Uniform pointwise estimates for ultraspherical polynomials
We prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in arbitrary dimension, and are instrumental in the proof, discussed in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2022-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.255/ |
| _version_ | 1797651555694936064 |
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| author | Casarino, Valentina Ciatti, Paolo Martini, Alessio |
| author_facet | Casarino, Valentina Ciatti, Paolo Martini, Alessio |
| author_sort | Casarino, Valentina |
| collection | DOAJ |
| description | We prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in arbitrary dimension, and are instrumental in the proof, discussed in a companion paper, of sharp multiplier theorems for those operators. |
| first_indexed | 2024-03-11T16:16:30Z |
| format | Article |
| id | doaj.art-a1c0efc1c530424eae5336bb3802741c |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:30Z |
| publishDate | 2022-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-a1c0efc1c530424eae5336bb3802741c2023-10-24T14:19:17ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692022-01-01359101239125010.5802/crmath.25510.5802/crmath.255Uniform pointwise estimates for ultraspherical polynomialsCasarino, Valentina0Ciatti, Paolo1Martini, Alessio2Università degli Studi di Padova, DTG, Stradella san Nicola 3, I-36100 Vicenza, ItalyUniversità degli Studi di Padova, DICEA, Via Marzolo 9, I-35100 Padova, ItalySchool of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United KingdomWe prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in arbitrary dimension, and are instrumental in the proof, discussed in a companion paper, of sharp multiplier theorems for those operators.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.255/ |
| spellingShingle | Casarino, Valentina Ciatti, Paolo Martini, Alessio Uniform pointwise estimates for ultraspherical polynomials Comptes Rendus. Mathématique |
| title | Uniform pointwise estimates for ultraspherical polynomials |
| title_full | Uniform pointwise estimates for ultraspherical polynomials |
| title_fullStr | Uniform pointwise estimates for ultraspherical polynomials |
| title_full_unstemmed | Uniform pointwise estimates for ultraspherical polynomials |
| title_short | Uniform pointwise estimates for ultraspherical polynomials |
| title_sort | uniform pointwise estimates for ultraspherical polynomials |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.255/ |
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