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

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

2009-01-29

arxiv.org/abs/0901.4659v1

Mathematics

Classical Analysis and ODEs

Submitted to Sampta09 conference

Scientific paper

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.

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