Berger-Coburn-Lebow representation for pure isometric representations of product system over $\mathbb N^2_0
Journal of Mathematical Analysis and Applications (2023): 127807 We obtain Berger-Coburn-Lebow (BCL)-representation for pure isometric covariant representation of product system over $\mathbb{N}_0^2$. Then the corresponding complete set of (joint) unitary invariants is studied, and the BCL- represen...
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| creator | Saini, Dimple Trivedi, Harsh Veerabathiran, Shankar |
| description | Journal of Mathematical Analysis and Applications (2023): 127807 We obtain Berger-Coburn-Lebow (BCL)-representation for pure isometric
covariant representation of product system over $\mathbb{N}_0^2$. Then the
corresponding complete set of (joint) unitary invariants is studied, and the
BCL- representations are compared with other canonical multi-analytic
descriptions of the pure isometric covariant representation. We characterize
the invariant subspaces for the pure isometric covariant representation. Also,
we study the connection between the joint defect operators and Fringe
operators, and the Fredholm index is introduced in this case. Finally, we
introduce the notion of congruence relation to classify the isometric covariant
representations of the product system over $\mathbb{N}_0^2$. |
| doi_str_mv | 10.48550/arxiv.2209.04600 |
| format | Article |
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covariant representation of product system over $\mathbb{N}_0^2$. Then the
corresponding complete set of (joint) unitary invariants is studied, and the
BCL- representations are compared with other canonical multi-analytic
descriptions of the pure isometric covariant representation. We characterize
the invariant subspaces for the pure isometric covariant representation. Also,
we study the connection between the joint defect operators and Fringe
operators, and the Fredholm index is introduced in this case. Finally, we
introduce the notion of congruence relation to classify the isometric covariant
representations of the product system over $\mathbb{N}_0^2$.</description><identifier>DOI: 10.48550/arxiv.2209.04600</identifier><language>eng</language><subject>Mathematics - Functional Analysis ; Mathematics - Mathematical Physics ; Mathematics - Operator Algebras ; Physics - Mathematical Physics</subject><creationdate>2022-09</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2209.04600$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.1016/j.jmaa.2023.127807$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.2209.04600$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Saini, Dimple</creatorcontrib><creatorcontrib>Trivedi, Harsh</creatorcontrib><creatorcontrib>Veerabathiran, Shankar</creatorcontrib><title>Berger-Coburn-Lebow representation for pure isometric representations of product system over $\mathbb N^2_0</title><description>Journal of Mathematical Analysis and Applications (2023): 127807 We obtain Berger-Coburn-Lebow (BCL)-representation for pure isometric
covariant representation of product system over $\mathbb{N}_0^2$. Then the
corresponding complete set of (joint) unitary invariants is studied, and the
BCL- representations are compared with other canonical multi-analytic
descriptions of the pure isometric covariant representation. We characterize
the invariant subspaces for the pure isometric covariant representation. Also,
we study the connection between the joint defect operators and Fringe
operators, and the Fredholm index is introduced in this case. Finally, we
introduce the notion of congruence relation to classify the isometric covariant
representations of the product system over $\mathbb{N}_0^2$.</description><subject>Mathematics - Functional Analysis</subject><subject>Mathematics - Mathematical Physics</subject><subject>Mathematics - Operator Algebras</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpdz7tOxDAUBFA3FGjhA6hwQZtw_YiTlBDxklbQbImIbOcGIkgcXTsL-_ewCxXVNDMjHcbOBOS6Kgq4tPQ1bHMpoc5BG4Bj9n6N9IqUNcEtNGVrdOGTE86EEadk0xAm3gfi80LIhxhGTDT4f43IQ89nCt3iE4-7mHDkYYvEL55Hm96c448vsoUTdtTbj4inf7lim9ubTXOfrZ_uHpqrdWZNCVlVCOOwl6LStewBoPPWGo9Oodeqqr1XrjCdEKVXulLKOeOV-FmYwmtpSrVi57-3B2070zBa2rV7dXtQq2-bolQx</recordid><startdate>20220910</startdate><enddate>20220910</enddate><creator>Saini, Dimple</creator><creator>Trivedi, Harsh</creator><creator>Veerabathiran, Shankar</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220910</creationdate><title>Berger-Coburn-Lebow representation for pure isometric representations of product system over $\mathbb N^2_0</title><author>Saini, Dimple ; Trivedi, Harsh ; Veerabathiran, Shankar</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a670-8516bef218492f000dcaa6ceb3ec4389cc3b56d117c34833bb6c31bef65c42673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Functional Analysis</topic><topic>Mathematics - Mathematical Physics</topic><topic>Mathematics - Operator Algebras</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Saini, Dimple</creatorcontrib><creatorcontrib>Trivedi, Harsh</creatorcontrib><creatorcontrib>Veerabathiran, Shankar</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Saini, Dimple</au><au>Trivedi, Harsh</au><au>Veerabathiran, Shankar</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Berger-Coburn-Lebow representation for pure isometric representations of product system over $\mathbb N^2_0</atitle><date>2022-09-10</date><risdate>2022</risdate><abstract>Journal of Mathematical Analysis and Applications (2023): 127807 We obtain Berger-Coburn-Lebow (BCL)-representation for pure isometric
covariant representation of product system over $\mathbb{N}_0^2$. Then the
corresponding complete set of (joint) unitary invariants is studied, and the
BCL- representations are compared with other canonical multi-analytic
descriptions of the pure isometric covariant representation. We characterize
the invariant subspaces for the pure isometric covariant representation. Also,
we study the connection between the joint defect operators and Fringe
operators, and the Fredholm index is introduced in this case. Finally, we
introduce the notion of congruence relation to classify the isometric covariant
representations of the product system over $\mathbb{N}_0^2$.</abstract><doi>10.48550/arxiv.2209.04600</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Functional Analysis Mathematics - Mathematical Physics Mathematics - Operator Algebras Physics - Mathematical Physics |
| title | Berger-Coburn-Lebow representation for pure isometric representations of product system over $\mathbb N^2_0 |
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