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Best $ L\sp{p}$-approximation of generalized biaxisymmetric potentials


Author: Peter A. McCoy
Journal: Proc. Amer. Math. Soc. 79 (1980), 435-440
MSC: Primary 30E10; Secondary 31A35, 35C99
DOI: https://doi.org/10.1090/S0002-9939-1980-0567987-5
MathSciNet review: 567987
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Abstract: Let F be a real-valued generalized biaxisymmetric potential (GBASP ) in $ {L^p}(p \geqslant 1)$ on $ \Sigma $, the open unit sphere about the origin. Convergence of a sequence of best harmonic polynomial approximates to F in $ {L^p}$ identifies those F that harmonically continue as entire function GBASP and determines their order and type. The analysis utilizes the Bergman and Gilbert Integral Operator Method to extend results from classical function theory on the best polynomial approximation of analytic functions of one complex variable.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0567987-5
Keywords: Generalized biaxisymmetric potentials, harmonic polynomial approximates in $ {L^p}$, entire functions, Bergman and Gilbert Integral Operator Method
Article copyright: © Copyright 1980 American Mathematical Society

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