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Translation and dilation invariant subspaces of L2 (R).

Research output: Contribution to journalJournal article

Published

Journal publication date1/11/2002
JournalJournal fur die reine und angewandte Mathematik (Crelle's Journal)
Journal number552
Volume2002
Number of pages29
Pages101-129
Original languageEnglish

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.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics