Polynomial interpolation of holomorphic functions based on Radon projections

ABSTRACT

We study polynomial interpolation of Hermite type of holomorphic functions based on Radon projections. We give two kinds of interpolation schemes and show that the interpolation polynomials are continuous with respect to the angles and the distances. When the chords are suitably distributed, we prove that the interpolation polynomials converge geometrically on the closed unit disk to the functions.

Keywords:

• Polynomial interpolation
• radon projections
• holomorphic functions

AMS Subject Classifications:

• 41A05
• 41A63

Acknowledgments

We are grateful to an anonymous referee for his/her constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Vietnam Institute for Advanced Study in Mathematics under project number B2018-VNCCCT-02.