THESIS
2017
viii, 134 pages : illustrations ; 30 cm
Abstract
We develop a function theory that the Wilson divided-difference operator gives
rise to. Firstly, we study entire functions by developing a Wiman-Valiron theory
for a polynomial series whose basis interacts nicely with the Wilson operator.
Secondly, we extend this polynomial basis so as to obtain a Laurent-type series,
and formulate a residue theory regarding the functions defined by this kind of
series. Thirdly, we study meromorphic functions by giving a Nevanlinna theory
of the Wilson operator, and we obtain a Wilson analogue of the little Picard
theorem. Finally, we investigate the images of holomorphic curves in the complex
projective space CP
n which miss certain hyperplanes in the sense of the Wilson
operator, and formulate a Picard-type result about these holomorphic curves....[
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We develop a function theory that the Wilson divided-difference operator gives
rise to. Firstly, we study entire functions by developing a Wiman-Valiron theory
for a polynomial series whose basis interacts nicely with the Wilson operator.
Secondly, we extend this polynomial basis so as to obtain a Laurent-type series,
and formulate a residue theory regarding the functions defined by this kind of
series. Thirdly, we study meromorphic functions by giving a Nevanlinna theory
of the Wilson operator, and we obtain a Wilson analogue of the little Picard
theorem. Finally, we investigate the images of holomorphic curves in the complex
projective space CP
n which miss certain hyperplanes in the sense of the Wilson
operator, and formulate a Picard-type result about these holomorphic curves.
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