
APPROXIMATIONS AND THE LINEARITY OF THE SHEPP SPACEAPPROXIMATIONS AND THE LINEARITY OF THE SHEPP SPACEAA10994346 
"/Honda, Aoi/"Honda, Aoi ,
"/Okazaki, Yoshiaki/"Okazaki, Yoshiaki ,
"/Sato, Hiroshi/"Sato, Hiroshi
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, pp.173

194 , 20150609 , Faculty of Mathematics, Kyushu University
ISSN:13406116
NCID:AA10994346
Description
Suggested by Shepp [Ann. Math. Statist. 36(4) (1965), 11071112] we defined a sequence space Λ_p(f) determined by a single function f(≠ 0) ∈ L_p(R, dx), 1 ≤ p < +∞, and discussed the structure of it. The problems are the linearity and the visible sequential representation of Λ_p(f). In this paper we name Λ_p(f) a Shepp space and discuss the problems in the case of p = 2 by defining an inner approximation Λ^0_2(f) and an outer approximation Λ^φ_2(f) of Λ_2 (f), and we give a necessary and sufficient condition for Λ^0_2(f) =Λ^φ_2 (f) in terms of doubling dimension. In this case Λ_2(f) is a linear space and those approximationsare its visible sequential representations. We also give an example such that Λ_2(f) is a linear space butΛ^0_2 (f) ≠Λ^φ_2.