Wiman-Valiron theory for a polynomial series based on the Askey-Wilson operator

Wiman-Valiron theory for a polynomial series based on the Wilson operator

We establish a Wiman-Valiron theory for a polynomial series based on the Wilson operator $\mathcal{D}_\mathrm{W}$. For an entire function $f$ of order smaller than $\frac13$, this theory includes (i) an estimate which shows that $f$ behaves locally like a polynomial consisting of the terms near the maximal term in its Wilson series expansion, and (ii) an estimate of $\mathcal{D}_\mathrm{W}^n f$ compared to $f$. We then apply this theory in studying the growth of entire solutions to difference equations involving the Wilson operator.

多复变量中对数偏导数的估计与Wiman-Valiron理论

Estimation for the logarithmic partial derivative and Wiman-Valiron theory in several complex variables

本文旨在将Gundersen和Cao的结果推广到高维，估计多复变量亚纯函数的对数偏导数，发展Wiman-Valiron理论，并研究一类复偏微分方程解的增长率。

Wiman-Valiron discs and the dimension of Julia sets

We show that the Hausdorff dimension of the set of points of bounded orbit in the Julia set of a meromorphic map with a simply connected direct tract and a certain restriction on the singular values is strictly greater than one. This result is obtained by proving new results related to Wiman-Valiron theory.

Baire categories and classes of analytic functions in which the Wiman-Valiron type inequality can be almost surely improved

Let $f(z)=\sum_{n=0}^{+\infty} a_nz^n$\ $(z\in\mathbb{C})$\ be an analytic function in the unit disk and $f_t$ be an analytic function of the form $f_t(z)=\sum_{n=0}^{+\infty} a_ne^{iθ_nt}z^n,$ where $t\in\mathbb{R},$ $θ_n\in\mathbb{N},$ and $h$ be a positive continuous function on $(0, 1)$ increasing to $+\infty$ and such that $ \int_{r_0}^1h(r)dr=+\infty, r_0\in(0,1).$\ If the sequence $(θ_n)_{n\geq0}$ satisfies the inequality $$ \varlimsup_{n\to+\infty}\frac1{\ln n}\ln\frac{θ_n}{θ_{n+1}-θ_n}\leqδ\in[0,1/2), $$ then for all analytic functions $f_t$ almost surely for $t$ there exists a set $E…

单位圆盘内有限对数测度集合外的Wiman-Valiron不等式

Wiman-Valiron inequalities in the unit disk outside sets of finite logarithmic measure

本文肯定回答了Grosse-Erdmann关于单位圆盘内Wiman-Valiron不等式的两个问题，在有限对数测度例外集外建立迭代对数不等式，并给出Rosenbloom复合估计的圆盘类比，关键利用Khinchin族方差界，且指数1/2不可改进。

Wiman-Valiron方法用于分数导数及线性分数微分方程中α-解析解的精确增长估计

Wiman-Valiron method for fractional derivatives and sharp growth estimates of $α$-analytic solutions for linear fractional differential equations

本文通过扩展Wiman-Valiron理论，研究了分数微分方程中α-解析解的精确增长估计，并推广了Kochubei的结果。

随机解析函数的增长率，并应用于线性动力学

Rate of growth of random analytic functions, with an application to linear dynamics

本文建立随机整函数与单位圆盘随机解析函数的 Wiman–Valiron 型不等式，改进已有结果，并用于刻画任意混沌加权后移算子频繁超循环函数在例外集外的增长率。