On the zeros of generalized axially symmetric potentials

McCoy, Peter A.

doi:10.1090/S0002-9939-1976-0477095-9

On the zeros of generalized axially symmetric potentials
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Proc. Amer. Math. Soc. 61 (1976), 54-58 Request permission

Abstract:

Generalized axially symmetric potentials may be expanded as Fourier-Jacobi series in terms of the complete system ${r^k}C_k^{n/2 - 1}(\cos \theta )$ on axisymmetric regions $\Omega \subset {E^n}(n \geqslant 3)$ about the origin. The values of these potentials are characterized by the nonnegativity of sequences of determinants drawn from the Fourier coefficients in a manner analogous to the characterization of the values of analytic functions of one complex variable by the theorems of Carathéodory-Toeplitz and Schur.

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