Orthogonality criteria for compactly supported refinable functions and refinable function vectors
作者:Jeffrey C. Lagarias、Yang Wang
DOI:10.1007/bf02510658
日期:2000.3
A refinable function phi(x) : R-n --> R or, more generally, a refinable function vector Phi(x) = [phi(1)(x),..., phi(r)(x)](T) is an L-1 solution of a system of (vector-valued) refinement equations involving expansion by a dilation matrix A, which is an expanding integer matrix. A refinable function vector is called orthogonal if phi(j)(x - alpha) : alpha epsilon Z(n), 1 less than or equal to j less than or equal to r} form an orthogonal set of functions in L-2(R-n). Compactly supported orthogonal refinable functions and function vectors can be used to construct orthonormal wavelet and multi-wavelet buses of L-2(R-n). In this paper we give ct comprehensive set of necessary and sufficient conditions for the orthogonality of compactly supported refinable functions and refinable function vectors.