Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate functions and the adjoint to that Hausdorff operator of the given function. We find estimates for the rate of approximation in various metrics in terms of the parameter of truncation and the components of the Hausdorff operator. Explicit rates of approximation of functions and comparison with approximate identities are given in the case of continuous functions from the class.
|Number of pages||18|
|Journal||Canadian Mathematical Bulletin|
|State||Published - 13 Aug 2020|
Bibliographical noteFunding Information:
Alberto Debernardi was supported by the ERC starting grant No. 713927 and the ISF grant No. 447/16. Elijah Liflyand is the corresponding author.
© Canadian Mathematical Society 2020.
- Approximation in Lebesgue spaces
- Hausdorff operators
- Moduli of continuity