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On monogenic Q_p functions
by
Klaus Guerlebeck
Bauhaus-Universitaet Weimar, Institut f. Mathematik/Physik
We consider a scale of weighted spaces of quaternion-valued functions of three real variables. This scale generalizes the idea of Qp-spaces in the complex function theory. We prove some basic properties and relate the quaternionic Qp-spaces to other important function spaces. The main result is the equivalent characterization of Qp-functions by the coefficients of quaternionic Taylor series and Fourier series expansions. At the end we discuss generalizations of other scales, as for instance of the Bq-scale.
Date received: August 3, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahz-22.