zonal functions
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Author(s):  
Willi Freeden ◽  
M. Zuhair Nashed ◽  
Michael Schreiner
Keyword(s):  


2017 ◽  
Vol 58 ◽  
pp. 238
Author(s):  
Zhixiang Chen ◽  
Feilong Cao


2017 ◽  
Vol 58 (3-4) ◽  
pp. 238-246
Author(s):  
ZHIXIANG CHEN ◽  
FEILONG CAO

We address the construction and approximation for feed-forward neural networks (FNNs) with zonal functions on the unit sphere. The filtered de la Vallée-Poussin operator and the spherical quadrature formula are used to construct the spherical FNNs. In particular, the upper and lower bounds of approximation errors by the FNNs are estimated, where the best polynomial approximation of a spherical function is used as a measure of approximation error.



2013 ◽  
Vol 404 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Agata Bezubik ◽  
Aleksander Strasburger
Keyword(s):  


2008 ◽  
Vol 90 (1) ◽  
pp. 70-81 ◽  
Author(s):  
Agata Bezubik ◽  
Agata Da̧browska ◽  
Aleksander Strasburger


2002 ◽  
Vol 96 (1) ◽  
pp. 55-75
Author(s):  
Christine Bachoc ◽  
Gabriele Nebe




1972 ◽  
Vol 24 (1) ◽  
pp. 60-71
Author(s):  
Charles F. Dunkl

One of the main uses of harmonic analysis on the sphere is to discover new theorems about series of ultraspherical (Gegenbauer) polynomials. In this paper, we will construct singular integral operators from scalar functions on the sphere to vector functions. These operators when restricted to zonal functions give Lp-bounded (1 < p < ∞ ) operators on ultraspherical series.We will use [7, Chapter 9] as our main reference. Let G denote a compact group, with identity e, and Ĝ its dual, the set of equivalence classes of continuous irreducible unitary representations of G.



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