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XVIII.—On the Consistency of Cardinal Function Interpolation. Parts I, II

Published online by Cambridge University Press:  15 September 2014

W. L. Ferrar
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Extract

In a previous paper on the Cardinal Function it was proved that, calling

the cardinal function of the table of values αr at the point α + rw], “the cardinal function of the table of values [C(rw′) at the point rw′] is a function C1(x) which coincides with C(x) provided that 0<w′<w, and Σ | αn/n |, Σ |α−n/n| are convergent.”

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 47 , 1928 , pp. 230 - 242
Copyright
Copyright © Royal Society of Edinburgh 1928

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References

page 230 note * Proc. Roy. Soc. Edin., 46 (1926), 323–333.

page 230 note † Math. Zeitschrift, 25 (1926), 321–347.

page 230 note ‡ Proc. London Math. Soc. (2), 26 (1926), 1–11.

page 231 note * Proc. Edin. Math. Soc. (2), 1 (1927), 41–46.

page 232 note * K denotes a fixed constant.

page 233 note * Cf. Goursat, , Cours d'Analyse, 2 (1918), p. 171 Google Scholar; or Jordan, , Cours d'Analyse, 2 (1913), p. 333.Google Scholar

page 237 note * Picard's theorem extended to meromorphic functions, cf. Julia, , Leçons sur les Fonctions Uniformes (Collection Borel), 1924.Google Scholar

page 238 note * Proc. Edin. Math. Soc. (2), 1 (1927), 41–46.

page 239 note * Cf. Hobson, , Theory of Functions of a Real Variable, vol ii. (1926), p. 599.Google Scholar

page 239 note † Hobson, , loc. cit., § 399, p. 614.Google Scholar

page 240 note * Hobson, , loc. cit., p. 599.Google Scholar

page 242 note * Math. Zeitschrift, 25 (1926), 321–347.