Gleason's problem and tangential homogeneous interpolation for hyperholomorphic quaternionic functions

Abstract

We study a version of Gleason's problem in the setting of functions of class C¹ in the unit ball of ℂ². We use the setting of hyperholomorphic functions to define and solve the problem. Finally, we briefly discuss a tangential interpolation problem for hyperholomorphic functions.

Keywords:

• Gleason's problem
• Hyperholomorphic functions
• Tangential interpolation

Acknowledgement

The research of Daniel Alpay was supported by the Israel Science Foundation (Grant No. 322/00). The research of Michael Shapiro was partially supported by CONACYT projects as well as by Instituto Politécnico Nacional in the framework of COFAA and CGPI programs.

Notes

†E-mail: [email protected]

Additional information

Notes on contributors

M. Shapiro†

†E-mail: [email protected]