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Journal article
Stability of wavelet frames with matrix dilations 10.1090/S0002-9939-05-08134-7
Under certain assumptions we show that a wavelet frame {Tau(A(j), b(j,k))psi} (j,k is an element of Z) := {vertical bar detA(j)vertical bar(-1/2) psi(A(j)(-1)(x - b(j,k)))} (j,k is an element of Z) in L-2(R-d) remains a frame when the dilation matrices A(j) and the translation parameters b(j,k) are perturbed. As a special case of our result, we obtain that if {Tau(A(j), A(j)Bn)psi} (j is an element of Z, n is an element of Zd) is a frame for an expansive matrix A and an invertible matrix B, then {Tau(A'(j), A(j)B lambda(n))psi}(j is an element of Z,) (n is an element of) (Zd) is a frame if ...
Year: 2006
Language: English
