info:eu-repo/semantics/article
Unconditional Schauder frames of translates in Lp(ℝd)
Fecha
2020-07Registro en:
Berasategui, Miguel Hernán; Carando, Daniel Germán; Unconditional Schauder frames of translates in Lp(ℝd); Hebrew Univ Magnes Press; Israel Journal Of Mathematics; 238; 2; 7-2020; 687-713
0021-2172
CONICET Digital
CONICET
Autor
Berasategui, Miguel Hernán
Carando, Daniel Germán
Resumen
We show that, for 1 < p ≤ 2, the space Lp(ℝd) does not admit unconditional Schauder frames {fi, f′i}i∈ℕ where {fi} is a sequence of translates of finitely many functions and {f′i} is seminormalized. In fact, the only subspaces of Lp(ℝd) admitting such Banach frames are those isomorphic to ℓp. On the other hand, if 2 < p < +∞ and {λi}i∈ℕ ⊆ ℝd is an unbounded sequence, there is a subsequence {λmi}i∈ℕ, a function f ∈ Lp(ℝd), and a seminormalized sequence of bounded functionals {λ′i}i∈ℕ such that {Tλmif,fi′}i∈ℕ is an unconditional Schauder frame for Lp(ℝd).