Boundary Interpolation for Slice Hyperholomorphic Schur Functions

Authors

Khaled Abu-Ghanem, Ben Gurion University of the Negev
Daniel Alpay, Chapman UniversityFollow
Fabrizio Colombo, Politecnico di Milano
David P. Kimsey, Ben Gurion University of the Negev
Irene Sabadini, Politecnico di Milano

Document Type

Article

Publication Date

2015

Abstract

A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers κ1,…,κN, quaternions p1,…,pN all of modulus 1, so that the 2-spheres determined by each point do not intersect and pu≠1 for u=1,…,N, and quaternions s1,…,sN, we wish to find a slice hyperholomorphic Schur function s so that
limr→1r∈(0,1)s(rpu)=suforu=1,…,N,
and
limr→1r∈(0,1)1−s(rpu)su¯¯¯¯¯1−r≤κu,foru=1,…,N.
Our arguments relies on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Integral Equations and Operator Theory, volume 82, in 2015 following peer review. The final publication is available at Springer via DOI: 10.1007/s00020-014-2184-3

Recommended Citation

Kh. Abu-Ghanem,D. Alpay, F. Colombo,D. Kimsey and I. Sabadini. Boundary interpolation for slice hyperholomorphic Schur functions. Integral Equations and Operator Theory, vol. 82 (2015), 223-248.

Peer Reviewed

1

Copyright

Springer