English

On the $L^2$-norms of periodizations of functions

Classical Analysis and ODEs 2007-05-23 v1

Abstract

We prove that the L2([0,1]d)×SO(d))L^2([0,1]^d) \times SO(d)) norm of periodizations of a function from L1(Rd)L^1(R^d) is equivalent to the L2(Rd)L^2(R^d) norm of the function itself in higher dimensions.

Keywords

Cite

@article{arxiv.math/0202020,
  title  = {On the $L^2$-norms of periodizations of functions},
  author = {Oleg Kovrijkine},
  journal= {arXiv preprint arXiv:math/0202020},
  year   = {2007}
}