Harmonic interpolation of Hermite type based on Radon projections with constant distances

ABSTRACT

We study harmonic interpolation of Hermite type of harmonic functions based on Radon projections with constant distances of chords. We show that the interpolation polynomials are continuous with respect to the angles and the distances. When the chords coalesce to some points on the unit circle, we prove that the interpolation polynomials tend to a Hermite interpolation polynomial at the coalescing points.

Keywords:

• Polynomial interpolation
• Radon projections
• harmonic polynomials

AMS Subject Classifications:

• 41A05
• 41A63

Acknowledgments

We are grateful to an anonymous referee for his/her constructive comments. This paper has been partially done during a visit of the first named author at the Institute de Mathématiques de Toulouse in 2017.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Phung Van Manh wishes to thank Institute de Mathématiques de Toulouse, LIA-Formath Vietnam and Prof. Jean-Paul Calvi for financial support and warm hospitality. This research is funded by the Vietnam Ministry of Education and Training under grant number B2018-SPH-57.