TY - JOUR
T1 - Frames, Riesz systems and multiresolution analysis in Hilbert spaces
AU - Eijndhoven, van, S.J.L.
AU - Oonincx, P.J.
PY - 1999
Y1 - 1999
N2 - The concept of multiresolution analysis (MRA) is introduced for arbitrary separable Hilbert spaces H. It is put in the general terms of unitary operators U1 and U2.1, …, U2.d, d e Z and a generating element f. Each MRA yields a system ¿ = 1kU2,1l1 … U2,dld¿n ¦ N = 0,…, N - 1, k e Z, l e Zd, where the ¿n are related to f. Necessary and sufficient conditions on U1, U2,1,…, U2,d, f and ¿n are given, by means of properties of matrix-valued functions on the unit circle, such that V is a Riesz system or Riesz basis in H.
AB - The concept of multiresolution analysis (MRA) is introduced for arbitrary separable Hilbert spaces H. It is put in the general terms of unitary operators U1 and U2.1, …, U2.d, d e Z and a generating element f. Each MRA yields a system ¿ = 1kU2,1l1 … U2,dld¿n ¦ N = 0,…, N - 1, k e Z, l e Zd, where the ¿n are related to f. Necessary and sufficient conditions on U1, U2,1,…, U2,d, f and ¿n are given, by means of properties of matrix-valued functions on the unit circle, such that V is a Riesz system or Riesz basis in H.
U2 - 10.1016/S0019-3577(99)80029-9
DO - 10.1016/S0019-3577(99)80029-9
M3 - Article
SN - 0023-3358
VL - 10
SP - 369
EP - 382
JO - Indagationes Mathematicae. New Series
JF - Indagationes Mathematicae. New Series
IS - 3
ER -