An "algebraic" reconstruction of piecewise-smooth functions from integral measurements

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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.
Submitted to Sampta09 conference

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Classical Analysis and ODEs

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http://salesiana.dossiersoluciones.com/handle/123456789/217815

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0901.4659
 http://arxiv.org/abs/0901.4659

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arXiv