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Translation and dilation invariant subspaces of L2 (R).

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Translation and dilation invariant subspaces of L2 (R). / Katavolos, A.; Power, S. C.
In: Journal für die reine und angewandte Mathematik (Crelle's Journal), Vol. 2002, No. 552, 01.11.2002, p. 101-129.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Katavolos, A & Power, SC 2002, 'Translation and dilation invariant subspaces of L2 (R).', Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 2002, no. 552, pp. 101-129. https://doi.org/10.1515/crll.2002.087

APA

Katavolos, A., & Power, S. C. (2002). Translation and dilation invariant subspaces of L2 (R). Journal für die reine und angewandte Mathematik (Crelle's Journal), 2002(552), 101-129. https://doi.org/10.1515/crll.2002.087

Vancouver

Katavolos A, Power SC. Translation and dilation invariant subspaces of L2 (R). Journal für die reine und angewandte Mathematik (Crelle's Journal). 2002 Nov 1;2002(552):101-129. doi: 10.1515/crll.2002.087

Author

Katavolos, A. ; Power, S. C. / Translation and dilation invariant subspaces of L2 (R). In: Journal für die reine und angewandte Mathematik (Crelle's Journal). 2002 ; Vol. 2002, No. 552. pp. 101-129.

Bibtex

@article{d684d113749344e79fc0face46967572,
title = "Translation and dilation invariant subspaces of L2 (R).",
abstract = "The closed subspaces of the Hilbert space L2{\dh}R{\TH} which are invariant under multiplication by Hy{\dh}R{\TH} functions and the dilation operators f {\dh}x{\TH} ! f {\dh}sx{\TH}, 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.",
author = "A. Katavolos and Power, {S. C.}",
note = "RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics",
year = "2002",
month = nov,
day = "1",
doi = "10.1515/crll.2002.087",
language = "English",
volume = "2002",
pages = "101--129",
journal = "Journal f{\"u}r die reine und angewandte Mathematik (Crelle's Journal)",
issn = "0075-4102",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "552",

}

RIS

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 -