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Interpolation and Approximation by Entire Functions
In this note we study the connection between best approximation and interpolation by entire functions on the real line. A general representation for entire interpolants is outlined. As an illustration, best upper and lower approximations from the class of functions of fixed exponential type to the Gaussian are constructed. §1. Approximation Background The Fourier transform of φ ∈ L(R) is define...
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In 1877, E. I. Zolotarev [19, 2] found an explicit expression, in terms of elliptic functions, of the rational function of given degree m which is uniformly closest to sgn (x) on the union of two intervals [−1,−a] ∪ [a, 1]. This result was subject to many generalizations, and it has applications in electric engineering. Surprisingly, to the best of our knowledge, the similar problem for polynom...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1955
ISSN: 0026-2285
DOI: 10.1307/mmj/1031710533