Rick Sanchez C-666's user avatar
Rick Sanchez C-666's user avatar
Rick Sanchez C-666's user avatar
Rick Sanchez C-666
  • Member for 3 years, 11 months
  • Last seen this week
23 votes
1 answer
575 views

Calculate $\lim_{n \to\infty}\sqrt[n]{\{\sqrt{2}\}\{2\sqrt{2}\}\{3\sqrt{2}\}\cdots\ \{n\sqrt{2}\} }$

8 votes
3 answers
2k views

Is $L^2(\mathbb R)$ isometrically isomorphic with $\ell^2(\mathbb Z)?$

3 votes
0 answers
81 views

If $k_n$ is good kernel & $f\in C(\mathbb T )$ then $f*k_n\rightarrow f$ uniformly opposite way

3 votes
1 answer
136 views

If $f(x)=x^3-\lambda x$ then $\Big\{ x\in\mathbb R : \Big| \lim_{n\to \infty}f^n(x)\Big|<+\infty \Big\}$ is a Cantor set.

3 votes
1 answer
81 views

$A_n\subseteq A: \mu(A_n)\xrightarrow{n}0 \Rightarrow \int_{A_n} f \xrightarrow{n} 0 $ [duplicate]

2 votes
1 answer
87 views

Show that $T^n\left( \left[ \frac{k}{2^n},\frac{k+1}{2^n}\right]\right) = [0,1] , \forall n\in\mathbb N, 0<\frac{k}{2^n}<1$

2 votes
0 answers
105 views

Completeness and Topology of $\ell ^p,0<p<1$

2 votes
1 answer
641 views

${α⋅ \log(n)}$ is not uniformly distributed mod1 in $[0,1]$

2 votes
1 answer
75 views

Completeness of $(\mathcal M (2,\mathbb R),\lVert \cdot\rVert)$

2 votes
1 answer
126 views

$X_1,...,X_n \text{ iid }X_1\sim \operatorname{Ge}\big( \theta\big)\implies \mathbf X =(X_1,...,X_n)^T \in \text{ Exponential Family}$

2 votes
1 answer
131 views

Calculate $X_A(x) $ and $m_A(x) $ of a matrix $A\in \mathbb{C}^{n\times n}:a_{ij}=i\cdot j$ [duplicate]

2 votes
1 answer
895 views

Calculate $\int_Sxyz \cdot dS$ where $S$ is the triangle $(1,0,0),(0,2,0),(0,1,1)$

1 vote
2 answers
61 views

Finding $\int_S z\,dS$ where $S=\left\{ \big(x,y,z\big):x^2+y^2+z^2=a^2,z\ge 0, a>0\right\}$

1 vote
1 answer
97 views

Find the eventually periodic points of the function $f(x)=\lvert x-1 \rvert$

1 vote
1 answer
79 views

Periodic points of $\sin(x)$ on $(-1,1)$

1 vote
1 answer
69 views

Show that $f^{n}(x)\xrightarrow{n} x_0\forall x\in X$

1 vote
1 answer
49 views

$T:P_n\longrightarrow P_n : Tp(t)=\frac{d}{dt}p(t)\text{ Find the norm of the operator}$

1 vote
0 answers
76 views

Construct a function $f$ which is $Lip-α$ but not $Lip-β$.

1 vote
1 answer
107 views

$(X,f)$ is $minimal$ $\iff$ $X$ has no proper non-empty closed subset $Y $ which is $f-invariant$

1 vote
1 answer
155 views

Prove that the topologically transitive dynamical system $(X,f):\frac{1}{n}\sum_{k=0}^{n-1}\phi\circ f^k(x) \rightarrow g(x)$ is uniqualy ergodic

1 vote
1 answer
115 views

Is the map $f(x)=x+\cfrac{1}{4}\sin^2(\pi x)$ uniquely ergodic?

1 vote
2 answers
102 views

Is the following sequence equidistributed mod$1$ : $x_n=\{10^n\cdot a\}_{n\in\mathbb N}, a\in\mathbb R\setminus\mathbb Q ?$

0 votes
1 answer
58 views

If $F\in\mathcal D \implies \left\lvert \frac{F^n(0)}{n} - F(0)\right\rvert\le\frac{n-1}{n}\, ,\forall \,n\in\mathbb N$

0 votes
1 answer
76 views

If $X\subset\mathbb R,f:X\rightarrow X: \forall I,J \subset X \exists n\in\mathbb N:J\subset f^n(I)$, then $f$ is Topologically Transitive.

0 votes
1 answer
139 views

The ideal $\langle x-y+1,y-3\rangle$ of $\mathbb C[x,y]$ is maximal

0 votes
1 answer
171 views

$(C^1(\mathbb T),\|\cdot\|) , \|f\|:=|f(0)|+\|f′\|_{L^2(\mathbb T)}$ is not a Banach space.

0 votes
1 answer
42 views

If $f(a)=a,f'(a)=1,f''(a)>0$ then $\exists \delta >0:(a,a+\delta)\subset W^c$

-1 votes
3 answers
2k views

$T(n)=4T(n/3)+n\log_2(n)$