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Nov
21
comment Continuous function on a compact metric space is uniformly continuous
@shilov You should look at the last line of the proof. The inequality should explain it.
Nov
3
comment Fourier transform of the characteristic function
@user929304 I see. I don't know if it makes sense, this is beyond my modest knowledge of Fourier transforms. It's not very useful but: Surely the decaying properties of $\mathcal F (\chi_{[c,d]}$ and $\mathcal F (\chi_{[0,1]}$ are almost identical?
Nov
3
comment Fourier transform of the characteristic function
@user929304 It's not clear to me what you mean. For example, "not differentiable in the usual sense" -- well apart from the points $c,d$ its derivative is 0, or am I missing something? And as for the FT of $\chi_{[c,d]}$: It looks to me like it's decaying. The expression is term one minus term two where each term is of the form one over something exponential times linear. But I might be missing something, it's been a while.
Nov
3
comment invertibility in C*-algebra
I don't understand why you would try to prove that $a-\lambda$ is invertible if by assumption ($\lambda \in \sigma (a)$) it isn't. What is your question?
Nov
3
comment Is it true that $\mathbb{Q}(\sqrt{3},\sqrt{7})=\mathbb{Q}(\sqrt{3},\sqrt{21})$?
Related: math.stackexchange.com/q/93463/5798
Nov
2
comment Proving $2\mathbb Z$ is maximal ideal of $\mathbb Z$
@RobertoMilandro Yes, exactly.
Nov
2
comment Proving $2\mathbb Z$ is maximal ideal of $\mathbb Z$
Regarding your second sentence: It's not possible for any ideal in $\mathbb Z$ to have more elements than $\mathbb Z$.
Oct
29
comment Let $F\subseteq K $ and $V$ is a vector space over $K$ with a basis. What is the basis of $V$ over $F$?
So... $K$ is a field with a basis $e_i$? Does that mean $K$ is also a vector space?
Oct
3
comment Calculating $\int_\gamma \frac{1}{1+z^2}\,dz$
@Tom-Tom Great, thank you.
Oct
2
comment Calculating $\int_\gamma \frac{1}{1+z^2}\,dz$
What's a primitive function?
Oct
2
comment How to prove function $f(x,y)=\frac{1}{xy}$ is not uniformly continuous?
Nicely done. ${}$
Sep
29
comment Branching points of the function $(z^2-1)^{2/3}$
Why are $\pm 1$ branch points? I looked up the definition and as far as I understand a critical point $z_0$ is called branch point it the winding number of a path around $f(z_0)$ is greater than one. In this case, $f(\pm 1) = 0$ but since there is no pole at $0$ it is not clear to me why the winding number around $0$ would not be $0$. What am I missing?
Sep
28
comment Showing that an inclusion is null homotopic
@morphic I don't remember.
Sep
28
comment finding a linear transformation
I might be missing something but is there any reason why you can't just define $\theta = \alpha \oplus \beta$?
Sep
22
comment Reference for guided exercises in Group Theory
Have a look at Joseph Gallian's Contemporary Abstract Algebra. It contains solutions to all odd numbered problems.
Sep
19
comment $f,g,h$ be a holomorphic functions such that $|f(z)|+|g(z)|+|h(z)|=1$
@Potato Ok, right, of course it's enough to show they are constant on an open subset. I believe you but I don't yet see how to get the open subset. Concretely, if they are not constant each one has some open subset on which they are non zero, say $U_f, U_g$ and $U_h$. How do we guarantee that their intersection is non empty?
Sep
19
comment $f,g,h$ be a holomorphic functions such that $|f(z)|+|g(z)|+|h(z)|=1$
So $g$ is the square root of $f$ but if $f$ is zero anywhere the square root is not differentiable in which case $g$ would not be holomorphic. So your answer assumes that $f,g,h$ are non-zero on $U$. Or am I missing something here?
Sep
18
comment Functions of a Complex Variable and Complex Differentiability
Did you mean $f'(z)\neq0$?
Sep
18
comment Suppose that $f: D \to D$ is analytic with $f(0) = 0$. Show $f$ assumes all values $z$ with $|z| \leq 1/2$ with given assumption
$D$ is most probably the open unit disk in the complex plane.
Sep
18
comment Complex Differentiability with respect to x and y
@user251257 Got it. Thank you for your comments! I will edit the answer.