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A note on approximation by automorphic images of functions in L1 and L∞

Published online by Cambridge University Press:  09 April 2009

S. R. Harasymiv
S. R. Harasymiv
Affiliation:
Department of MathematicsInstitute of Advanced Studies Australian National University
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In [1], it was shown that if ƒ ∈ Lp(Rn), where 1 < p < ∞, then the closed subspace of Lp (Rn) spanned by functions of the form [where a1, …, an, b1, …, bn, are real numbers; ak, ≠ 0; k = 1, …, n] coincides with the whole of Lp(Rn). In the present note, analogous results are derived for the spaces of integrable functions, essentially bounded measurable functions, bounded continuous functions, and continuous functions vanishing at infinity.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 2 , May 1968 , pp. 222 - 230
Copyright
Copyright © Australian Mathematical Society 1968

References

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