Vol. 94, No. 1, 1981

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Ultraspherical expansions and pseudo analytic functions

Allan Fryant

Vol. 94 (1981), No. 1, 83–105
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
Authors
Allan Fryant