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On some constructive aspects of monogenic function theory in ℝ 4
Author(s) -
Morais J.,
Le H. T.,
Sprößig W.
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1474
Subject(s) - mathematics , square integrable function , constructive , orthonormal basis , integrable system , pure mathematics , generalization , unit sphere , cauchy distribution , polynomial , unit cube , orthonormality , algebra over a field , mathematical analysis , discrete mathematics , process (computing) , computer science , operating system , physics , quantum mechanics
As is well known, a possible generalization to ℝ 4 of the classical Cauchy–Riemann system leads to the so‐called Riesz system. The main goal of this paper is to construct explicitly a complete orthonormal system of polynomial solutions of this system with respect to a certain inner product. This will be done in the spaces of square integrable functions on the unit ball over ℝ. Copyright © 2011 John Wiley & Sons, Ltd.