08/06/2021, 12:15 AM
I want to point out the maximum modulus principle , jensens formula and nevanlinna theory are strongly related and important here.
Why ? because by those we can bound the value of the log(z) by the value of the log in the neighbourhood : log(z+y).
Jensen also confirms that multiplicity does not go crazy locally in the limit process.
This all helps to prove boundedness , convergeance and analyticity.
remember that log(0) and 0 do not occur by taking the log^[n] , hence making these theorems valid !!
And therefore helping in both the inner and outer proof methods.
( by induction , assuming it starts as true , which we can numerically check ( very likely ) )
regards
tommy1729
Tom Marcel Raes
Why ? because by those we can bound the value of the log(z) by the value of the log in the neighbourhood : log(z+y).
Jensen also confirms that multiplicity does not go crazy locally in the limit process.
This all helps to prove boundedness , convergeance and analyticity.
remember that log(0) and 0 do not occur by taking the log^[n] , hence making these theorems valid !!
And therefore helping in both the inner and outer proof methods.
( by induction , assuming it starts as true , which we can numerically check ( very likely ) )
regards
tommy1729
Tom Marcel Raes