Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity
Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity
复制标题
变化规律序列空间中的计算机辅助傅里叶分析
DOI：
--
复制
发表时间：
2017
影响因子：
2
通讯作者：
J. Mireles
中科院分区：
文献类型：
--
作者：
J. Lessard;J. Mireles
这项工作将计算机辅助傅立叶分析，可用于获得数学上严格的误差界限的数值近似解微分方程的功能分析框架。利用一个抽象的后验定理，得到了满足0 <kleq infty$或k = omega$的C^k$问题解的存在性和正则性结果.主要工具是某些无限序列空间的快速衰减系数：我们采用序列空间的代数和指数衰减率，以表征我们的结果的规律性。我们说明了该方法的实施和有效性，在各种规律类。我们还研究了空间的有效性的代数衰变研究的问题的解决方案附近的故障的解析性。
This work treats a functional analytic framework for computer assisted Fourier analysis which can be used to obtain mathematically rigorous error bounds on numerical approximations of solutions of differential equations. An abstract a posteriori theorem is employed in order to obtain existence and regularity results for $C^k$ problems with $0 < k leq infty$ or $k = omega$. The main tools are certain infinite sequence spaces of rapidly decaying coefficients: we employ sequence spaces of algebraic and exponential decay rates in order to characterize the regularity of our results. We illustrate the implementation and effectiveness of the method in a variety of regularity classes. We also examine the effectiveness of spaces of algebraic decays for studying solutions of problems near the breakdown of analyticity.