It is shown that a continuous 2p-periodic function is uniquely recovered (on the whole real line) by sequences of its Fejér sums values at the given finite set of points if and only if there exist two of these points with the distance between them incommensurable with p. And that full sets of Fejér integrals at any two different points always uniquely recover continuous absolutely Lebesgue integrable on the real line function. Wherein known sequence of Fejér sums values at a fixed single point x ∈ R and full set of Fejér integrals at this point determines uniquely a function only in the class of continuous functions with an even shift by x.
- Continuous 2p-periodic functions
- Continuous absolutely Lebesgue integrable on the real line functions
- Fejér integrals
- Fejér sums
- Uniquely recovering