Linear independence of translations

Journal of the Australian Mathematical Society

Joseph Rosenblatt¹ 

关键词: 39A10;    42A38;   

DOI  :  10.1017/S1446788700038519

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

It was shown by Edgar and Rosenblatt that f ∈ Lp (ℝn), 1 ≤ p < 2n/ (n-1), and f ≠0, then f has linearly independent translates. Using a result of Hömander, it is shown here that the same theorem holds if p = 2n / (n−1). This gives a sharp result because for n ≥2, there exists f ∈C0 (ℝn), f ≠0, which is simultaneously in all Lp (ℝn), p > 2n/(n−1), that has a linear dependence relation among its translates. References and some discussion are included.

【 授权许可】

Unknown