Author:
Jarczyk Justyna,Jarczyk Witold
Abstract
UDC 517.9
We find all nonnegative solutions
f
of the equation
f
(
x
)
=
∏
j
=
1
n
f
(
s
j
x
)
p
j
,
defined in a one-sided vicinity of
0
and having a prescribed asymptotic at
0.
The main theorem extends a result obtained by J. A. Baker [Proc. Amer. Math. Soc., <strong>121</strong>, 767–773 (1994)].
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Reference13 articles.
1. J. Aczél, Lectures on functional equations and their applications, Academic Press, New York, London (1966).
2. J. A. Baker, A functional equation from probability theory, Proc. Amer. Math. Soc., 121, 767–773 (1994).
3. G. Baxter, On a characterization of the normal law, Proc. Nat. Acad. Sci. USA, 41, 383–385 (1955).
4. L. Davies, R. Shimizu, On identically distributed linear statistics, Ann. Inst. Statist. Math., 28, 469–489 (1976).
5. R. G. Laha, E. Lukacs, On a functional equation which occurs in a characterization problem, Aequationes Math., 16, 259–274 (1977).