摘要
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 L^p,q-stability of the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1）. We first show that the shifts Φ（·- k） （k∈Z^d＋1） are L^p,q-stable if and only if for any ξ ∈R^d＋1,∑κ∈Z^d＋1 ]｜Φ^^（ξ ＋ 2πκ）]^2 〉 0. Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1） to be L^p,q-stable which improves some known results.
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 L^p,q-stability of the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1）. We first show that the shifts Φ（·- k） （k∈Z^d＋1） are L^p,q-stable if and only if for any ξ ∈R^d＋1,∑κ∈Z^d＋1 ]｜Φ^^（ξ ＋ 2πκ）]^2 〉 0. Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces L^p,q（R^d＋1） to be L^p,q-stable which improves some known results.
基金
Supported by the National Natural Science Foundation of China(Grant Nos.11371200,11401435,11601383and 11671214)
Hundred Young Academia Leaders Program of Nankai University
