8 citations · 29 across the 22 of their papers we have counts for
6 papers · 1 filter
An operator-theoretic existence proof of solutions to planar Dirichlét problems
Timothy H. McNicholl
By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichlét problems for planar Jordan domains with at least two…
Computing links and accessing arcs
Timothy H. McNicholl
Sufficient conditions are given for the computation of accessing arcs and arcs that links boundary components of multiply connected domains. The existence of a not-computably-acces…
Computing boundary extensions of conformal maps
Timothy H. McNicholl
Let be a conformal map of the unit disk onto a domain , and suppose has a boundary extension. We show that arbitrarily good approximations of the boundary extension of $…
An effective Caratheodory Theorem
Timothy H. McNicholl
By means of the property of effective local connectivity, the computability of finding the Carathéodory extension of a conformal map of a Jordan domain onto the unit disk is demons…
The power of backtracking and the confinement of length
Timothy H. McNicholl
We show that there is a point on a computable arc that does not belong to any computable rectifiable curve. We also show that there is a point on a computable rectifiable curve wit…
Effective local connectivity properties
Dale Daniel, Timothy H. McNicholl
We investigate, and prove equivalent, effective versions of local connectivity and uniformly local arcwise connectivity for connected and computably compact subspaces of Euclidean…