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The cardinal series in Hilbert space

Published online by Cambridge University Press:  24 October 2008

J. D. Weston
J. D. Weston
Affiliation:
The UniversitySheffield
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Extract

The name ‘cardinal function’ was given to

by E. T. Whittaker (1), who considered it as a ‘smooth’ approximation to a function f(x), having the same values as f(x) at the points a + rw (r = 0, ± 1, ± 2, …). It has since been extensively studied (2), mainly from the point of view of interpolation theory. Hardy (3), however, observed that the functions νr(t) defined by

form a normal orthogonal set on the interval (−∞, ∞), for r = 0, ± 1, ± 2, …. This fact suggests a discussion of the cardinal series from the point of view of mean-square approximation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 3 , July 1949 , pp. 335 - 341
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

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