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On a generalized Appell system and monogenic power series

✍ Scribed by S. Bock; K. Gürlebeck

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
291 KB
Volume
33
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

Recently Appell systems of monogenic polynomials in ℝ^3^ were constructed by several authors. Main purpose of this paper is the description of another Appell system that is complete in the space of square integrable quaternion‐valued functions. A new Taylor‐type series expansion based on the Appell polynomials is presented, which can be related to the corresponding Fourier series analogously as in the complex one‐dimensional case. These results find applications in the description of the hypercomplex derivative, the monogenic primitive of a monogenic function and the characterization of functions from the monogenic Dirichlet space. Copyright © 2009 John Wiley & Sons, Ltd.

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