Annihilation Operators for Exponential Spaces in Subdivision

Analytic functions in shift-invariant spaces and analytic limits of level dependent subdivision

The structure of exponential subspaces of finitely generated shift-invariant spaces is well understood and the role of such subspaces for the approximation power of refinable function vectors and related multi-wavelets is well studied. In this paper, in the univariate setting, we characterize all analytic subspaces of finitely generated shift-invariant spaces and provide explicit descriptions of elements of such subspaces. Consequently, we depict the analytic functions generated by level dependent (non-stationary) subdivision schemes with masks of unbounded support. And we confirm the belief t…

具有级别依赖性的插值Hermite细分方案和小波

Level-dependent interpolatory Hermite subdivision schemes and wavelets

本文研究了具有级别依赖性的Hermite细分方案，重点研究保持多项式和指数数据的性质，通过预测-校正方法得到插值方案，推导出多小波系数衰减结果。

离散卷积算子与细分算子的核

Kernels of discrete convolutions and subdivision operators

研究离散卷积算子的核及偏差分算子的齐次解，证明其必为指数多项式，并探讨多项式空间与多变量多项式公共零点乘性的关系。

再生指数多项式的广义Daubechies小波的正则性

Regularity of generalized Daubechies wavelets reproducing exponential polynomials

本文研究基于非平稳插值细分方案的非平稳正交小波，该方案再生给定指数集，主要贡献是证明了这类Daubechies型小波的光滑性。

保椭圆的赫尔米特插值与细分

Ellipse-preserving Hermite interpolation and subdivision

本文提出了一类分段指数函数，具有赫尔米特插值性质，用于曲线点与切线的联合插值，并能完美再现椭圆。通过格林函数方法分析其多分辨率和逼近性质，推导出可快速实现的向量和标量细分方案，其渐进行为与经典三次赫尔米特样条算法相同，保证了四阶逼近精度。

从逼近到插值非平稳细分格式：保持相同生成性质

From approximating to interpolatory non-stationary subdivision schemes with the same generation properties

本文提出一种通用计算策略，从满足温和假设的对称非平稳非插值细分格式推导出一族插值非平稳细分格式，并证明所得插值格式能复现与原逼近格式相同的指数多项式空间。

在Riemannian壳空间中实现关键帧的平滑插值

Smooth Interpolation of Key Frames in a Riemannian Shell Space

本文研究了将插值样条和细分方案推广到具有弯曲和膜变形度量的壳面Riemannian流形，通过平滑插值关键帧控制网格实现壳体动画。