All Questions

Let $p \in [1, +\infty)$, $(b_0(n)), \dots (b_m(n)), (a_1(n)), \dots, (a_m(n))$ suitable sequences of real numbers and consider the map $\phi: \ell^p \to \ell^p$, $x \mapsto y$ defined by: \begin{...

This is related to discrete dynamical systems, with the initial condition $X_1$ being a random variable with a non singular distribution. The system is driven by the iteration $X_{n+1} = g(X_n)$ for ...

Let $W$ be the Wiener measure on $C_0(\mathbb{R})$ and let $T\in L(C_0(\mathbb{R}),C_0(\mathbb{R}))$ be a hypercylic operator; i.e. there exists some $f \in C_0(\mathbb{R})$ such that $\{T^n(f)\}_{n=1}...

$\DeclareMathOperator\C{C}\DeclareMathOperator\HC{HC}$Definitions: Let $T:X\rightarrow X$ be a bonded linear operator on a separable (infinite-dimensional) Banach space and define the sets: $ \HC(T)\...

Let $(X,d)$ be a metric space and $f:X\rightarrow X$ be continuous. Then, is there any meaning/research done on the metric $$ D(x,y)\triangleq \sum_{n \in \mathbb{N}} \frac1{2^n} d(f^n(x),f^n(y)); $$ ...