Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Translation and dilation invariant subspaces of L2 (R).
AU - Katavolos, A.
AU - Power, S. C.
N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
PY - 2002/11/1
Y1 - 2002/11/1
N2 - The closed subspaces of the Hilbert space L2ðRÞ which are invariant under multiplication by HyðRÞ functions and the dilation operators f ðxÞ ! f ðsxÞ, 1 < s < y, are determined as the two parameter family of subspaces L2½a; b, 0ea, bey, which are reducing for multiplication operators, together with a four parameter family of nonreducing subspaces. The lattice and topological structure are determined and using operator algebra methods the corresponding family of orthogonal projections, with the weak operator topology, is identified as a compact connected 4-manifold.
AB - The closed subspaces of the Hilbert space L2ðRÞ which are invariant under multiplication by HyðRÞ functions and the dilation operators f ðxÞ ! f ðsxÞ, 1 < s < y, are determined as the two parameter family of subspaces L2½a; b, 0ea, bey, which are reducing for multiplication operators, together with a four parameter family of nonreducing subspaces. The lattice and topological structure are determined and using operator algebra methods the corresponding family of orthogonal projections, with the weak operator topology, is identified as a compact connected 4-manifold.
U2 - 10.1515/crll.2002.087
DO - 10.1515/crll.2002.087
M3 - Journal article
VL - 2002
SP - 101
EP - 129
JO - Journal für die reine und angewandte Mathematik (Crelle's Journal)
JF - Journal für die reine und angewandte Mathematik (Crelle's Journal)
SN - 0075-4102
IS - 552
ER -