Translation and dilation invariant subspaces of L2 (R).

Katavolos, A. and Power, S. C. (2002) Translation and dilation invariant subspaces of L2 (R). Journal für die reine und angewandte Mathematik (Crelle's Journal), 2002 (552). pp. 101-129. ISSN 0075-4102

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Abstract

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.

Item Type:
Journal Article
Journal or Publication Title:
Journal für die reine und angewandte Mathematik (Crelle's Journal)
Additional Information:
RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
Uncontrolled Keywords:
/dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
ID Code:
2384
Deposited By:
Deposited On:
01 Apr 2008 11:19
Refereed?:
Yes
Published?:
Published
Last Modified:
07 Apr 2020 01:15