are there two non-zero functons $f, g$ in $L^1(\mathbb{R})$ such that $f\ast g=0$ a.e
114609
Does the Banach algebra $L^1(\mathbb{R})$ have zero divisors?
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle
90649
Consider $f(x)=mx$ and $g(x) =bx$ in which $m>0$ and $b>0$. Does there exist any homeomorphism $h$ such that $h \circ f$ = $g \circ h$
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
92089
If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
6450
Show $\mathbb{E}[f(X)g(X)] \geq \mathbb{E}[f(X)]\mathbb{E}[g(X)]$ for $f,g$ bounded, nondecreasing
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?
49769
A function for which one-sided limits are zero and infinity
126821
Let $f:[0,1]\to \mathbb{R}$. Show that $\{a \in [0,1]: f(a)\neq 0\} = \bigcup_{n=1}^{\infty} \{a \in [0,1]: |f(a)|\geq 1/n\}$
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
44761
Is $f'(x)-3f(x) = 0$ subspace of differentiable functions $f\colon (0,1)\to \mathbb{R}$
123249
An analytic function $f$ on $|z|<1$ with $\sup_{|z|<1} |f(z)|=1$ and $|f(0)|=\frac{1}{2}$ has no zeros in $|z|<\frac{1}{2}$
74810
A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.