1
vote
1answer
82 views

Analytic continuation of function given as integral

I have a function $I(D)$ defined by the following integral representation $$ I(D)=\int_0^\infty\mathrm{d}\alpha\,(1+2\alpha)^{-D/2} $$ which is clearly only sensible for $D>2$. The result of the ...
2
votes
1answer
261 views

Area and locally one-to-one analytic mappings of the unit disk.

We learned about conformal mappings and various properties of locally one-to-one, analytic mappings of the unit disk. I am having trouble with the following problem, can anyone help? Let $f(z) ...
6
votes
3answers
341 views

Expressing the area of the image of a holomorphic function by the coefficients of its expansion

I have the following problem. Let $f:D\to \mathbb C$ be a holomorphic function, where $D=\{z:|z|\leq 1\}.$ Let $$f(z)=\sum_{n=0}^\infty c_nz^n.$$ Let $l_2(A)$ denote the Lebesgue measure of a set ...