椭圆问题通过线性和非线性映射的最优逼近 III：框架
Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames
AI总结：
研究通过特定框架的n项逼近求解算子方程的最优逼近，定义非线性框架宽度并分析最坏情况误差与最优收敛阶。
摘要：
我们研究通过特定框架类的某些n项逼近对算子方程解的最优逼近。我们研究最坏情况误差和最优收敛阶，并定义合适的非线性框架宽度。与我们在早期论文中研究的Riesz基相比，框架的主要优势在于我们现在可以处理任意有界Lipschitz域——这也适用于上界。关键词：椭圆算子方程，最坏情况误差，框架，非线性逼近，最佳n项逼近，流形宽度，Lipschitz域上的Besov空间。
英文摘要：
We study the optimal approximation of the solution of an operator equation by certain n-term approximations with respect to specific classes of frames. We study worst case errors and the optimal order of convergence and define suitable nonlinear frame widths. The main advantage of frames compared to Riesz basis, which were studied in our earlier papers, is the fact that we can now handle arbitrary bounded Lipschitz domains--also for the upper bounds. Key words: elliptic operator equation, worst case error, frames, nonlinear approximation, best n-term approximation, manifold width, Besov spaces on Lipschitz domains
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
