Reconstruction of functions on the basis of sequences of linear functionals (Q1904376)

The author studies the question about a reconstruction of functions from a certain class. The reconstruction is realized on the basis of sequences of linear functionals \(\ln(f)= \sum^{m(n)}_{k= 0} a_{nk} f(x_{nk})\). An explicit expression for the reconstructed function is given. The author studies the sequences of linear functionals of the form defined above and shows some new examples which have the property that \(\ln(f)= 0\) implies \(f= 0\). Then he also gives an explicit expression for \(f\) on the basis for information of \(\ln(f)\).