Approximation of the Hilbert Transform on the unit circle
<|reference_start|>Approximation of the Hilbert Transform on the unit circle: The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szeg\"o and anti-Szeg\"o quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accuracy through their averaged results. Their computation involves a free parameter associated with the corresponding para-orthogonal polynomials. Here, it is suitably chosen to construct a Szeg\"o and anti-Szeg\"o formula whose nodes are strategically distanced from the singularity of the Hilbert kernel. Numerical experiments demonstrate the accuracy of the proposed method.<|reference_end|>
@article{fermo2024approximation,
    title={Approximation of the Hilbert Transform on the unit circle},
    author={Luisa Fermo, Valerio Loi},
    journal={arXiv preprint arXiv:2409.07810},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.07810},
    primaryClass={math.NA cs.NA}
}