(08/30/2010, 09:32 AM)tommy1729 Wrote: let me recap

A is carleman of z.

B is carleman of base^z.

carleman f(z) = A/(1+B)

but why is 1+B invertible for bases > eta ??

Let M=(I+B), W = M^-1;

ß some eigenvalue of B |ß|>1 , µ =ß+1 eigenvalue of M

w = 1/(1+ß) the according eigenvalue of W

- Heuristically it converges when size is increased (no proof yet).

- I suppose: because all |ß|>=1, ==> µ =/= zero,

or equivalently

- 0 < |1/(1+ß)| < 1 for all ß

No proof yet

Gottfried Helms, Kassel