G the Stackman

### Questions (87)

 7 We have two red, two white and two green marbles in an urn 6 Computing Fréchet derivative of $F(f)(x) = \int^{x}_{0} \cos(f(t)^{2})dt, x \in [0,1]$ 6 Is the Set of Continuous Functions that are the Sum of Even and Odd Functions Meager? 5 Determining if $f\in L^{p}(\mathbb R)$ from a bound on the measure of the level sets $\{|f|>\lambda\}$ for all $\lambda>0.$ 5 Is a set of measure zero in $\mathbb{R}$ totally disconnected?

### Reputation (1,385)

 +15 Trouble with example of sequences $(f_n)_n,(g_n)_n\in\ell^1$ with $\|f_n\|_\infty\to0,\,\|f_n\|_2\to\infty$ and $\|g_n\|_2\to0,\,\|g_n\|_1\to\infty.$ +10 How to prove that $\int_{0}^{1}\vert\cos(nx)\vert\,dx\not\to 0$ as $n\to\infty$? +15 If $f,h,g\in L^{2}(\mathbb R^2)$, then $\int_{\mathbb R^3}\vert f(x,y)g(y,z)h(z,x)\vert d(x,y,z)\leq\|f\|_2\|g\|_2\|h\|_2$ +5 Convolution of $L^{1}$ functions is well-defined

 3 Example to disprove the statement: for all real numbers $x$ and $y$, if $x + \lfloor x \rfloor = y + \lfloor y \rfloor$ then $x = y$ 2 Let $a,b,c,d$ be real numbers such that $a0 \}$ 1 Method of interpolation and solving for $x$

### Tags (64)

 4 algebra-precalculus × 2 1 pde × 3 3 real-numbers 1 harmonic-functions × 2 2 formal-proofs 1 greens-function × 2 2 discrete-mathematics 1 laplacian × 2 2 proof-writing 0 real-analysis × 53