Abstract
In this thesis, there are three main goals. Firstly, we analyze a series expansion of entire functions in a polynomial basis based on the Wilson operator. Secondly, we formulate a Wilson analogue of the lemma on logarithmic derivatives, which helps us to derive a Wilson operator version of Nevanlinna’s Second Fundamental Theorem, and to obtain some defect relations and give a Wilson analogue of Picard’s Theorem on exceptional values. Thirdly, we give a pointwise estimate of the logarithmic Wilson difference, which will provide us with applications to the growth of meromorphic solutions to some linear Wilson difference equations and Wilson interpolation equations.