Besov Reconstruction
The reconstruction theorem tackles the problem of building a global distribution, on ℝ d or on a manifold, for a given family of sufficiently coherent local approximations. This theorem is a critical tool within Hairer’s theory of Regularity Structures. In this paper, we establish a reconstruction t...
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| Veröffentlicht in: | Potential analysis 2023-12, Vol.59 (4), p.1875-1912 |
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| container_title | Potential analysis |
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| creator | Broux, Lucas Lee, David |
| description | The reconstruction theorem tackles the problem of building a global distribution, on
ℝ
d
or on a manifold, for a given family of sufficiently coherent local approximations. This theorem is a critical tool within Hairer’s theory of Regularity Structures. In this paper, we establish a reconstruction theorem in the Besov setting, extending recent results of Caravenna and Zambotti. A Besov reconstruction theorem was first formulated by Hairer and Labbé in the context of regularity structures, exploiting nontrivial results from wavelet analysis. Our calculations follow the more elementary approach of coherent germs due to Caravenna and Zambotti. With this formulation our results are both stated and proved with tools from the theory of distributions without the need of the theory of Regularity Structures. As an application, we present an alternative proof of a (Besov) Young multiplication theorem which does not require the use of para-differential calculus. |
| doi_str_mv | 10.1007/s11118-022-10028-7 |
| format | Article |
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ℝ
d
or on a manifold, for a given family of sufficiently coherent local approximations. This theorem is a critical tool within Hairer’s theory of Regularity Structures. In this paper, we establish a reconstruction theorem in the Besov setting, extending recent results of Caravenna and Zambotti. A Besov reconstruction theorem was first formulated by Hairer and Labbé in the context of regularity structures, exploiting nontrivial results from wavelet analysis. Our calculations follow the more elementary approach of coherent germs due to Caravenna and Zambotti. With this formulation our results are both stated and proved with tools from the theory of distributions without the need of the theory of Regularity Structures. As an application, we present an alternative proof of a (Besov) Young multiplication theorem which does not require the use of para-differential calculus.</description><identifier>ISSN: 0926-2601</identifier><identifier>EISSN: 1572-929X</identifier><identifier>DOI: 10.1007/s11118-022-10028-7</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Differential calculus ; Functional Analysis ; Geometry ; Mathematics ; Mathematics and Statistics ; Potential Theory ; Probability ; Probability Theory and Stochastic Processes ; Reconstruction ; Regularity ; Theorems ; Wavelet analysis</subject><ispartof>Potential analysis, 2023-12, Vol.59 (4), p.1875-1912</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2022.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c353t-6797a866218f6e889b3e92e363e47cd26a27084e540ac0e91c18cb04e149b8b63</citedby><cites>FETCH-LOGICAL-c353t-6797a866218f6e889b3e92e363e47cd26a27084e540ac0e91c18cb04e149b8b63</cites><orcidid>0000-0001-9387-3342</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11118-022-10028-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11118-022-10028-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27903,27904,41467,42536,51297</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03902166$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Broux, Lucas</creatorcontrib><creatorcontrib>Lee, David</creatorcontrib><title>Besov Reconstruction</title><title>Potential analysis</title><addtitle>Potential Anal</addtitle><description>The reconstruction theorem tackles the problem of building a global distribution, on
ℝ
d
or on a manifold, for a given family of sufficiently coherent local approximations. This theorem is a critical tool within Hairer’s theory of Regularity Structures. In this paper, we establish a reconstruction theorem in the Besov setting, extending recent results of Caravenna and Zambotti. A Besov reconstruction theorem was first formulated by Hairer and Labbé in the context of regularity structures, exploiting nontrivial results from wavelet analysis. Our calculations follow the more elementary approach of coherent germs due to Caravenna and Zambotti. With this formulation our results are both stated and proved with tools from the theory of distributions without the need of the theory of Regularity Structures. As an application, we present an alternative proof of a (Besov) Young multiplication theorem which does not require the use of para-differential calculus.</description><subject>Differential calculus</subject><subject>Functional Analysis</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Potential Theory</subject><subject>Probability</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Reconstruction</subject><subject>Regularity</subject><subject>Theorems</subject><subject>Wavelet analysis</subject><issn>0926-2601</issn><issn>1572-929X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLAzEQRoMoWKs3T54ETx6ik8l2khxrUSsUBFHwFrIx1Za6qcluwX9v6orenEuY8L6P4TF2IuBCAKjLLMpoDoi87Ki52mEDMVLIDZrnXTYAg8SRQOyzg5yXUCCl9IAdX4UcN6cPwccmt6nz7SI2h2xv7lY5HP28Q_Z0c_04mfLZ_e3dZDzjXo5ky0kZ5TQRCj2noLWpZTAYJMlQKf-C5FCBrsKoAuchGOGF9jVUQVSm1jXJITvve9_cyq7T4t2lTxvdwk7HM7v9A2kABdFGFPasZ9cpfnQht3YZu9SU8ywaMERGIBYKe8qnmHMK899aAXZryvambDFlv01ZVUKyD-UCN68h_VX_k_oCxM9nrw</recordid><startdate>20231201</startdate><enddate>20231201</enddate><creator>Broux, Lucas</creator><creator>Lee, David</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0001-9387-3342</orcidid></search><sort><creationdate>20231201</creationdate><title>Besov Reconstruction</title><author>Broux, Lucas ; Lee, David</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c353t-6797a866218f6e889b3e92e363e47cd26a27084e540ac0e91c18cb04e149b8b63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Differential calculus</topic><topic>Functional Analysis</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Potential Theory</topic><topic>Probability</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Reconstruction</topic><topic>Regularity</topic><topic>Theorems</topic><topic>Wavelet analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Broux, Lucas</creatorcontrib><creatorcontrib>Lee, David</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Potential analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Broux, Lucas</au><au>Lee, David</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Besov Reconstruction</atitle><jtitle>Potential analysis</jtitle><stitle>Potential Anal</stitle><date>2023-12-01</date><risdate>2023</risdate><volume>59</volume><issue>4</issue><spage>1875</spage><epage>1912</epage><pages>1875-1912</pages><issn>0926-2601</issn><eissn>1572-929X</eissn><abstract>The reconstruction theorem tackles the problem of building a global distribution, on
ℝ
d
or on a manifold, for a given family of sufficiently coherent local approximations. This theorem is a critical tool within Hairer’s theory of Regularity Structures. In this paper, we establish a reconstruction theorem in the Besov setting, extending recent results of Caravenna and Zambotti. A Besov reconstruction theorem was first formulated by Hairer and Labbé in the context of regularity structures, exploiting nontrivial results from wavelet analysis. Our calculations follow the more elementary approach of coherent germs due to Caravenna and Zambotti. With this formulation our results are both stated and proved with tools from the theory of distributions without the need of the theory of Regularity Structures. As an application, we present an alternative proof of a (Besov) Young multiplication theorem which does not require the use of para-differential calculus.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11118-022-10028-7</doi><tpages>38</tpages><orcidid>https://orcid.org/0000-0001-9387-3342</orcidid></addata></record> |
| fulltext | fulltext |
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| ispartof | Potential analysis, 2023-12, Vol.59 (4), p.1875-1912 |
| issn | 0926-2601 1572-929X |
| language | eng |
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| source | SpringerLink Journals |
| subjects | Differential calculus Functional Analysis Geometry Mathematics Mathematics and Statistics Potential Theory Probability Probability Theory and Stochastic Processes Reconstruction Regularity Theorems Wavelet analysis |
| title | Besov Reconstruction |
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