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Epsilon Away
  • Member for 3 years, 10 months
  • Last seen more than a week ago
  • Cape Town, South Africa
8 votes
0 answers
113 views

When can a double limit $\lim_{k\to\infty}\lim_{m\to\infty}f_{k,m}(x)$ be combined into $\lim_{k\to\infty}f_{k,k}(x)$?

5 votes
2 answers
349 views

Reference request to the theory and examples of the spectrum of the Laplace-Beltrami operator on different compact manifolds

5 votes
0 answers
75 views

Why a measure over the points of a billiard which reflect infinitely often in finite time vanish, i.e. why $\int_{N\cap M}f(x^{-})d\mu_1(x^{-1})=0$

5 votes
2 answers
268 views

Finding the probability that at most n events take place on any interval during a given time period

5 votes
1 answer
143 views

What does the efficacy of a vaccine mean, i.e. what does it model?

4 votes
4 answers
144 views

Finding which complex numbers satisfy $\left|z + 1\right| + \left|z - 1\right| = 4$

4 votes
1 answer
62 views

There exists $j>i\geq 1$ such that $\mu(A\cap f^{-(k_j-k_i)}(A))>0$ when $\mu(A\cap f^{-n_j}(A))>0$ for a probability measure $\mu$ and sequence $n_j$

4 votes
1 answer
369 views

Kolmogorov's 0-1 law, tail events and bounded sequence of random variables.

3 votes
1 answer
228 views

Standard machine and the proof that $\int_Af|_Ad\mu_A = \int_{\Omega}1_Afd\mu$ in a measure space $(\Omega, F, \mu)$.

3 votes
1 answer
144 views

Determining whether a sequence of averages converges almost surely at all

3 votes
0 answers
46 views

Conditions on sets $A \subset B \subset X$ for the equality $\mu[B\setminus A] = \mu[B] - \mu[A]$ to hold

3 votes
1 answer
86 views

What there is to be learned from Dynkin's identification theorem?

3 votes
1 answer
77 views

Determining whether a given mapping between tangent bundle $TU$ and $\phi(U)\times\mathbb{R}$ is also a diffeomorphism

3 votes
1 answer
70 views

Sigma-algebra used in the theorem of Lebesgue-Radon-Nikodym of Rudin's Real and Complex Analysis

3 votes
1 answer
52 views

$\mu,\nu$ are Borel pr. measures s.t. $|\int fd\nu-\int fd\mu|<\epsilon$ for some Lipschitz $f$ then the inequality holds for some bounded $g\in C(X)$

3 votes
1 answer
191 views

Showing that $\{\sqrt{2}\sin(\pi n x): n\in\mathbb{N}_0\}$ is an orthonormal basis for the space $L^2([0,1])$ given that $e^{2\pi il x}$ forms a basis

3 votes
0 answers
49 views

Showing that $||(A-\lambda I)||^{-1}=\frac{1}{d(\lambda,\sigma(A))}$ for $A\in B(H)$ self-adjoint, $\lambda\in\mathbb{C}\setminus\sigma(A)$

3 votes
0 answers
40 views

What does it mean to integrate some complex valued function with respect to a projection valued measure of an operator in functional calculus?

3 votes
2 answers
46 views

Determining when $A(e_n) = \alpha_n\sum_{i=n}^{2n}e_i$ is a bounded linear function on $l^1(\mathbb{N})$

3 votes
1 answer
157 views

Proving that a non-homogeneous wave equation preserves energy $E(t)\equiv\int_{B}(u_t^2+c^2|\nabla u|^2)dx$

3 votes
1 answer
119 views

Why does $|\hat{\mu}(x)|\leq|x|^{-s/2} \implies \int_{\mathbb{R}^n}|\hat{\mu}(x)|^2|x|^{s-n}dx<\infty$ for the Fourier transform of a measure $\mu$

3 votes
0 answers
81 views

Intuition for the differences between two notions of quantum ergodicity: One given by weak-* convergence and one by pseudodifferential operators

3 votes
1 answer
449 views

Trouble understanding the proof that the orbit of every $x\in S^1$ is dense under the mapping $R_\alpha x = x + \alpha \mod 1$ for irrational $\alpha$

3 votes
1 answer
66 views

Showing that the Fourier transform of $f_n(t)=e^{\pi t^2}\frac{d^n}{dt^n}e^{-2\pi t^2}$ is $\hat{f_n} = (-i)^nf_n$

3 votes
1 answer
82 views

Showing that $k^*(H_f)\lrcorner k^*\sigma=k^*(H_f\lrcorner\sigma)$for symplectomorphism $k$, contraction $\lrcorner$ and symplectic product $\sigma$

3 votes
0 answers
536 views

Prerequisites for rigorous Fourier analysis

3 votes
1 answer
376 views

Brouwer's fixed-point theorem, permutations and coffee

3 votes
1 answer
62 views

How to find the limit of $\frac{\frac{1 - 2n}{n}}{5 + 3^{-n}}$

3 votes
1 answer
48 views

Verification of Evan's representation formula $e^{-itB(y)}=\frac{1}{2\pi i}\int_\Gamma e^{-itz}(zI - B(y))^{-1}dz$ for $t$ independent $B(y)$

3 votes
1 answer
124 views

Is it possible to derive an explicit expression for the inverse branches of $f(x)=x + x^{1+p}\mod 1, p > 0, 0\leq x\leq 1$?

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