 |  |  | Functional equations and group actions |
Functional equations and group actions
Investigating the apparent motion of the so-called "mean sun" one is lead to
the functional equation
M(l,j)·x(s+m)= M(l+m,j)·x(s),
where x(s) is a unit vector in R3 and M(l,j) is
a matrix representing the local coordinate system in a point P on the
earth's surface, which represents the directions to the east, the north and
to the zenith.
This equation can be solved quite easily (cf. [41]).
But if one assumes that also M is unknown and if one considers a more
general setting, one is lead to the equation
g(s)·x(t+u)= g(s+t)·x(u),
where now ·: G´X -> X is a group action of some group G on a set
X (and g as well as x are unknown).
The special case X=Rn, G=GLn(R) would be of
particular interest.
It should be mentioned that with respect to this topic there are close
connections to earlier projects P12642 - MAT
and P10189 - MAT.
harald.fripertinger@kfunigraz.ac.at,
last changed: February 9, 2001
| | | Functional equations and group actions |