Fundamental sets of continuous functions on spheres
Copyright policy )Fundamental sets of continuous functions on spheres
Let \(S^m\) and \(S^\infty\) denote the unit spheres in \(\mathbb{R}^{m+1}\) 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.
- The University of Texas at Austin United States
- Missouri State University United States
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Approximation by arbitrary linear expressions, Multidimensional problems, Positive definite functions in one variable harmonic analysis, fundamental sets of continuous functions, Completeness of sets of functions in one variable harmonic analysis, Approximation by other special function classes, Completeness of sets of functions in nontrigonometric harmonic analysis
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Approximation by arbitrary linear expressions, Multidimensional problems, Positive definite functions in one variable harmonic analysis, fundamental sets of continuous functions, Completeness of sets of functions in one variable harmonic analysis, Approximation by other special function classes, Completeness of sets of functions in nontrigonometric harmonic analysis
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