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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the zeros of generalized axially symmetric potentials

Author: Peter A. McCoy
Journal: Proc. Amer. Math. Soc. 61 (1976), 54-58
MSC: Primary 31B15; Secondary 35B99
MathSciNet review: 0477095
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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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Keywords: Bergman and Gilbert's integral operators, Gilbert-Hadamard theorem, Carathéodory-Toeplitz and Schur theorems, zeros of potentials
Article copyright: © Copyright 1976 American Mathematical Society