TY - JOUR
T1 - The C-property for slice regular functions and applications to the Bergman space
AU - Colombo, Fabrizio
AU - González-Cervantes, J. Oscar
AU - Sabadini, Irene
PY - 2013/10
Y1 - 2013/10
N2 - This article has a twofold purpose: on one hand, we deepen the study of slice regular functions by studying their behaviour with respect to the so-called C-property and anti-C-property. We show that, for any fixed basis of the algebra of quaternions ℍ any slice regular function decomposes into the sum of four slice regular components, each of them satisfying the C-property. Then, we will use these results to show a reproducing property of the Bergman kernels of the second kind.
AB - This article has a twofold purpose: on one hand, we deepen the study of slice regular functions by studying their behaviour with respect to the so-called C-property and anti-C-property. We show that, for any fixed basis of the algebra of quaternions ℍ any slice regular function decomposes into the sum of four slice regular components, each of them satisfying the C-property. Then, we will use these results to show a reproducing property of the Bergman kernels of the second kind.
KW - Bergman kernel
KW - C-property
KW - slice regular functions
UR - http://www.scopus.com/inward/record.url?scp=84887887099&partnerID=8YFLogxK
U2 - 10.1080/17476933.2012.674521
DO - 10.1080/17476933.2012.674521
M3 - Artículo
SN - 1747-6933
VL - 58
SP - 1355
EP - 1372
JO - Complex Variables and Elliptic Equations
JF - Complex Variables and Elliptic Equations
IS - 10
ER -