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 Yearling
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May
24
comment Given $|f(x)|=1$,how to construct an $f(x)$, such that $\int ^{+\infty }_{0}f\left( x\right) dx$ converges
You can take $e^{i x^2} $. It's essentially what paul garrett wrote. See also [Fresnel integrals]( en.m.wikipedia.org/wiki/Fresnel_integral).
May
24
revised Counter example in Sobolev spaces: Is there a standard example for showing that $H^1(\mathbb{R}^2)\not\subset L^\infty(\mathbb R^2)$?
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May
24
revised Counter example in Sobolev spaces: Is there a standard example for showing that $H^1(\mathbb{R}^2)\not\subset L^\infty(\mathbb R^2)$?
added 162 characters in body
May
24
awarded  Yearling
May
24
answered Counter example in Sobolev spaces: Is there a standard example for showing that $H^1(\mathbb{R}^2)\not\subset L^\infty(\mathbb R^2)$?
May
9
comment Let $(a_n)$ be any sequence and $(b_n)=n(a_n-a_{n+1})$. If $\sum a_n$ and $\sum b_n$ converges then $\lim_{n\to \infty}na_n=0$
Summation by parts
May
2
revised Relation between $\int_0^{\infty} \frac{e^{-ax}}{1+x^2}\,\,dx$ and $\int_0^{\infty} \frac{e^{-2ax}}{1+x^2}\,\,dx$
added 47 characters in body
May
2
answered Relation between $\int_0^{\infty} \frac{e^{-ax}}{1+x^2}\,\,dx$ and $\int_0^{\infty} \frac{e^{-2ax}}{1+x^2}\,\,dx$
Dec
20
awarded  Caucus
Dec
14
revised Definite integral involving Error function
improved formatting
Dec
14
revised Definite integral involving Error function
added 484 characters in body
Dec
13
comment Definite integral involving Error function
Yes, sure. But then you end up with an integral over powers of $erf$, which I do not know how to evaluate either.
Dec
13
asked Definite integral involving Error function
Jul
2
awarded  Curious
Jun
23
awarded  Nice Question
May
23
awarded  Tumbleweed
Feb
23
revised Closure of Schwartz space in homogeneous Besov space
improved title
Feb
23
asked Closure of Schwartz space in homogeneous Besov space
Aug
5
awarded  Nice Answer
Jan
25
awarded  Nice Answer