Mapping properties of analytic functions on the unit disk

Mapping Properties of Analytic Functions on the Disk

There is a universal constant 0 < r0 < 1 with the following property. Suppose that f is an analytic function on the unit disk D, and suppose that there exists a constant M > 0 so that the Euclidean area, counting multiplicity, of the portion of f(D) which lies over the disk D(f(0), M), centered at f(0) and of radius M , is strictly less than the area of D(f(0), M). Then f must send r0D into D(f...

Notes on functions on the unit disk

As usual, R denotes the real numbers, Z denotes the integers, and C denotes the complex numbers. Thus each α ∈ C can be expressed as a + b i, where a, b are real numbers and i = −1. We call a, b the real and imaginary parts of α, and denote them Reα, Imα, respectively. If z is a complex number, with z = x + y i where x, y are the real and imaginary parts of z, then we write z for the complex co...

the effect of vocabulary instruction through semantic mapping on learning and recall of efl learners

چکیده ندارد.

On the Derivatives of Functions Analytic in the Unit Circle.

Properties of Analytic Functions

In the last few sections, we completely described entire functions through the use of everywhere convergent power series. Our goal for the following sections is to instead consider functions which are analytic almost everywhere and see which results generalize. We shall see that we do get some generalizations (like representations of functions via convergent power series), but unlike the entire...