Orthogonality criteria for compactly supported refinable functions and refinable function vectors
摘要:
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.
Riesz bounds of Wilson bases generated byB-splines
作者:Bernhard Trebels、Gabriele Steidl
DOI:10.1007/bf02510659
日期:2000.3
In this paper we are concerned with biorthogonal Wilson buses having B-splines as well as powers of sinc functions as window functions. We prove properties of B-splines and exponential Euler splines and use there properties to estimate the Riesz bounds of the Wilson bases.
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.