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Interpolation

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Complex Analysis

Part of the book series: Universitext ((UTX))

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Abstract

In this chapter we study we study interpolation by holomorphic functions from a different point of view from that used in 12. In particular, the Germay Theorem (12.14) says that there exists an entire function that interpolates given values at a given sequence of points. There are three major approaches that can be taken to proving such a theorem. The first is via the Mittag-Leffler Theorem and Weierstrass products, which involves writing an explicit formula. The second is via solving infinitely many linear equations in infinitely many unknowns, the Taylor coefficients. (See [M. Eidelheit] and [P. J. Davis].) The third is via functional analysis—specifically the Banach-Dieudonné theorem. Kere we take the third route, obtaining in the process a functional analysis proof of Theorem 12.18.

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© 1984 Springer-Verlag New York Inc.

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Luecking, D.H., Rubel, L.A. (1984). Interpolation. In: Complex Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8295-9_18

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  • DOI: https://doi.org/10.1007/978-1-4613-8295-9_18

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90993-6

  • Online ISBN: 978-1-4613-8295-9

  • eBook Packages: Springer Book Archive

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