Toeplitz and related operators on polyanalytic Fock spaces
We give a characterization of compact and Fredholm operators on polyanalytic Fock spaces in terms of limit operators. As an application we obtain a generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin type transform. We then apply this theorem to Toeplitz and Hankel operators...
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| creator | Hagger, Raffael |
| description | We give a characterization of compact and Fredholm operators on polyanalytic
Fock spaces in terms of limit operators. As an application we obtain a
generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin
type transform. We then apply this theorem to Toeplitz and Hankel operators to
obtain necessary and sufficient conditions for compactness. As it turns out,
whether or not a Toeplitz or Hankel operator is compact does not depend on the
polyanalytic order. For Hankel operators this even holds on the true
polyanalytic Fock spaces. |
| doi_str_mv | 10.48550/arxiv.2201.10230 |
| format | Article |
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Fock spaces in terms of limit operators. As an application we obtain a
generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin
type transform. We then apply this theorem to Toeplitz and Hankel operators to
obtain necessary and sufficient conditions for compactness. As it turns out,
whether or not a Toeplitz or Hankel operator is compact does not depend on the
polyanalytic order. For Hankel operators this even holds on the true
polyanalytic Fock spaces.</description><identifier>DOI: 10.48550/arxiv.2201.10230</identifier><language>eng</language><subject>Mathematics - Functional Analysis</subject><creationdate>2022-01</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2201.10230$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2201.10230$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Hagger, Raffael</creatorcontrib><title>Toeplitz and related operators on polyanalytic Fock spaces</title><description>We give a characterization of compact and Fredholm operators on polyanalytic
Fock spaces in terms of limit operators. As an application we obtain a
generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin
type transform. We then apply this theorem to Toeplitz and Hankel operators to
obtain necessary and sufficient conditions for compactness. As it turns out,
whether or not a Toeplitz or Hankel operator is compact does not depend on the
polyanalytic order. For Hankel operators this even holds on the true
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Fock spaces in terms of limit operators. As an application we obtain a
generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin
type transform. We then apply this theorem to Toeplitz and Hankel operators to
obtain necessary and sufficient conditions for compactness. As it turns out,
whether or not a Toeplitz or Hankel operator is compact does not depend on the
polyanalytic order. For Hankel operators this even holds on the true
polyanalytic Fock spaces.</abstract><doi>10.48550/arxiv.2201.10230</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Functional Analysis |
| title | Toeplitz and related operators on polyanalytic Fock spaces |
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