Romeo

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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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60 Questions

views newest activity votes

2

14

votes

2

answers

479

views

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

aug 14 at 15:15 t.b. 43.1k

11

votes

1

answer

118

views

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

aug 17 at 17:29 Zarrax 19.7k

5

10

votes

3

answers

193

views

A trigonometric series

homework sequences-and-series

jun 8 '12 at 21:01 Norbert 20k

1

8

votes

4

answers

296

views

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

aug 13 at 9:21 Davide Giraudo 56.2k

1

8

votes

4

answers

249

views

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

jul 26 at 19:53 Norbert 20k

1

7

votes

1

answer

89

views

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

real-analysis analysis derivatives

feb 24 at 15:51 vonbrand 6,568

3

6

votes

1

answer

90

views

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

functional-analysis convergence

dec 31 at 19:28 Olivier Bégassat 3,649

5

votes

1

answer

114

views

Bounded and compact sets in a subspace of $\mathbb R^{\mathbb N}$

functional-analysis compactness topological-vector-spaces

dec 27 at 18:11 Brian M. Scott 154k

5

votes

2

answers

111

views

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

measure-theory lebesgue-integral

dec 7 at 1:50 Mercy 4,460

5

votes

1

answer

100

views

Is $\ell^1 \subset \ell^2$ meagre? [duplicate]

functional-analysis baire-category

oct 13 at 12:40 Martin Sleziak 20.3k

2

5

votes

3

answers

194

views

Continuous solutions of $f(x) = \lambda \int_0^{\pi/2} \cos({x-y)}f(y)\,dy$ [duplicate]

functional-analysis integral-equations

aug 24 at 14:00 Jayesh Badwaik 1,215

1

5

votes

3

answers

351

views

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

real-analysis functional-analysis operator-theory compact-operators

aug 15 at 14:34 Jon Bannon 1,235

3

5

votes

1

answer

181

views

Classifing groups of order 56: problems with the semidirect product

abstract-algebra group-theory finite-groups

aug 5 at 9:03 Romeo 1,531

4

votes

2

answers

121

views

Do weak convergence and convergence of norms imply convergence in $L^2$?

functional-analysis convergence

dec 26 at 14:57 Davide Giraudo 56.2k

4

votes

2

answers

73

views

If $A \in M_2(\mathbb R)$ non identical with $A^3=I $ then $\text{tr}(A)=-1$

matrices

sep 15 at 10:22 tomasz 6,984

4

votes

2

answers

59

views

If $f \colon [-1,1] \to \mathbb R$ satisfies $\vert f'' \vert \le k$ then $\vert f \vert \le \frac{k}{2}$

real-analysis

sep 14 at 17:14 Alex Becker 27.9k

1

4

votes

3

answers

261

views

Zero-divisors and units in $\mathbb Z_4[x]$

abstract-algebra polynomials

sep 14 at 8:32 Hurkyl 21.5k

1

4

votes

2

answers

122

views

About the convergence of $f_n:=\sin{\sqrt{t+4n^2\pi^2}}$

real-analysis sequences-and-series

jul 22 at 20:35 Peter Tamaroff 25.5k

1

4

votes

3

answers

257

views

$f$ has an essential singularity in $z_0$. What about $1/f$?

complex-analysis

jul 7 at 1:11 Micah 6,415

1

3

votes

1

answer

99

views

Trivial tangent bundle and orientability

differential-geometry manifolds vector-bundles

feb 15 at 14:07 Damien L 3,489

3

votes

0

answers

44

views

Questions on a sub-bundle of $\mathbb R^3\setminus \{0\}$

differential-geometry differential-forms vector-bundles

feb 14 at 10:40 Romeo 1,531

1

3

votes

1

answer

63

views

Equicontinuity and uniform boundedness for “distributions”

functional-analysis distribution-theory

dec 22 at 22:19 Vobo 880

3

votes

1

answer

303

views

Fourier transform of $\cos x^2$

real-analysis fourier-analysis

dec 1 at 15:24 Josh 110

3

votes

2

answers

147

views

Does uniform convergence imply convergence of the integrals?

measure-theory

nov 10 at 16:15 Amr 8,803

3

votes

2

answers

96

views

If $f\colon (0+\infty) \to \mathbb R$ and $f(x)=f(2x)$ what can we say about $f$?

real-analysis

sep 14 at 9:00 Marc van Leeuwen 23.8k

3

votes

3

answers

204

views

The 32nd derivative of a real function

calculus real-analysis

sep 7 at 9:35 Mark Bennet 9,868

3

votes

2

answers

160

views

Dividing open domains in $\mathbb R^2$ in parts of equal area

geometry

sep 5 at 19:40 Byron Schmuland 15.4k

3

votes

1

answer

40

views

Evaluating $\int_{I^n} \left( \min_{1\le i \le n}x_i \right)^{\alpha}\,\, dx$

integral definite-integral

aug 12 at 14:18 Romeo 1,531

1

3

votes

1

answer

67

views

Image of $\partial B_r $ under an holomorphic function

homework complex-analysis

aug 3 at 21:29 Davide Giraudo 56.2k

1

3

votes

1

answer

93

views

If $g(x) := \int_1^2 f(xt)dt \equiv 0$ then $f \equiv 0$

real-analysis functional-equations

jul 23 at 20:14 Davide Giraudo 56.2k

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