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- Title
The L<sup>p,q</sup>-stability of the Shifts of Finitely Many Functions in Mixed Lebesgue Spaces L<sup>p,q</sup>(ℝ<sup>d+1</sup>).
- Authors
Li, Rui; Liu, Bei; Liu, Rui; Zhang, Qing Yue
- Abstract
The stability is an expected property for functions, which is widely considered in the study of approximation theory and wavelet analysis. In this paper, we consider the Lp,q-stability of the shifts of finitely many functions in mixed Lebesgue spaces Lp,q(ℝd+1). We first show that the shifts ϕ(· − k) (k ∈ ℤd+1) are Lp,q-stable if and only if for any ξ ∈ ℝd+1, ∑k∈Zd+1|ϕ^(ξ+2πk)|2>0<inline-graphic></inline-graphic>. Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces Lp,q(ℝd+1) to be Lp,q-stable which improves some known results.
- Subjects
RADON integrals; APPROXIMATION theory; MATHEMATICAL formulas; MATHEMATICAL convolutions; EQUATIONS
- Publication
Acta Mathematica Sinica, 2018, Vol 34, Issue 6, p1001
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-018-7333-1