Completeness of integer translates in function spaces on R

[摘要] We show that each of the Banach spaces C-0(R) and L(p)(R), 2 < p < infinity,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 L(2)(R). (3) Its integer translates form a minimal system. A similar result holds for the corresponding Sobolev space, for certain weighted L(2) spaces, and in the multivariate setting. We also prove some results in the opposite direction. (C) 1996 Academic Press, Inc.

[发布日期] 1996-12-01