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Romeo

Age: 22

I am currently a graduate Math student. My main interests are Real Analysis, Functional Analysis, Measure Theory and Partial Differential Equations. I am also interested in Differential Geometry and I really would like to study some Abstract Harmonic Analysis (sooner or later I will study it).

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Top Questions
14 votes

If $\lim_n f_n(x_n)=f(x)$ for every $x_n \to x$ then $f_n \to f$ uniformly on $[0,1]$?

real-analysis convergence continuity asked Aug 13 '12 at 21:57
math.stackexchange.com

11 votes

Does $f_n \to 0$ in $L^1(\mathbb R^2)$ imply that $f_{n_k}(x,\cdot)\to 0$ in $L^1(\mathbb R)$ for almost every $x \in \mathbb R$?

measure-theory convergence lebesgue-integral asked Aug 17 '12 at 13:22
math.stackexchange.com

10 votes

A trigonometric series

homework sequences-and-series asked Jun 7 '12 at 20:05
math.stackexchange.com

8 votes

If $\phi \in C^1_c(\mathbb R)$ then $ \lim_n \int_\mathbb R \frac{\sin(nx)}{x}\phi(x)\,dx = \pi\phi(0)$.

real-analysis limit asked Jul 24 '12 at 20:09
math.stackexchange.com

8 votes

Proving that $\lim\limits_{n\to\infty}n\left( \int_0^1 f(t)\, dt -\frac1n\sum_{k=0}^{n-1}f\left(\frac k n\right) \right)=\frac{f(1)-f(0)}{2}$

integral integration asked Aug 12 '12 at 20:20
math.stackexchange.com

7 votes

Does $f\colon \Omega \to \mathbb R$ differentiable imply $f$ locally Lipschitz?

real-analysis analysis derivatives asked Feb 24 at 15:03
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6 votes

How many well-behaved norms are there on $C[0,1]$?

functional-analysis convergence asked Dec 31 '12 at 17:49
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5 votes

A compact operator in $L^2(\mathbb R)$

real-analysis functional-analysis operator-theory compact-operators asked Jul 25 '12 at 11:58
math.stackexchange.com

5 votes

Classifing groups of order 56: problems with the semidirect product

abstract-algebra group-theory finite-groups asked Aug 4 '12 at 17:15
math.stackexchange.com

5 votes

Derivative of $t \mapsto \Vert f+tg \Vert_p^p$

measure-theory lebesgue-integral asked Dec 6 '12 at 21:02
math.stackexchange.com

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