摘要： Example 1. Let $E=\{a_n\}_{n\ge 1}\subset R$ satisfying the conditon : there exist $C>0$ and $0<\alpha<1$ such that $$C^{-1}\alpha^n\le a_n\le C\alpha 阅读全文

摘要： Let $E$ be a subset of a metric sapce $(X, d)$ and $r>0.$ The set $E$ is called $r$-discrete if $d(x,y)\ge r$ whenever $x,y\in E, x\not=y.$ Let $N_r(B 阅读全文

摘要： If $\mu,\nu$ are two finite Borel measures on $R^d,$ the their convolution is the push-down of $\mu\times \nu$ under the addition map $(x,y)\to x+y,$ 阅读全文

摘要： Let $\{Y_i: i\in J\}$ be zero mean independent complex-valued random variables satisfying $|Y_i|\le R.$ Then for all $c>0,$ $$P\left(|\sum_{i\in J}Y_i 阅读全文

摘要： Let $\mu$ be a finite Borel measure on $R$. We define it Fourier transformation as follows: $$\widehat{\mu}(\xi)=\int e^{-2\pi i\xi x}d\mu(x).$$ Fact 阅读全文

摘要： Let $A=\{a_1<a_2<\cdots<a_n<\cdots\}\subset N$ be a integer sequence. The upper exponential density of it is defined by $$\overline{\varepsilon}(A)=\l 阅读全文

摘要： Let $0<r_1\le r_2\le\cdots$ be a real sequence satisfying $\lim\limits_{n\to \infty}r_n=+\infty$. The convergence exponent of the sequence is defined 阅读全文

摘要： Let $0<H<1.$ a real-valued Gaussian process $(B_H(t))_{t\ge 0}$ is called fractional Brownian motion (fBm) if $E(B_H(t))=0$ and $$E(B_H(t)B_H(s))=\fra 阅读全文

摘要： Let $\mu$ be a Borel probability measure on $R^d$. We say that $\mu$ is an $M_\beta$-measure if its Fourier transformation $\widehat{\mu}$ possesses t... 阅读全文

摘要： We denote by $L^1(R^n)$ the space of Lebesgue integrable functions on $R^n$. For $f\in L^1(R^n)$, the Fourier transformation $\widehat{f}$ of $f$ is d... 阅读全文