TY - JOUR

T1 - Completeness of integer translates in function spaces on ℝ

AU - Atzmon, A.

AU - Olevskiǐ, A.

PY - 1996/12

Y1 - 1996/12

N2 - We show that each of the Banach spaces C0(ℝ) and Lp(ℝ), 2 < p < ∞, contains a function whose integer translates are complete. This function can also be chosen so that one of the following additional conditions hold: (1) Its non-negative integer translates are already complete. (2) Its integer translates form an orthonormal system in L2(ℝ). (3) Its integer translates form a minimal system. A similar result holds for the corresponding Sobolev space, for certain weighted L2 spaces, and in the multivariate setting. We also prove some results in the opposite direction.

AB - We show that each of the Banach spaces C0(ℝ) and Lp(ℝ), 2 < p < ∞, contains a function whose integer translates are complete. This function can also be chosen so that one of the following additional conditions hold: (1) Its non-negative integer translates are already complete. (2) Its integer translates form an orthonormal system in L2(ℝ). (3) Its integer translates form a minimal system. A similar result holds for the corresponding Sobolev space, for certain weighted L2 spaces, and in the multivariate setting. We also prove some results in the opposite direction.

UR - http://www.scopus.com/inward/record.url?scp=0030529188&partnerID=8YFLogxK

U2 - 10.1006/jath.1996.0106

DO - 10.1006/jath.1996.0106

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AN - SCOPUS:0030529188

SN - 0021-9045

VL - 87

SP - 291

EP - 327

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 3

ER -