On Riesz systems of harmonic conjugates in R3

被引：5
作者：
Morais, J. [1 ]
Avetisyan, K. [1 ]
Guerlebeck, K. [1 ]
机构：
[1] Univ Aveiro, CIDMA, P-3810193 Aveiro, Portugal
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2013年 / 36卷 / 12期
关键词：
quaternion analysis; spherical harmonics; Riesz system; monogenic functions; harmonic conjugates; Hardy space; Bergman space; ORTHOGONAL APPELL SYSTEMS; MEAN-VALUES;
D O I：
10.1002/mma.2709
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In continuation of recent studies, we discuss two constructive approaches for the generation of harmonic conjugates to find null solutions to the Riesz system in R3. This class of solutions coincides with the subclass of monogenic functions with values in the reduced quaternions. Our first algorithm for harmonic conjugates is based on special systems of homogeneous harmonic and monogenic polynomials, whereas the second one is presented by means of an integral representation. Some examples of function spaces illustrating the techniques involved are given. More specifically, we discuss the (monogenic) Hardy and weighted Bergman spaces on the unit ball in R3 consisting of functions with values in the reduced quaternions. We end up proving the boundedness of the underlying harmonic conjugation operators in certain weighted spaces. Copyright (c) 2013 John Wiley & Sons, Ltd.
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收藏
页码：1598 / 1614
页数：17
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