Value Distribution of Axisymmetric Potentials
Copyright policy )Value Distribution of Axisymmetric Potentials
where g is an analytic function referred to as the associate of *. The domain of g, W, is an axiconvex subset of the complex plane, C, meaning that whenever g is contained in w then the entire line segment joining g and C is in o. The domain of j is the axisymmetric region obtained by rotating o abolut the real axis. Marden (4, p. 142) employs methods drawn from the analytic theory of polynomials in one complex variable to study A. S. P. and G. A. S. P. whose associates are rational functions. In particular. the set of points in C where the rational function assumes an assigned value is used to determine a pair of cones in E3 and more generally El, n > 4, where the corresponding A. S. P. or G. A. S. P. omits this value.
Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Special integral transforms (Legendre, Hilbert, etc.), Harmonic, subharmonic, superharmonic functions in higher dimensions, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Special integral transforms (Legendre, Hilbert, etc.), Harmonic, subharmonic, superharmonic functions in higher dimensions, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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