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On the
general solution of the system of cocycle equations without
regularity conditions |
On the general solution of the system of cocycle equations
without regularity conditions
Jointly written with LUDWIG REICH.
Aequationes
mathematicae 68, 200 - 229, 2004.
Abstract: We describe the general solution
(α,β), where α=(α(s,x))s∈
ℂ and β=(β(s,x))s∈ ℂ
are families of formal power series in C[[x]], of the two
so-called cocycle equations
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α(s+t,x)= α(s,x)α(t,π(s,x)),
s,t∈ ℂ |
(Co1) |
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| β(s+t,x)=
β(s,x)α(t,π(s,x)) +β(t,π(s,x)),
s,t∈ ℂ |
(Co2) |
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together with the boundary condition
where π=(π(s,x))s∈ ℂ is an iteration
group in C[[x]]. Our method is based on the knowledge of the
regular solutions of (Co1) and (Co2) and on a well-known and often
used theorem concerning the algebraic relations between exponential
functions and additive functions.
harald.fripertinger "at" uni-graz.at, April 22,
2024
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GDPR |
On the
general solution of the system of cocycle equations without
regularity conditions |
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