3
votes
1answer
168 views

Uniform convergent series

Let $\Omega$ be domain in $\mathbb C^2$. For each compact set $K_j$ define the holomorphic function $f_j$ on $\Omega$, such that $$\sup_{k_j}|f_j|<2^{-j}.$$ Define $$f= ...
1
vote
1answer
118 views

Domain of convergence of Mulitvariable series

What is region of convergence $(D\subset \mathbb C^2)$ of $$\sum_{n=0}^\infty(z_1^kz_2^l)^n$$ for fixed $k$ and $l$ integers. $z_1$ and $z_2$ are elements of complex plane. What is method of ...