers, \(D= {d\over dx}\) and \(m\in\mathbb{N}\). Results obtained by several authors for the periodic case are extended to the antiperiodic case. In particular, solvability is established when \(n\) as well as \(m\) are even. In this case a periodic solution does not exist. Cited in 1 ReviewCited in 29 Documents MSC: 42A15 Trigonometric interpolation Keywords:antiperiodic trigonometric polynomials; lacunary trigonometric interpolation PDFBibTeX XMLCite \textit{F.-J. Delvos} and \textit{L. Knoche}, BIT 39, No. 3, 439--450 (1999; Zbl 0931.42003) Full Text: DOI