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[Regular tetration] [Iteration series] norming fixpoint-dependencies
#7
(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
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Messages In This Thread
RE: [Regular tetration] norming fixpoint-dependencies - by Gottfried - 08/30/2010, 10:25 AM

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