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Feb
4
comment Computation of an iterated integral
Very good Answer! (+1)
Feb
2
comment If $f(x)$ is continuous at $ x=0$
Your assumtion is that $f = O(x^{2})$ near $x=0$
Jan
30
answered Reflexive Banach spaces, compactness
Jan
30
answered Problem calcualting Fourier coeff. of tent function.
Jan
24
comment Compute the limit and show that uN converges weakly
Riesz representation tells you exactly what the continuous linear functionals are. My suggestion is to try to compute $\lim _{N \rightarrow \infty\langle{u^{N},e_{j}\rangle}$, for each $j$ and
Jan
22
comment Do these series converge uniformly?
Hints: For the first one, what can be said about the series for $x\leq 0$? For the second one, try splitting the sum
Jan
11
revised Integration of $\int_0^{+\infty} \frac{\ln(1/x)}{1-x^2}\,dx$
added 2 characters in body; added 88 characters in body
Jan
11
answered Integration of $\int_0^{+\infty} \frac{\ln(1/x)}{1-x^2}\,dx$
Jan
10
comment Deciding whether a function $f$, defined on $\mathbb{R}^2$, is Lebesgue-integrable over two sets
For (ii): If $f(x,y)$ where integrable, then the integral of $|f(x,y)|$ over $A$ should be finite, independent of the order of integration. But..
Jan
10
comment Prove that $τ(m^n)$ and $n$ are coprime $(m,n ∈ N^+)$
$m^{n}$ might have more distinct divisors, if say $m$ is not a prime. But there is a way to work around it, by utilizing the multiplicativity of $\tau$
Jan
7
revised On uniqueness of extension of linear functional on $\ell^{1}$
added 29 characters in body
Jan
5
comment Show that $\int_0^1 f(x)g(x)\,dx=0$ for all $g\in C([0,1])$ implies $f=0$ almost everywhere
Well, that works as long as we remain continuous.
Jan
5
comment Show that $\int_0^1 f(x)g(x)\,dx=0$ for all $g\in C([0,1])$ implies $f=0$ almost everywhere
Well, maybe i should had required a bit more of our $g_{n}$'s. Namely that $||g_{n}||_{\infty} \leq 1$ for all $n\geq 1$. Do you agree that this can be done?
Jan
5
comment Show that $\int_0^1 f(x)g(x)\,dx=0$ for all $g\in C([0,1])$ implies $f=0$ almost everywhere
First you say $sgn(f)$ is in $\mathcal{L}^{1}([0,1])$, in which continuous functions are dense. So you pick $\left\{g_{n}\right\}_{n\geq1}\subset C([0,1])$ such that $||g_{n}-sgn(f)||_{\mathcal{L}^{1}([0,1])}\rightarrow 0$. Then we can extract a subsequence $\left\{g_{n_{j}}\right\}$ such that $g_{n_{j}}\rightarrow sgn(f)$ pointwise a.e.
Jan
5
answered Show that $\int_0^1 f(x)g(x)\,dx=0$ for all $g\in C([0,1])$ implies $f=0$ almost everywhere
Jan
4
comment Solving $\int {dx\over(1+x^2)\sqrt{1-(\arctan x)^2}}$
$\arcsin(\arctan(x)) + c$
Jan
3
revised How to compute this multivariable limit?
deleted 10 characters in body
Jan
3
accepted $\mathcal{L}^2$-norm of the Laplace transform
Jan
3
revised Definite integral $\int_0^1 \frac{\arctan x}{x\,\sqrt{1-x^2}}\,\text{d}x$
added 20 characters in body
Jan
3
answered Definite integral $\int_0^1 \frac{\arctan x}{x\,\sqrt{1-x^2}}\,\text{d}x$