TY - JOUR
T1 - Discrete Translates in Function Spaces
AU - Olevskii, A.
AU - Ulanovskii, A.
N1 - Publisher Copyright:
© 2018, Akadémiai Kiadó, Budapest, Hungary.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - For a wide class of separable Banach function spaces X on ℝ, we construct a Schwartz function φ such that the set of translates {φ(t − λ), λ ∈ Λ} spans X whenever Λ is an exponentially small perturbation of integers. Essentially, the only exception is the space L1(ℝ), which cannot be spanned by a uniformly discrete translates of a single function.
AB - For a wide class of separable Banach function spaces X on ℝ, we construct a Schwartz function φ such that the set of translates {φ(t − λ), λ ∈ Λ} spans X whenever Λ is an exponentially small perturbation of integers. Essentially, the only exception is the space L1(ℝ), which cannot be spanned by a uniformly discrete translates of a single function.
KW - completeness of translates
KW - tempered distribution
KW - uniformly discrete set
UR - http://www.scopus.com/inward/record.url?scp=85048593939&partnerID=8YFLogxK
U2 - 10.1007/s10476-018-0209-x
DO - 10.1007/s10476-018-0209-x
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AN - SCOPUS:85048593939
SN - 0133-3852
VL - 44
SP - 251
EP - 261
JO - Analysis Mathematica
JF - Analysis Mathematica
IS - 2
ER -