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Functions which operate on positive definite functions

Published online by Cambridge University Press:  24 October 2008

Daniel Rider
Daniel Rider
Affiliation:
University of Wisconsin
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Extract

1. Introduction. Let P be a collection of functions mapping some set into the complex plane C and let δ be a subset of C. A function F: δ → C is said to operate on P provided the composition F o φ belongs to P whenever φ ∈ P and the range of φ is contained in δ. The basic problem is to characterize the functions which operate.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 1 , January 1971 , pp. 87 - 97
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Herz, C. S.Fonctionsopérant surles fonctions définies-positive. Ann. Inst. Fourier (Grenoble) 13 (1963), 161–180.CrossRefGoogle Scholar
(2)Hewitt, E. and Ross, K. A.Abstract harmonic analysis. I (Springer-Verlag; Heidelberg, 1963).Google Scholar
(3)Rudin, W.Positive definite sequences and absolute monotonic functions. Duke Math. J. 26 (1959), 617–622.CrossRefGoogle Scholar
(4)Rudin, W.Fourier analysis on groups (Interscience; New York, 1962).Google Scholar
(5)Widder, D. V.The Laplace transform (Princeton, 1941).Google Scholar