Overconvergence of polynomial expansions of harmonic functions

ABSTRACT

This paper concerns homogeneous polynomial expansions of harmonic functions. It presents new results on the relationship between their gap structure and their overconvergence properties outside the ball of convergence.

COMMUNICATED BY:

• D. Khavinson

KEYWORDS:

• Harmonic approximation
• Ostrowski gaps
• universal functions

AMS SUBJECT CLASSIFICATIONS:

• 31B05

Acknowledgments

I am grateful to Professor Stephen Gardiner for his valuable advice and encouragement.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by a Government of Ireland postgraduate scholarship from the Irish Research Council.