Proof of a result relating to orthogonal scaling functions series expansions
Ting Liu, Christopher J. Zarowski · 2002
In Zarowski the projection error behaviour of the scaling function series expansion was considered, and a closed form expression (which is valid when /spl phi/(t) satisfies certain moment constraints) for the error /spl epsiv/(t)=x(t)-a(t)(a(t) is the projection of x(t) onto subspace V/sub L/ of L/sup 2/(R)) was given in Zarowski (2000) for x(t)={ts,t/spl ges/0; 0,t<0 with s/spl isin/{0,1,2,...}. However, a proof of the validity of the stated expression for /spl epsiv/(t) was not given except for a few special values of s. In this paper we give a proof which is valid for all s/spl isin/{0,1,2,...}. Some miscellaneous facts about /spl epsiv/(t) are also presented.