4 problems

Let $f$ have $d$ continuous derivatives on each interval between its jump discontinuities, and suppose its Fourier data are used in Eckhoff's algebraic reconstruction method. Let…

Algebraic reconstruction conjecture. There is a nonlinear algebraic procedure reconstructing any such signal from its first $N$ Fourier coefficients with overall accuracy of order

Reconstruction conjecture. For each $n>2N+1$, the points $x_i$ and the values of $f$ between the points $x_i$ can be reconstructed from the first $n$ Fourier coefficients of $f$ wi…

Let $f$ be a piecewise $C^{d}$ function, and let $k$ denote the number of its first Fourier coefficients available for reconstruction. Batenkov–Ettinger's conjecture. The locations…