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.
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