Ultraspherical expansions and pseudo analytic functions

Allan Fryant

Vol. 94 (1981), No. 1, 83–105

DOI: 10.2140/pjm.1981.94.83

Abstract

This paper takes up the function theoretic approach to the study of ultraspherical expansions, their conjugates, the associated elliptic equations, and first order systems. The theory of pseudo analytic functions and Bergman-Gilbert type integral operators are employed, and the relation between these two approaches is examined. Throughout, results obtained are analogs of well known theorems from the theory of analytic functions of a single complex variable, and the related study of harmonic functions and Fourier series.

Mathematical Subject Classification 2000

Primary: 30G20

Secondary: 31A35, 35C99

Milestones

Received: 9 October 1978

Published: 1 May 1981