Artículo
Unconditional Schauder frames of translates in Lp(ℝd)
Fecha de publicación:
07/2020
Editorial:
Hebrew Univ Magnes Press
Revista:
Israel Journal Of Mathematics
ISSN:
0021-2172
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
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).
Palabras clave:
Schauder frames
,
Unconditionality
,
Frames of translates
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
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
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