Unconditional structures of translates for Lp(ℝd)
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© 2014, Hebrew University of Jerusalem. We prove that a sequence (fi)i=1∞ of translates of a fixed f ∈ Lp(ℝ) cannot be an unconditional basis of Lp(ℝ) for any 1 ≤ p < ∞. In contrast to this, for every 2 < p < ∞, d ∈ ℕ and unbounded sequence (λn)n∈ℕ ⊂ ℝd we establish the existence of a function f ∈ Lp(ℝd) and sequence (gn*)n∈ℕ ⊂ Lp*(ℝd) such that (Formula Presented) forms an unconditional Schauder frame for Lp(ℝd). In particular, there exists a Schauder frame of integer translates for Lp(ℝ) if (and only if) 2 < p < ∞.
author list (cited authors)
Freeman, D., Odell, E., Schlumprecht, T. h., & Zsák, A.