{"id":{"repo_id":"western-cape","oai_identifier":"oai:uwcscholar.uwc.ac.za:10566/22868"},"canonical_url":"https://search.dev.ndltd.org/etd/western-cape/oai:uwcscholar.uwc.ac.za:10566/22868","repository":{"repo_id":"western-cape","name":"University of the Western Cape","base_url":"https://uwcscholar.uwc.ac.za:8443/server/oai/request"},"display":{"title":"Block Toeplitz operators with rational symbols and discrete singular systems","abstract":"This thesis concerns block Toeplitz operators (equations). Consider the block Toeplitz operator T = [<I> k-j ]k,j=O' where the <I>k are complex m x m matrices such that 00 (0.1) v=-oo The norm in (0.1) is the usual operator norm on an m x m matrix. The condition (0.1) means that the symbol 00 ( 0.2) v=-oo belongs t.o the Wiener class w mxm of all absolutely convergent sequences of complex m x m matrices. Let 1 ~ p ~ oo be fixed. The block Toeplitz operator T induces a bounded linear operator (also denoted by T) on l'';, namely, 00 (0.3) Yk = (Tx )k = L <I>k-vXv , k = 0, 1, 2, ... ' v=O where x = (xo, x 1,X2, ... ) Et;.","abstract_html":"This thesis concerns block Toeplitz operators (equations). Consider the block Toeplitz operator T = [&lt;I&gt; k-j ]k,j=O&#x27; where the &lt;I&gt;k are complex m x m matrices such that 00 (0.1) v=-oo The norm in (0.1) is the usual operator norm on an m x m matrix. The condition (0.1) means that the symbol 00 ( 0.2) v=-oo belongs t.o the Wiener class w mxm of all absolutely convergent sequences of complex m x m matrices. Let 1 ~ p ~ oo be fixed. The block Toeplitz operator T induces a bounded linear operator (also denoted by T) on l&#x27;&#x27;;, namely, 00 (0.3) Yk = (Tx )k = L &lt;I&gt;k-vXv , k = 0, 1, 2, ... &#x27; v=O where x = (xo, x 1,X2, ... ) Et;.","abstract_has_math":false,"creators":["Konegerie, Abraham"],"institution":"University of the Western Cape","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2001,"date_issued":"2001","date_published":"2001","updated_at":"2026-07-24T06:00:32Z","subjects":["Block Toeplitz operators","MATHEMATICS","Equation","Applied Mathematics"],"languages":[],"rights":[],"rights_urls":["https://uwcscholar.uwc.ac.za/bitstreams/7809267f-ba55-40d1-bb84-757735d58c4b/download"],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Konegerie, Abraham"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2001"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of the Western Cape"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://hdl.handle.net/10566/22868"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Block Toeplitz operators","MATHEMATICS","Equation","Applied Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["https://uwcscholar.uwc.ac.za/bitstreams/7809267f-ba55-40d1-bb84-757735d58c4b/download"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://uwcscholar.uwc.ac.za/bitstreams/95f0a327-b214-4856-a65b-b87292e8e49b/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis concerns block Toeplitz operators (equations). Consider the block Toeplitz operator T = [<I> k-j ]k,j=O' where the <I>k are complex m x m matrices such that 00 (0.1) v=-oo The norm in (0.1) is the usual operator norm on an m x m matrix. The condition (0.1) means that the symbol 00 ( 0.2) v=-oo belongs t.o the Wiener class w mxm of all absolutely convergent sequences of complex m x m matrices. Let 1 ~ p ~ oo be fixed. The block Toeplitz operator T induces a bounded linear operator (also denoted by T) on l'';, namely, 00 (0.3) Yk = (Tx )k = L <I>k-vXv , k = 0, 1, 2, ... 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The block Toeplitz operator T induces a bounded linear operator (also denoted by T) on l'';, namely, 00 (0.3) Yk = (Tx )k = L <I>k-vXv , k = 0, 1, 2, ... ' v=O where x = (xo, x 1,X2, ... ) Et;."],"dc:format.checksum.md5":["32be042a0e8927ff01293f282214573b","bb9bdc0b3349e4284e09149f943790b4","c92ad9efc2a2096859b2f401085a75dd"],"dc:identifier.uri":["https://uwcscholar.uwc.ac.za/bitstreams/95f0a327-b214-4856-a65b-b87292e8e49b/download"],"dc:publisher.institution":["University of the Western Cape"],"dc:relation.isreferencedby":["https://hdl.handle.net/10566/22868"],"dc:rights":["https://uwcscholar.uwc.ac.za/bitstreams/7809267f-ba55-40d1-bb84-757735d58c4b/download"],"dc:subject":["Block Toeplitz operators","MATHEMATICS","Equation","Applied Mathematics"],"dc:title":["Block Toeplitz operators with rational symbols and discrete singular systems"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T06:00:32Z"}