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Generalized Pólya condition for Birkhoff interpolation with lacunary polynomials. (English) Zbl 1020.41004

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 \(k_j= j-1\).

MSC:

41A05 Interpolation in approximation theory
41A10 Approximation by polynomials
26C05 Real polynomials: analytic properties, etc.
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