Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 31B15, 35B99

Retrieve articles in all journals with MSC: 31B15, 35B99


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0477095-9
PII: S 0002-9939(1976)0477095-9
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