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Interpolation and approximation by rational functions in the complex domain / J. L. Walsh

Auteur principal : Walsh, Joseph Leonard, 1895-1973, AuteurType de document : MonographieCollection : Colloquium publications, 20Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 1969Description : 1 vol. (x, 405 p.) ; 26 cmISBN : 9780821810200.ISSN : 0065-9258.Bibliographie : Bibliogr. pp. 382-386. Index.Sujet MSC : 30C15, Functions of a complex variable -- Geometric function theory, Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
41A05, Approximations and expansions -- Approximations and expansions, Interpolation
30E10, Functions of a complex variable -- Miscellaneous topics of analysis in the complex domain, Approximation in the complex domain
En-ligne : Zentralblatt | MathSciNet | AMS
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Bibliogr. pp. 382-386. Index

The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title "Generalizations of Taylor's Series" would be appropriate. (source : AMS)

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