The local geometry of idempotent Schur multipliers

A Schur multiplier is a linear map on matrices which acts on its entries by multiplication with some function, called the symbol. We consider idempotent Schur multipliers, whose symbols are indicator functions of smooth Euclidean domains. Given \(1

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2024-04
Hauptverfasser: Parcet, Javier, de la Salle, Mikael, Tablate, Eduardo
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Parcet, Javier
de la Salle, Mikael
Tablate, Eduardo
description A Schur multiplier is a linear map on matrices which acts on its entries by multiplication with some function, called the symbol. We consider idempotent Schur multipliers, whose symbols are indicator functions of smooth Euclidean domains. Given \(1
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2898888222</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2898888222</sourcerecordid><originalsourceid>FETCH-proquest_journals_28988882223</originalsourceid><addsrcrecordid>eNqNissKwjAQAIMgWLT_sOC5UDetxrMo3u29lLq1KUk35nHw7-3BD3Auc5hZiQylPBSqQtyIPISpLEs8nrCuZSawGQkM952BF7Gl6D_AA-gnWceR5giPfkwebDJRO6PJh51YD50JlP-8FfvbtbncC-f5nSjEduLk5yW1qM5qARHlf9cX_no0Tg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2898888222</pqid></control><display><type>article</type><title>The local geometry of idempotent Schur multipliers</title><source>Freely Accessible Journals</source><creator>Parcet, Javier ; de la Salle, Mikael ; Tablate, Eduardo</creator><creatorcontrib>Parcet, Javier ; de la Salle, Mikael ; Tablate, Eduardo</creatorcontrib><description>A Schur multiplier is a linear map on matrices which acts on its entries by multiplication with some function, called the symbol. We consider idempotent Schur multipliers, whose symbols are indicator functions of smooth Euclidean domains. Given \(1&lt;p\neq 2&lt;\infty\), we provide a local characterization (under some mild transversality condition) for the boundedness on Schatten \(p\)-classes of Schur idempotents in terms of a lax notion of boundary flatness. We prove in particular that all Schur idempotents are modeled on a single fundamental example: the triangular projection. As an application, we fully characterize the local \(L_p\)-boundedness of smooth Fourier idempotents on connected Lie groups. They are all modeled on one of three fundamental examples: the classical Hilbert transform, and two new examples of Hilbert transforms that we call affine and projective. Our results in this paper are vast noncommutative generalizations of Fefferman's celebrated ball multiplier theorem. They confirm the intuition that Schur multipliers share profound similarities with Euclidean Fourier multipliers |even in the lack of a Fourier transform connection| and complete, for Lie groups, a longstanding search of Fourier \(L_p\)-idempotents.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Fourier transforms ; Hilbert transformation ; Lie groups ; Mathematical analysis ; Matrices (mathematics) ; Multipliers</subject><ispartof>arXiv.org, 2024-04</ispartof><rights>2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</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>780,784</link.rule.ids></links><search><creatorcontrib>Parcet, Javier</creatorcontrib><creatorcontrib>de la Salle, Mikael</creatorcontrib><creatorcontrib>Tablate, Eduardo</creatorcontrib><title>The local geometry of idempotent Schur multipliers</title><title>arXiv.org</title><description>A Schur multiplier is a linear map on matrices which acts on its entries by multiplication with some function, called the symbol. We consider idempotent Schur multipliers, whose symbols are indicator functions of smooth Euclidean domains. Given \(1&lt;p\neq 2&lt;\infty\), we provide a local characterization (under some mild transversality condition) for the boundedness on Schatten \(p\)-classes of Schur idempotents in terms of a lax notion of boundary flatness. We prove in particular that all Schur idempotents are modeled on a single fundamental example: the triangular projection. As an application, we fully characterize the local \(L_p\)-boundedness of smooth Fourier idempotents on connected Lie groups. They are all modeled on one of three fundamental examples: the classical Hilbert transform, and two new examples of Hilbert transforms that we call affine and projective. Our results in this paper are vast noncommutative generalizations of Fefferman's celebrated ball multiplier theorem. They confirm the intuition that Schur multipliers share profound similarities with Euclidean Fourier multipliers |even in the lack of a Fourier transform connection| and complete, for Lie groups, a longstanding search of Fourier \(L_p\)-idempotents.</description><subject>Fourier transforms</subject><subject>Hilbert transformation</subject><subject>Lie groups</subject><subject>Mathematical analysis</subject><subject>Matrices (mathematics)</subject><subject>Multipliers</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNissKwjAQAIMgWLT_sOC5UDetxrMo3u29lLq1KUk35nHw7-3BD3Auc5hZiQylPBSqQtyIPISpLEs8nrCuZSawGQkM952BF7Gl6D_AA-gnWceR5giPfkwebDJRO6PJh51YD50JlP-8FfvbtbncC-f5nSjEduLk5yW1qM5qARHlf9cX_no0Tg</recordid><startdate>20240410</startdate><enddate>20240410</enddate><creator>Parcet, Javier</creator><creator>de la Salle, Mikael</creator><creator>Tablate, Eduardo</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20240410</creationdate><title>The local geometry of idempotent Schur multipliers</title><author>Parcet, Javier ; de la Salle, Mikael ; Tablate, Eduardo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_28988882223</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Fourier transforms</topic><topic>Hilbert transformation</topic><topic>Lie groups</topic><topic>Mathematical analysis</topic><topic>Matrices (mathematics)</topic><topic>Multipliers</topic><toplevel>online_resources</toplevel><creatorcontrib>Parcet, Javier</creatorcontrib><creatorcontrib>de la Salle, Mikael</creatorcontrib><creatorcontrib>Tablate, Eduardo</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Parcet, Javier</au><au>de la Salle, Mikael</au><au>Tablate, Eduardo</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>The local geometry of idempotent Schur multipliers</atitle><jtitle>arXiv.org</jtitle><date>2024-04-10</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>A Schur multiplier is a linear map on matrices which acts on its entries by multiplication with some function, called the symbol. We consider idempotent Schur multipliers, whose symbols are indicator functions of smooth Euclidean domains. Given \(1&lt;p\neq 2&lt;\infty\), we provide a local characterization (under some mild transversality condition) for the boundedness on Schatten \(p\)-classes of Schur idempotents in terms of a lax notion of boundary flatness. We prove in particular that all Schur idempotents are modeled on a single fundamental example: the triangular projection. As an application, we fully characterize the local \(L_p\)-boundedness of smooth Fourier idempotents on connected Lie groups. They are all modeled on one of three fundamental examples: the classical Hilbert transform, and two new examples of Hilbert transforms that we call affine and projective. Our results in this paper are vast noncommutative generalizations of Fefferman's celebrated ball multiplier theorem. They confirm the intuition that Schur multipliers share profound similarities with Euclidean Fourier multipliers |even in the lack of a Fourier transform connection| and complete, for Lie groups, a longstanding search of Fourier \(L_p\)-idempotents.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2024-04
issn 2331-8422
language eng
recordid cdi_proquest_journals_2898888222
source Freely Accessible Journals
subjects Fourier transforms
Hilbert transformation
Lie groups
Mathematical analysis
Matrices (mathematics)
Multipliers
title The local geometry of idempotent Schur multipliers
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T17%3A27%3A22IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=The%20local%20geometry%20of%20idempotent%20Schur%20multipliers&rft.jtitle=arXiv.org&rft.au=Parcet,%20Javier&rft.date=2024-04-10&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2898888222%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2898888222&rft_id=info:pmid/&rfr_iscdi=true