Pub Date : 2023-01-25DOI: 10.1007/s00365-023-09616-6
Rostyslav Kozhan
{"title":"Correction to: Jost Asymptotics for Matrix Orthogonal Polynomials on the Real Line","authors":"Rostyslav Kozhan","doi":"10.1007/s00365-023-09616-6","DOIUrl":"https://doi.org/10.1007/s00365-023-09616-6","url":null,"abstract":"","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":"1 1","pages":"1-5"},"PeriodicalIF":2.7,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42782501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01Epub Date: 2023-04-07DOI: 10.1007/s00365-023-09638-0
Josef Dick, Martin Ehler, Manuel Gräf, Christian Krattenthaler
To numerically approximate Borel probability measures by finite atomic measures, we study the spectral decomposition of discrepancy kernels when restricted to compact subsets of . For restrictions to the Euclidean ball in odd dimensions, to the rotation group , and to the Grassmannian manifold , we compute the kernels' Fourier coefficients and determine their asymptotics. The -discrepancy is then expressed in the Fourier domain that enables efficient numerical minimization based on the nonequispaced fast Fourier transform. For , the nonequispaced fast Fourier transform is publicly available, and, for , the transform is derived here. We also provide numerical experiments for and .
{"title":"Spectral Decomposition of Discrepancy Kernels on the Euclidean Ball, the Special Orthogonal Group, and the Grassmannian Manifold.","authors":"Josef Dick, Martin Ehler, Manuel Gräf, Christian Krattenthaler","doi":"10.1007/s00365-023-09638-0","DOIUrl":"10.1007/s00365-023-09638-0","url":null,"abstract":"<p><p>To numerically approximate Borel probability measures by finite atomic measures, we study the spectral decomposition of discrepancy kernels when restricted to compact subsets of <math><msup><mrow><mi>R</mi></mrow><mi>d</mi></msup></math>. For restrictions to the Euclidean ball in odd dimensions, to the rotation group <math><mrow><mtext>SO</mtext><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math>, and to the Grassmannian manifold <math><msub><mi>G</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></math>, we compute the kernels' Fourier coefficients and determine their asymptotics. The <math><msub><mi>L</mi><mn>2</mn></msub></math>-discrepancy is then expressed in the Fourier domain that enables efficient numerical minimization based on the nonequispaced fast Fourier transform. For <math><mrow><mtext>SO</mtext><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math>, the nonequispaced fast Fourier transform is publicly available, and, for <math><msub><mi>G</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></math>, the transform is derived here. We also provide numerical experiments for <math><mrow><mtext>SO</mtext><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math> and <math><msub><mi>G</mi><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></msub></math>.</p>","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":"57 3","pages":"983-1026"},"PeriodicalIF":2.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10264311/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9655527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-15DOI: 10.1007/s00365-023-09666-w
R. Ferreira, T. Simon
{"title":"On the Log-Concavity of the Wright Function","authors":"R. Ferreira, T. Simon","doi":"10.1007/s00365-023-09666-w","DOIUrl":"https://doi.org/10.1007/s00365-023-09666-w","url":null,"abstract":"","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":" ","pages":""},"PeriodicalIF":2.7,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46483566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-19DOI: 10.1007/s00365-022-09602-4
A. G. Georgiadis, G. Kyriazis
{"title":"Duals of Besov and Triebel-Lizorkin Spaces Associated with Operators","authors":"A. G. Georgiadis, G. Kyriazis","doi":"10.1007/s00365-022-09602-4","DOIUrl":"https://doi.org/10.1007/s00365-022-09602-4","url":null,"abstract":"","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":"57 1","pages":"547-577"},"PeriodicalIF":2.7,"publicationDate":"2022-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48132097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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