Document Type: Regular Paper
Department of Mathematics, Shantou University, Shantou, P. R. China
In this paper, we study L1 -solutions of the following two-direction poly-scale refinement equation
We prove that the vector space of all L1 -solutions of the above equation is at most one-dimensional and
consists of compactly supported functions of constant sign. We also show that any- L1 solution of the above
equation is either positive or negative on its support under a special assumption. With regard to the -
solutions of the equation, some simple sufficient conditions for the existence of nontrivial -solutions and
the nonexistence of such solutions are given.