The existence and bounding properties of the various multipoint Padé approximants, and their complements, with respect to functions representable by series of Stieltjes, are established by using a generalized Hylleraas variational principle. The main discussion uses the phraseology of a typical frequency dependent polarizability function, and in an appendix the results are simply generalized.
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Epstein et al. (1973) studied this question.
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