TY - JOUR
T1 - Gleason’s problem, rational functions and spaces of left-regular functions
T2 - The split-quaternion setting
AU - Alpay, Daniel
AU - Luna-Elizarrarás, María E.
AU - Shapiro, Michael
AU - Struppa, Daniele
N1 - Publisher Copyright:
© 2018, Hebrew University of Jerusalem.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We study Gleason’s problem, rational functions and spaces of regular functions in the setting of split-quaternions. There are two natural symmetries in the algebra of split-quaternions. The first symmetry allows to define positive matrices with split-quaternionic entries, and also reproducing Hilbert spaces of regular functions. The second leads to reproducing kernel Krein spaces.
AB - We study Gleason’s problem, rational functions and spaces of regular functions in the setting of split-quaternions. There are two natural symmetries in the algebra of split-quaternions. The first symmetry allows to define positive matrices with split-quaternionic entries, and also reproducing Hilbert spaces of regular functions. The second leads to reproducing kernel Krein spaces.
UR - http://www.scopus.com/inward/record.url?scp=85046713003&partnerID=8YFLogxK
U2 - 10.1007/s11856-018-1696-y
DO - 10.1007/s11856-018-1696-y
M3 - Article
AN - SCOPUS:85046713003
SN - 0021-2172
VL - 226
SP - 319
EP - 349
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -