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Construction of Parseval wavelets from redundant filter systems
We consider wavelets in L 2 ( R d ) which have generalized multiresolutions. This means that the initial resolution subspace V 0 in L 2 ( R d ) is not singly generated. As a result, the representation of the integer lattice Z d restricted to V 0 has a nontrivial multiplicity function. We show how th...
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| Published in: | Journal of mathematical physics 2005-08, Vol.46 (8), p.083502-083502-28 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c447t-51c0e4501b35c6b5264bc7b84a8dec696e70efbef7df7ee33b83c8d841330f0f3 |
| container_end_page | 083502-28 |
| container_issue | 8 |
| container_start_page | 083502 |
| container_title | Journal of mathematical physics |
| container_volume | 46 |
| creator | Baggett, L. W. Jorgensen, P. E. T. Merrill, K. D. Packer, J. A. |
| description | We consider wavelets in
L
2
(
R
d
)
which have generalized multiresolutions. This means that the initial resolution subspace
V
0
in
L
2
(
R
d
)
is not singly generated. As a result, the representation of the integer lattice
Z
d
restricted to
V
0
has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on
R
d
can be constructed directly from the generalized wavelet filters. |
| doi_str_mv | 10.1063/1.1982768 |
| format | article |
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L
2
(
R
d
)
which have generalized multiresolutions. This means that the initial resolution subspace
V
0
in
L
2
(
R
d
)
is not singly generated. As a result, the representation of the integer lattice
Z
d
restricted to
V
0
has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on
R
d
can be constructed directly from the generalized wavelet filters.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.1982768</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>ALGEBRA ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; Exact sciences and technology ; HILBERT SPACE ; Mathematical methods in physics ; Mathematics ; MULTIPLICITY ; Physics ; RESOLUTION ; Sciences and techniques of general use ; VECTORS ; WAVE FUNCTIONS</subject><ispartof>Journal of mathematical physics, 2005-08, Vol.46 (8), p.083502-083502-28</ispartof><rights>American Institute of Physics</rights><rights>2005 American Institute of Physics</rights><rights>2005 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c447t-51c0e4501b35c6b5264bc7b84a8dec696e70efbef7df7ee33b83c8d841330f0f3</citedby><cites>FETCH-LOGICAL-c447t-51c0e4501b35c6b5264bc7b84a8dec696e70efbef7df7ee33b83c8d841330f0f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.1982768$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>230,314,780,782,784,795,885,27924,27925,76255</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17147719$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/20699349$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Baggett, L. W.</creatorcontrib><creatorcontrib>Jorgensen, P. E. T.</creatorcontrib><creatorcontrib>Merrill, K. D.</creatorcontrib><creatorcontrib>Packer, J. A.</creatorcontrib><title>Construction of Parseval wavelets from redundant filter systems</title><title>Journal of mathematical physics</title><description>We consider wavelets in
L
2
(
R
d
)
which have generalized multiresolutions. This means that the initial resolution subspace
V
0
in
L
2
(
R
d
)
is not singly generated. As a result, the representation of the integer lattice
Z
d
restricted to
V
0
has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on
R
d
can be constructed directly from the generalized wavelet filters.</description><subject>ALGEBRA</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>Exact sciences and technology</subject><subject>HILBERT SPACE</subject><subject>Mathematical methods in physics</subject><subject>Mathematics</subject><subject>MULTIPLICITY</subject><subject>Physics</subject><subject>RESOLUTION</subject><subject>Sciences and techniques of general use</subject><subject>VECTORS</subject><subject>WAVE FUNCTIONS</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQQIMoWKsH_0FAPChsTTbZJHtRpPgFBT3oOWSzE1zZbkqSVvrv7bKFClJPc3nzhnkInVMyoUSwGzqhpcqlUAdoRIkqMykKdYhGhOR5lnOljtFJjF-EUKo4H6G7qe9iCkubGt9h7_CbCRFWpsXfZgUtpIhd8HMcoF52tekSdk2bIOC4jgnm8RQdOdNGONvOMfp4fHifPmez16eX6f0ss5zLlBXUEuAFoRUrrKiKXPDKykpxo2qwohQgCbgKnKydBGCsUsyqWnHKGHHEsTG6GLw-pkZH2ySwn9Z3HdikcyLKkvFyQ10NlA0-xgBOL0IzN2GtKdF9H031ts-GvRzYhYnWtC6YzjZxtyApl5L2ztuB64-aPtN-6e-Y2jvdx9wIrvcJVj7slvWidv_Bf1_4AQwZlu4</recordid><startdate>20050801</startdate><enddate>20050801</enddate><creator>Baggett, L. W.</creator><creator>Jorgensen, P. E. T.</creator><creator>Merrill, K. D.</creator><creator>Packer, J. A.</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>20050801</creationdate><title>Construction of Parseval wavelets from redundant filter systems</title><author>Baggett, L. W. ; Jorgensen, P. E. T. ; Merrill, K. D. ; Packer, J. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c447t-51c0e4501b35c6b5264bc7b84a8dec696e70efbef7df7ee33b83c8d841330f0f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>ALGEBRA</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>Exact sciences and technology</topic><topic>HILBERT SPACE</topic><topic>Mathematical methods in physics</topic><topic>Mathematics</topic><topic>MULTIPLICITY</topic><topic>Physics</topic><topic>RESOLUTION</topic><topic>Sciences and techniques of general use</topic><topic>VECTORS</topic><topic>WAVE FUNCTIONS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Baggett, L. W.</creatorcontrib><creatorcontrib>Jorgensen, P. E. T.</creatorcontrib><creatorcontrib>Merrill, K. D.</creatorcontrib><creatorcontrib>Packer, J. A.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Baggett, L. W.</au><au>Jorgensen, P. E. T.</au><au>Merrill, K. D.</au><au>Packer, J. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Construction of Parseval wavelets from redundant filter systems</atitle><jtitle>Journal of mathematical physics</jtitle><date>2005-08-01</date><risdate>2005</risdate><volume>46</volume><issue>8</issue><spage>083502</spage><epage>083502-28</epage><pages>083502-083502-28</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>We consider wavelets in
L
2
(
R
d
)
which have generalized multiresolutions. This means that the initial resolution subspace
V
0
in
L
2
(
R
d
)
is not singly generated. As a result, the representation of the integer lattice
Z
d
restricted to
V
0
has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on
R
d
can be constructed directly from the generalized wavelet filters.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.1982768</doi><tpages>28</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 2005-08, Vol.46 (8), p.083502-083502-28 |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_scitation_primary_10_1063_1_1982768 |
| source | American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list); American Institute of Physics |
| subjects | ALGEBRA CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Exact sciences and technology HILBERT SPACE Mathematical methods in physics Mathematics MULTIPLICITY Physics RESOLUTION Sciences and techniques of general use VECTORS WAVE FUNCTIONS |
| title | Construction of Parseval wavelets from redundant filter systems |
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