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Oct
24
comment Composition of a compact support function with a increasing one
I should search for a suitable $v \in H_0^1(\mathbb{R}^N)$
Oct
24
comment Composition of a compact support function with a increasing one
youƕ right what I know is that $$\tag{1} \int_{\mathbb{R}^N} \langle \nabla u,\nabla v\rangle = \int_{\mathbb{R}^N} \Big( f-c(u)\Big)\ v$$ $\forall v\in H_0^1(\mathbb{R}^N)$ and $f\in L^2(\mathbb{R^n})$
Oct
24
comment Composition of a compact support function with a increasing one
then is there no way that in some since $c(u(x))$ is bounded ? :(
Oct
24
asked Composition of a compact support function with a increasing one
Oct
22
answered Use the definition of derivative to prove ln(x+1)/x =1
Oct
21
revised Another theorem of Principal value
$\overline{\mathbb{H}}^+ = \{ z\in \mathbb{C} : \operatorname{Im} z \geqslant 0\}$ corection
Oct
21
suggested suggested edit on Another theorem of Principal value
Oct
14
comment A meromorphic function is open?
can you explain a little bit more the case $1/f(1/z)$ ?
Oct
14
awarded  Teacher
Oct
14
answered The Residues of an even function or an odd function on $U$ subset open symmetric
Oct
7
accepted Essential singularity in sine function
Oct
7
comment Essential singularity in sine function
I have but it's to hard
Oct
7
comment Essential singularity in sine function
but non-existence is not enougth to say that is an essential singularity.
Oct
7
asked Essential singularity in sine function
Oct
7
comment Exponential map of an isolated singularity
I found a good prove with the pole order I will post it soon :) thanks for everything
Oct
7
comment Exponential map of an isolated singularity
can I say that $f(z)= \displaystyle \frac{p(z)}{(z-z_0)^m} + h(z)$ where $h$ is holomorphic and $p$ is a polynomial of degree $<m$.
Oct
7
comment Exponential map of an isolated singularity
I feel like $f(\{ z : 0 < \lvert z-z_0\rvert < \varepsilon\})=T(\{ z : 0 < \lvert z-z_0\rvert < \varepsilon\})$ Where $T(z)=(z-z_0)^{-m}$
Oct
7
comment Exponential map of an isolated singularity
Mmmm I beeing thinking but I just know that $f(\{ z : 0 < \lvert z-z_0\rvert < \varepsilon\})$ is unbounded. And $exp(f)=exp(Real(f))exp(i Img(f))$
Oct
6
comment Exponential map of an isolated singularity
There is $h_1$, $h_2$ , holomorphic function in some $U-\{z_{0}\} $ such that, $h_{1}(z_{0})\neq0 ,h_{2}(z_{0})\neq0 $ and:\begin{cases} h_{1}(z)(z-z_{0})^{-m}=f(z) & in\,\, z\in U-\{z_{0}\}\\ h_{2}(z)(z-z_{0})^{-n}=exp(f(z)) & in\,\, z\in U-\{z_{0}\} \end{cases} for some $n,m\geq 1$. But i can't get something maybe I'm on the wrong track
Oct
6
comment Exponential map of an isolated singularity
if $z_0$ is an essential singularity of $f$ we have that $f(U-\{z_{0}\})$ is dense in $\mathbb{C}$ so $exp(f(U-\{z_{0}\}) )$ is dense in $\mathbb{C}$. by Casorati-Weierstraß we have that $z_0$ is a essential singularity of $exp(f)$