Define an

analytic function p : D [right arrow] C by

For convenience, write [PHI](z) := [PHI](a; c; z), and define an

analytic function p : D [right arrow] C by

for unbounded G, where f is an

analytic function on G with known boundary values on [GAMMA].

This class is called convex class of

analytic function.

In [7], the following Carleman boundary value problem for

analytic functions is given: Problem [C.

H](n) we may express the

analytic functions h and g as

Srivastava, The Hardy space of

analytic functions associated with certain one-parameter families of integral operators, J.

4) defines B(z) as an

analytic function in any simply connected domain that does not contain 0, for example in the plane cut along the negative real axis or along any other ray from 0.

We were hoping that the students would discover for themselves the following theorem: An

analytic function f (z) is conformal (preserving the magnitude and direction of angles) at all points where [florin]' (z) [not equal to] 0.

At present Sine approximation of the

analytic function on a real axis which exponentially decreases in its end points is thoroughly discussed in [10, 15].

If U(t) is a complex-valued

analytic function in a neighborhood of t = 0 and

infinity]] is an

analytic function of [omega] in the lower half of the [omega]-plane, and its inverse transform as a function of time t is equal to zero when t < 0.