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Abstract:
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There is a recent trend to describe physical
phenomena without the use of infinitesimals or infinites.
This has been accomplished replacing differential calculus
by the finite difference theory. Discrete function theory
was first introduced in l94l. This theory is concerned with
a study of functions defined on a discrete set of points in
the complex plane. The theory was extensively developed for
functions defined on a Gaussian lattice. In 1972 a very
suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0,
O < q < l, m, n 5 Z} was found and discrete analytic function
theory was developed. Very recently some work has been done
in discrete monodiffric function theory for functions
defined on H.
The theory of pseudoanalytic functions is a
generalisation of the theory of analytic functions. When the
generator becomes the identity, ie., (l, i) the theory of
pseudoanalytic functions reduces to the theory of analytic
functions. Theugh the theory of pseudoanalytic functions
plays an important role in analysis, no discrete theory is
available in literature. This thesis is an attempt in that
direction. A discrete pseudoanalytic theory is derived for
functions defined on H. |