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 [Regular tetration] [Iteration series] norming fixpoint-dependencies Gottfried Ultimate Fellow Posts: 767 Threads: 119 Joined: Aug 2007 08/30/2010, 10:25 AM (This post was last modified: 08/30/2010, 10:28 AM by Gottfried.) (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 « Next Oldest | Next Newest »

 Messages In This Thread [Regular tetration] [Iteration series] norming fixpoint-dependencies - by Gottfried - 07/28/2010, 03:04 PM RE: [Regular tetration] norming fixpoint-dependencies - by Gottfried - 07/28/2010, 09:49 PM RE: [Regular tetration] norming fixpoint-dependencies - by bo198214 - 07/29/2010, 04:53 AM RE: [Regular tetration] norming fixpoint-dependencies - by Gottfried - 07/29/2010, 11:36 AM RE: [Regular tetration] norming fixpoint-dependencies - by Gottfried - 08/29/2010, 10:31 PM RE: [Regular tetration] norming fixpoint-dependencies - by tommy1729 - 08/30/2010, 09:32 AM RE: [Regular tetration] norming fixpoint-dependencies - by Gottfried - 08/30/2010, 10:25 AM RE: [Regular tetration] norming fixpoint-dependencies - by tommy1729 - 08/30/2010, 11:08 AM RE: [Regular tetration] norming fixpoint-dependencies - by Gottfried - 08/30/2010, 12:34 PM RE: [Regular tetration] norming fixpoint-dependencies - by tommy1729 - 08/30/2010, 11:14 PM RE: [Regular tetration] norming fixpoint-dependencies - by Gottfried - 08/31/2010, 05:36 AM RE: [Regular tetration] norming fixpoint-dependencies - by tommy1729 - 08/31/2010, 11:55 PM

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