A construction of multiresolution analysis by integral equations

摘要

In this paper we present a versatile construction of multiresolution analysis of two variables by means of eigenvalue problems of the integral equation, for lambda = 2. As a consequence we show that if phi(x) is the solution of the equation phi(x) = lambda integral(R) h(2x - y)phi(y)dy with supp (h) over cap(omega) = [-pi, pi], then V-j = span {phi(2(j) x(1) - k(1)) phi(2(j) x(2) - k(2)) k(1), k(2) is an element of Z} constructs a two-variable multiresolution analysis. [References: 13]