SpringerIranian Journal of Science and Technology (Sciences)1028-627634420101201TWO-DIRECTION POLY-SCALE REFINEMENT EQUATIONS WITH NONNEGATIVE COEFFICIENTS321334218210.22099/ijsts.2010.2182ENS.YANGDepartment of Mathematics, Shantou University, Shantou, P. R. ChinaJ.LINDepartment of Mathematics, Shantou University, Shantou, P. R. ChinaJournal Article20090708In this paper, we study L1 -solutions of the following two-direction poly-scale refinement equation<br />We prove that the vector space of all L1 -solutions of the above equation is at most one-dimensional and<br />consists of compactly supported functions of constant sign. We also show that any- L1 solution of the above<br />equation is either positive or negative on its support under a special assumption. With regard to the -<br />solutions of the equation, some simple sufficient conditions for the existence of nontrivial -solutions and<br />the nonexistence of such solutions are given.http://ijsts.shirazu.ac.ir/article_2182_627de8f44897b33f1b0d477fdc205182.pdf