Many nonlinear optimal control and estimation problems can be formulated as Tikhonov variational problems in an infinite dimensional reproducing kernel Hilbert space. This paper shows that any closed hall contained in such spaces is compact in the sup-norm topology. This result is exploited to obtain conditions which guarantee existence Of Solutions for the aforementioned problems as well as numerical algorithms whose convergence is guaranteed in the space Of Continuous functions. (C) 2008 Elsevier Ltd. All rights reserved.