# A note on an integrated cauchy functional equation

A note on an integrated cauchy functional equation In characterizing the semistable law, [Shimizu reduced the problem to solving the equation $$H(x) = \int_0^\infty {H(x + y)} d(\mu - v)(y)$$ ,x≥0 whereμ andv are given positive measures on [0, ∞). In this note, we obtain a simple proof and show that some of his conditions can be weakened. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# A note on an integrated cauchy functional equation

, Volume 5 (2) – Jul 14, 2005
5 pages

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Publisher
Springer Journals
Copyright © 1989 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02009743
Publisher site
See Article on Publisher Site

### Abstract

In characterizing the semistable law, [Shimizu reduced the problem to solving the equation $$H(x) = \int_0^\infty {H(x + y)} d(\mu - v)(y)$$ ,x≥0 whereμ andv are given positive measures on [0, ∞). In this note, we obtain a simple proof and show that some of his conditions can be weakened.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 14, 2005

### References

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