Generalized axisymmetric elliptic functions

Peter A. McCoy

Vol. 59 (1975), No. 1, 211–221

DOI: 10.2140/pjm.1975.59.211

Abstract

A generalized axisymmetric elliptic function (GASE) Ψ_ν : Ω ⊂ Eⁿ → C of order ν ≧ 0 solving the partial differential equation

(1)

with analytic coefficients is subject to Cauchy data: Ψ_ν(x,0) = f(x),(∂∕∂ρ)(Ψ_ν(x,0)) = 0 along the singular line. These GASE may be generated from associated analytic functions of one complex variable or associated solutions to the corresponding nonsingular equation by certain integral operators. Convexity arguments geometrically characterize the values of GASE from those of the associates and kernel functions of the respective operators.

Mathematical Subject Classification 2000

Primary: 31B35

Secondary: 35Q05

Milestones

Received: 22 February 1974

Revised: 7 March 1975

Published: 1 July 1975