Palacios, Francisco; Rubió, Pere Generalized Pólya condition for Birkhoff interpolation with lacunary polynomials. (English) Zbl 1020.41004 Appl. Math. E-Notes 3, 124-129 (2003). Summary: Lacunary polynomials are polynomials of the form \(\sum_{i=1}^n a_i x^{k_1}\). We introduce the problem of Birkhoff interpolation with lacunary polynomials and formulate a generalized Pólya condition. In the framework of Birkhoff interpolation with lacunary polynomials, the generalized Pólya condition characterizes conditionally regular interpolation matrices. The generalized Pólya condition is simpler than the Pólya condition for algebraic Birkhoff interpolation and it is equivalent to the Pólya condition when \(k_j= j-1\). Reviewer: Boris I.Golubov (Dolgoprudny) Cited in 1 ReviewCited in 4 Documents MSC: 41A05 Interpolation in approximation theory 41A10 Approximation by polynomials 26C05 Real polynomials: analytic properties, etc. Keywords:Birkhoff interpolation; Pólya condition; lacunary polynomials; interpolation matrices PDFBibTeX XMLCite \textit{F. Palacios} and \textit{P. Rubió}, Appl. Math. E-Notes 3, 124--129 (2003; Zbl 1020.41004) Full Text: EuDML