Abstract
If f ∈ Lp(ℝd) is a bounded real valued continuous function which has a unique maximum or a unique minimum at a point x0 ∈ ℝd and if the inverse image of the neighborhoods of f(x 0) shrinks regularly to x 0, then span (Formula Presented) is a dense subset of Lp(ℝd), 1 ≤ p< ∞ where f m(x)=f(x)m and {e i} is the natural basis of Rd. The result extends to all homogeneous groups, Riemannian symmetric spaces of noncompact type, Damek-Ricci spaces etc.
Original language | English |
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Pages (from-to) | 186-198 |
Number of pages | 13 |
Journal | Journal of Fourier Analysis and Applications |
Volume | 20 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2014 |
Keywords
- Euclidean space
- Grid-translate
- Homogeneous group
- Riemannian symmetric space
ASJC Scopus subject areas
- Analysis
- General Mathematics
- Applied Mathematics