User eraldcoil

8 votes

1 answer

7k views

Infinitely differentiable functions with compact support are dense in $L^p$

asked Nov 29, 2018 at 5:41

6 votes

3 answers

788 views

Exercise $2.3.2$ of Grafakos, Classical Fourier Analysis.

asked Dec 31, 2019 at 23:13

5 votes

1 answer

2k views

The inverse image of a measurable set under a measurable function is measurable?

asked Nov 6, 2018 at 2:55

5 votes

1 answer

114 views

Showing whether an ideal in $\mathbb{Z}[x,y]$ is prime.

asked Jul 30, 2020 at 14:51

4 votes

1 answer

118 views

Finding the $\mathbb{Q}$-automorphisms of the splitting field of $x^p-2$ over $\mathbb{Q}$.

asked Oct 12, 2020 at 1:35

4 votes

1 answer

167 views

$\lim_{p\to r} \|f\|_p=\|f\|_r$

asked Jul 9, 2018 at 21:55

4 votes

3 answers

1k views

Dilatation of a measurable set is a measurable set.

asked Dec 3, 2018 at 23:18

4 votes

2 answers

1k views

Counterexample in Radon-Nikodym Theorem. Problem 38 Royden 2ed.

asked Jan 5, 2019 at 21:00

4 votes

1 answer

54 views

Taylor series in distribution sense?

asked Aug 30 at 5:13

3 votes

1 answer

86 views

Show that $G_t(x)=(2\pi)^{-n/2}\int_{\mathbb{R}^n}\mathbb{e}^{ix\cdot\xi}\mathrm{e}^{-t(1+|\xi|^2)^{\alpha}}\,d\xi$ is uniformly bounded in $L^1$.

asked Aug 28 at 4:07

3 votes

1 answer

205 views

Every quasiisometry is a quasiisometric embedding

asked Nov 3, 2018 at 3:57

3 votes

1 answer

564 views

Operator bounded then adjoint is bounded

asked Oct 23, 2018 at 0:27

3 votes

0 answers

337 views

Operator commutes with translation is a convolution with a measure. Stein.

asked Dec 25, 2019 at 2:25

3 votes

1 answer

174 views

Is $f(x,y)=\operatorname{sgn}(x-y)e^{-|x-y|}$ Lebesgue integrable?

asked Jun 9, 2019 at 1:10

3 votes

2 answers

2k views

Showing that a group of order 6 contains an element of order 2 and order 3. (Without Cauchy)

asked May 2, 2020 at 16:05

3 votes

1 answer

99 views

Showing that a function is an automorphism of $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$

asked Nov 26, 2020 at 7:20

3 votes

1 answer

360 views

Exercise 4 Conway, a course in functional analysis.

asked Jan 9, 2021 at 1:47

3 votes

3 answers

308 views

Prove that if $G$ is a finite group with an even class number, then $G$ is of even order. Give an example that the converse fails.

asked Feb 24, 2021 at 21:32

3 votes

1 answer

293 views

Any positive distribution is a measure.

asked Apr 19, 2021 at 10:48

3 votes

1 answer

155 views

Product of a Schwartz function and a function with polynomial bonuded derivatives is schwartz?

asked Nov 11, 2021 at 9:42

3 votes

1 answer

51 views

Proving that an operator converges in norm to the identity and that it is locally invertible.

asked Feb 4, 2022 at 17:31

3 votes

1 answer

112 views

Convergence of the exponential matrix.

asked Jun 19, 2022 at 6:15

3 votes

1 answer

30 views

Computing the vector field, matrix exponential, normal forms (Rossmann)

asked Apr 10 at 14:02

2 votes

0 answers

27 views

Is there a general definition for the kernel of a differential equation?

asked Sep 12, 2022 at 22:07

2 votes

0 answers

94 views

Sobolev spaces are isomorphic to $L^2$?

asked Nov 19, 2022 at 19:44

2 votes

2 answers

51 views

Understanding a solution of a differential equation from an approximation (Rauch)

asked Feb 13 at 15:08

2 votes

1 answer

61 views

Why a polynomial defined on $\mathbb{C}^n$ with $n>1$ has a infinitely many roots?

asked May 4 at 5:52

2 votes

1 answer

40 views

In what sense is the limit in the definition of infinitesimal generator?

asked Jun 29 at 21:47

2 votes

2 answers

43 views

Calculating the product of the exponential application using the Baker-Campbell formula

asked Jul 5 at 4:17

2 votes

1 answer

268 views

Extension of a densely defined and bounded operator.

asked Jun 23, 2022 at 0:39

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331 Questions

Infinitely differentiable functions with compact support are dense in $L^p$

Exercise $2.3.2$ of Grafakos, Classical Fourier Analysis.

The inverse image of a measurable set under a measurable function is measurable?

Showing whether an ideal in $\mathbb{Z}[x,y]$ is prime.

Finding the $\mathbb{Q}$-automorphisms of the splitting field of $x^p-2$ over $\mathbb{Q}$.

$\lim_{p\to r} \|f\|_p=\|f\|_r$

Dilatation of a measurable set is a measurable set.

Counterexample in Radon-Nikodym Theorem. Problem 38 Royden 2ed.

Taylor series in distribution sense?

Show that $G_t(x)=(2\pi)^{-n/2}\int_{\mathbb{R}^n}\mathbb{e}^{ix\cdot\xi}\mathrm{e}^{-t(1+|\xi|^2)^{\alpha}}\,d\xi$ is uniformly bounded in $L^1$.

Every quasiisometry is a quasiisometric embedding

Operator bounded then adjoint is bounded

Operator commutes with translation is a convolution with a measure. Stein.

Is $f(x,y)=\operatorname{sgn}(x-y)e^{-|x-y|}$ Lebesgue integrable?

Showing that a group of order 6 contains an element of order 2 and order 3. (Without Cauchy)

Showing that a function is an automorphism of $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$

Exercise 4 Conway, a course in functional analysis.

Prove that if $G$ is a finite group with an even class number, then $G$ is of even order. Give an example that the converse fails.

Any positive distribution is a measure.

Product of a Schwartz function and a function with polynomial bonuded derivatives is schwartz?

Proving that an operator converges in norm to the identity and that it is locally invertible.

Convergence of the exponential matrix.

Computing the vector field, matrix exponential, normal forms (Rossmann)

Is there a general definition for the kernel of a differential equation?

Sobolev spaces are isomorphic to $L^2$?

Understanding a solution of a differential equation from an approximation (Rauch)

Why a polynomial defined on $\mathbb{C}^n$ with $n>1$ has a infinitely many roots?

In what sense is the limit in the definition of infinitesimal generator?

Calculating the product of the exponential application using the Baker-Campbell formula

Extension of a densely defined and bounded operator.