Clifford-Valued Fractal Interpolation

Fractal Interpolation over Curves

This paper introduces the novel concept of fractal interpolation over curves in Banach spaces. The contents are based on the usual methodologies involving the fractal interpolation problem over intervals but the current approach considerably extends and generalizes them and paves the way to fractal interpolation over Banach submanifolds.

Fractal Interpolation: From Global to Local, to Nonstationary and Quaternionic

We present an introduction to fractal interpolation beginning with a global set-up and then extending to a local, a non-stationary, and finally the novel quaternionic setting. Emphasis is placed on the overall perspective with references given to the more specific questions.

半环、半向量空间与分形插值

Semi-Rings, Semi-Vector Spaces, and Fractal Interpolation

针对函数正性与单调性保持需求，本文在无需额外假设的完备半向量空间框架内建立分形插值，并具体研究 $C^+$ 与 $L_p^+$ 空间。

广义多元分形插值函数与α-分形函数

Generalized multivariate Fractal Interpolation Function and $α$-Fractal Function

本文提出基于Matkowski和Rakotch压缩映射的新方法，推广多元分形插值函数的已有构造技术，建立非线性迭代函数系统吸引子为插值理论数据点的多元函数图像，并探讨Rakotch压缩下的不变Borel概率测度存在性。

Box Dimension and Fractional Integrals of Multivariate Fractal Interpolation Functions

In this article, we construct the multivariate fractal interpolation functions for a given data points and explore the existence of $α$-fractal function corresponding to the multivariate continuous function defined on $[0,1]\times \cdots \times [0,1](q\text{-times})$. The parameters are selected such that the corresponding fractal version preserves some of the original function's properties, for instance, if the given function is Hölder continuous, then the corresponding $α$-fractal function is also Hölder continuous. Moreover, we explore the restriction of the $α$-fractal function on the co-o…

分形插值函数的能量与Laplacian

Energy and Laplacian of Fractal Interpolation Functions

本文首先刻画了后临界有限自相似集上分形插值函数的有限性。然后研究了Sierpinski垫片（SG）上具有均匀垂直尺度因子的分形插值函数的拉普拉斯算子。作为应用，我们证明了SG上的狄利克雷问题的解是一个具有一致垂直尺度因子$\frac{1}{5}$的FIF：$Δu=0$在$SG\setminus \{q_1,q_2,q_3\}$上，且有$u(q_i)=a_i$，$i=1,2,3$，其中$q_i$，$i=1,2,3$是SG的边界点.