基于积分测量的分段光滑函数的“代数”重构
An "algebraic" reconstruction of piecewise-smooth functions from integral measurements
摘要：
本文介绍了在代数信号采样和应用数学的其他领域的一个著名的问题的一些结果：重建分段光滑函数从他们的积分测量（如矩，傅里叶系数，Radon变换等）。我们的研究结果涉及重建（从时刻）的信号在两个特定的类：线性组合的一个给定的函数的移位，和“分段$D$ -有限的功能”，满足每个连续性区间的线性微分方程与多项式系数。
英文摘要：
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier coefficients, Radon transform, etc.). Our results concern reconstruction (from the moments) of signals in two specific classes: linear combinations of shifts of a given function, and "piecewise $D$-finite functions" which satisfy on each continuity interval a linear differential equation with polynomial coefficients.
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。
