Sobolev Orthogonal Polynomials on the Sierpinski Gasket
We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ( SG ), which is a fractal set that can be viewed as a limit of a sequence of finite graphs. These orthogonal polynomials arise through the Gram–Schmidt orthogonalisation process applied on the set of monomials on SG usin...
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| Veröffentlicht in: | The Journal of fourier analysis and applications 2021-06, Vol.27 (3), Article 38 |
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| container_title | The Journal of fourier analysis and applications |
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| creator | Jiang, Qingxuan Lan, Tian Okoudjou, Kasso A. Strichartz, Robert S. Sule, Shashank Venkat, Sreeram Wang, Xiaoduo |
| description | We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket (
SG
), which is a fractal set that can be viewed as a limit of a sequence of finite graphs. These orthogonal polynomials arise through the Gram–Schmidt orthogonalisation process applied on the set of monomials on
SG
using several notions of a Sobolev inner products. After establishing some recurrence relations for these orthogonal polynomials, we give estimates for their
L
2
,
L
∞
, and Sobolev norms, and study their asymptotic behavior. Finally, we study the properties of zero sets of polynomials and develop fast computational tools to explore applications to quadrature and interpolation. |
| doi_str_mv | 10.1007/s00041-021-09819-0 |
| format | Article |
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SG
), which is a fractal set that can be viewed as a limit of a sequence of finite graphs. These orthogonal polynomials arise through the Gram–Schmidt orthogonalisation process applied on the set of monomials on
SG
using several notions of a Sobolev inner products. After establishing some recurrence relations for these orthogonal polynomials, we give estimates for their
L
2
,
L
∞
, and Sobolev norms, and study their asymptotic behavior. Finally, we study the properties of zero sets of polynomials and develop fast computational tools to explore applications to quadrature and interpolation.</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-021-09819-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Approximations and Expansions ; Asymptotic properties ; Fourier Analysis ; Harmonic Analysis on Combinatorial Graphs ; Interpolation ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Mathematics, Applied ; Norms ; Partial Differential Equations ; Physical Sciences ; Polynomials ; Quadratures ; Science & Technology ; Signal,Image and Speech Processing ; Software</subject><ispartof>The Journal of fourier analysis and applications, 2021-06, Vol.27 (3), Article 38</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021</rights><rights>COPYRIGHT 2021 Springer</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>true</woscitedreferencessubscribed><woscitedreferencescount>1</woscitedreferencescount><woscitedreferencesoriginalsourcerecordid>wos000640782000001</woscitedreferencesoriginalsourcerecordid><citedby>FETCH-LOGICAL-c358t-24f3d7e8cfd9530e439e6c02050f6fb90ddbf59447afddb9aef261ce25d1136b3</citedby><cites>FETCH-LOGICAL-c358t-24f3d7e8cfd9530e439e6c02050f6fb90ddbf59447afddb9aef261ce25d1136b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00041-021-09819-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00041-021-09819-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,782,786,27931,27932,39265,41495,42564,51326</link.rule.ids></links><search><creatorcontrib>Jiang, Qingxuan</creatorcontrib><creatorcontrib>Lan, Tian</creatorcontrib><creatorcontrib>Okoudjou, Kasso A.</creatorcontrib><creatorcontrib>Strichartz, Robert S.</creatorcontrib><creatorcontrib>Sule, Shashank</creatorcontrib><creatorcontrib>Venkat, Sreeram</creatorcontrib><creatorcontrib>Wang, Xiaoduo</creatorcontrib><title>Sobolev Orthogonal Polynomials on the Sierpinski Gasket</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><addtitle>J FOURIER ANAL APPL</addtitle><description>We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket (
SG
), which is a fractal set that can be viewed as a limit of a sequence of finite graphs. These orthogonal polynomials arise through the Gram–Schmidt orthogonalisation process applied on the set of monomials on
SG
using several notions of a Sobolev inner products. After establishing some recurrence relations for these orthogonal polynomials, we give estimates for their
L
2
,
L
∞
, and Sobolev norms, and study their asymptotic behavior. Finally, we study the properties of zero sets of polynomials and develop fast computational tools to explore applications to quadrature and interpolation.</description><subject>Abstract Harmonic Analysis</subject><subject>Approximations and Expansions</subject><subject>Asymptotic properties</subject><subject>Fourier Analysis</subject><subject>Harmonic Analysis on Combinatorial Graphs</subject><subject>Interpolation</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics, Applied</subject><subject>Norms</subject><subject>Partial Differential Equations</subject><subject>Physical Sciences</subject><subject>Polynomials</subject><subject>Quadratures</subject><subject>Science & Technology</subject><subject>Signal,Image and Speech Processing</subject><subject>Software</subject><issn>1069-5869</issn><issn>1531-5851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>HGBXW</sourceid><recordid>eNqNkE1PHSEUhiemTbS2f6CrSbo0owcYZoalubFqYqKJdk0Y5nBF58ItcG389z12jO4aIYQTeB4-3qr6zuCYAfQnGQBa1gCnoQamGtirDpgUrJGDZJ-ohk5R3an96kvOD0Ck6MVB1d_GMc74VF-nch_XMZi5vonzc4gbb-Zcx1CXe6xvPaatD_nR1-cmP2L5Wn12tI_fXufD6tfPs7vVRXN1fX65Or1qrJBDaXjrxNTjYN2kpABshcLOAgcJrnOjgmkanVRt2xtHpTLoeMcscjkxJrpRHFY_lnO3Kf7eYS76Ie4SvTJrLhndAUpwoo4Xam1m1D64WJKx1CfceBsDOk_rpz0bWtaC6kngi2BTzDmh09vkNyY9awb6JVG9JKopJ_0vUQ0kDYv0B8fosvUYLL6JxHct9AOHl8ZWvpjiY1jFXSikHn1cJVosdCYirDG9f_o_z_sLuUiYxw</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Jiang, Qingxuan</creator><creator>Lan, Tian</creator><creator>Okoudjou, Kasso A.</creator><creator>Strichartz, Robert S.</creator><creator>Sule, Shashank</creator><creator>Venkat, Sreeram</creator><creator>Wang, Xiaoduo</creator><general>Springer US</general><general>Springer Nature</general><general>Springer</general><general>Springer Nature B.V</general><scope>BLEPL</scope><scope>DTL</scope><scope>HGBXW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210601</creationdate><title>Sobolev Orthogonal Polynomials on the Sierpinski Gasket</title><author>Jiang, Qingxuan ; Lan, Tian ; Okoudjou, Kasso A. ; Strichartz, Robert S. ; Sule, Shashank ; Venkat, Sreeram ; Wang, Xiaoduo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-24f3d7e8cfd9530e439e6c02050f6fb90ddbf59447afddb9aef261ce25d1136b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Approximations and Expansions</topic><topic>Asymptotic properties</topic><topic>Fourier Analysis</topic><topic>Harmonic Analysis on Combinatorial Graphs</topic><topic>Interpolation</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics, Applied</topic><topic>Norms</topic><topic>Partial Differential Equations</topic><topic>Physical Sciences</topic><topic>Polynomials</topic><topic>Quadratures</topic><topic>Science & Technology</topic><topic>Signal,Image and Speech Processing</topic><topic>Software</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jiang, Qingxuan</creatorcontrib><creatorcontrib>Lan, Tian</creatorcontrib><creatorcontrib>Okoudjou, Kasso A.</creatorcontrib><creatorcontrib>Strichartz, Robert S.</creatorcontrib><creatorcontrib>Sule, Shashank</creatorcontrib><creatorcontrib>Venkat, Sreeram</creatorcontrib><creatorcontrib>Wang, Xiaoduo</creatorcontrib><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>Web of Science - Science Citation Index Expanded - 2021</collection><collection>CrossRef</collection><jtitle>The Journal of fourier analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jiang, Qingxuan</au><au>Lan, Tian</au><au>Okoudjou, Kasso A.</au><au>Strichartz, Robert S.</au><au>Sule, Shashank</au><au>Venkat, Sreeram</au><au>Wang, Xiaoduo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sobolev Orthogonal Polynomials on the Sierpinski Gasket</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><stitle>J FOURIER ANAL APPL</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>27</volume><issue>3</issue><artnum>38</artnum><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket (
SG
), which is a fractal set that can be viewed as a limit of a sequence of finite graphs. These orthogonal polynomials arise through the Gram–Schmidt orthogonalisation process applied on the set of monomials on
SG
using several notions of a Sobolev inner products. After establishing some recurrence relations for these orthogonal polynomials, we give estimates for their
L
2
,
L
∞
, and Sobolev norms, and study their asymptotic behavior. Finally, we study the properties of zero sets of polynomials and develop fast computational tools to explore applications to quadrature and interpolation.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00041-021-09819-0</doi><tpages>38</tpages></addata></record> |
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| source | SpringerNature Journals; Web of Science - Science Citation Index Expanded - 2021<img src="https://exlibris-pub.s3.amazonaws.com/fromwos-v2.jpg" /> |
| subjects | Abstract Harmonic Analysis Approximations and Expansions Asymptotic properties Fourier Analysis Harmonic Analysis on Combinatorial Graphs Interpolation Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics, Applied Norms Partial Differential Equations Physical Sciences Polynomials Quadratures Science & Technology Signal,Image and Speech Processing Software |
| title | Sobolev Orthogonal Polynomials on the Sierpinski Gasket |
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