. ORTHOGONAL EXPANSIONS OP DISTRIBUTIONS

REMARK 7.2.1. If T = / , where / is a 1-periodic continuous funct ion, t hen v — f \ f(x)e~~27TUX dx. Indeed, we have

c„= J f(x)iP{x)e-i27TUXdx = Y J f{x)^{x)e-i2lxuxdx

] T Í f(uMcü + v)e-*2™"düü= f f(x 2

— Í2TTVX )e~l^vx dx.