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Fundamental sets of continuous functions on spheres. (English) Zbl 0886.41016
Let $S^m$ and $S^\infty$ denote the unit spheres in $\bbfR^{m+1}$ and $\ell^2$, respectively. The authors look for functions $f$ in $C[- 1,1]$ such that the family of functions $x\mapsto f(\langle x,v\rangle)$, where $v$ runs over $S^m$, is fundamental in the space $C(S^m)$. They also consider this problem for $C(S^\infty)$ when this space is given the topology of uniform convergence on compact sets.

##### MSC:
 41A30 Approximation by other special function classes 41A45 Approximation by arbitrary linear expressions 41A63 Multidimensional approximation problems 42A65 Completeness of sets of functions 42A82 Positive definite functions 42C10 Fourier series in special orthogonal functions 42C30 Completeness of sets of functions of non-trigonometric Fourier analysis
##### Keywords:
fundamental sets of continuous functions
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##### References:
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