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19h
answered Unit ball separable $\Longrightarrow$ Space separable
20h
comment Unit ball separable $\Longrightarrow$ Space separable
Your proof looks good to me.
May
21
comment $\sin(x^2)$ in terms of $\sin(x)$ and $\cos(x)$
This would only work if $x$ were an integer.
May
18
answered Gaining some insight about Picard–Lindelöf theorem.
May
17
comment proving that $\text{ri rge}\,A=\text{ri conv rge}\,A$
Could you perhaps provide a definition of $\text{rge}(A)$?
May
17
comment Sequence of monotone functions problem
OK mysterious downvote, state your issue...
May
17
answered Sequence of monotone functions problem
May
16
comment Trying to find a function such that $\lim_{x\to\infty} f(x)=0$ but $\lim_{x\to\infty} f'(x) \ \text{does not exist}$.
x^x isn't necessary, just x^2.
May
15
answered Trying to find a function such that $\lim_{x\to\infty} f(x)=0$ but $\lim_{x\to\infty} f'(x) \ \text{does not exist}$.
May
15
comment $\sum \frac {1}{n^2 a_n}$ is divergent
That inequality won't help. You would want it the other way around: $\frac{1}{n^2a_n}\geq \frac{1}{n}$.
May
12
answered What are the limitations /shortcomings of Fourier Transform and Fourier Series?
May
12
revised Suggest a follow up book to Axler's Linear Algebra Done Right?
added 668 characters in body
May
12
answered Suggest a follow up book to Axler's Linear Algebra Done Right?
May
10
comment What's so special about $p=2$ for the $L^p$ spaces?
Fair point, see edit. The point is that the integral will not define a bounded linear functional unless $g\in L^q$.
May
10
revised What's so special about $p=2$ for the $L^p$ spaces?
added 38 characters in body
May
10
answered What's so special about $p=2$ for the $L^p$ spaces?
May
9
comment Absolute Value of Complex Integral
I'm not sure it would be practical to try and prove this using Cauchy Schwartz, but one way to prove it is using Riemann sums. See here
May
9
answered Prove that $\int_0^{\infty} \frac{x^2}{x^4+5x^2+4}dx = \frac{\pi}{6}$
May
8
answered Is the “homogenous solution” to a second-order linear homogenous DE always valid?
May
8
comment Space of Tikhonov regularization of an Ill poised problems.
I don't see any reason why you would need that much abstraction. Most ill-posed problems have very concrete formulations in terms of integral operators or solutions of differential equations, so Sobolev spaces are usually the correct tool.