New concavity and convexity results for symmetric polynomials and their ratios

© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. We prove ‘power’ generalizations of Marcus–Lopes style (including McLeod and Bullen) concavity inequalities for elementary symmetric polynomials, and similar generalizations to convexity inequalities of McLeod and Baston for...

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Main Author: Sra, Suvrit
Format: Article
Language:English
Published: Informa UK Limited 2021
Online Access:https://hdl.handle.net/1721.1/136374
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author Sra, Suvrit
author_facet Sra, Suvrit
author_sort Sra, Suvrit
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description © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. We prove ‘power’ generalizations of Marcus–Lopes style (including McLeod and Bullen) concavity inequalities for elementary symmetric polynomials, and similar generalizations to convexity inequalities of McLeod and Baston for complete homogeneous symmetric polynomials. We also present additional concavity results for elementary symmetric polynomials, of which the main result is a concavity theorem that yields a well-known log-convexity 1972 result of Muir for positive definite matrices as a corollary.
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spelling mit-1721.1/1363742021-10-28T03:02:21Z New concavity and convexity results for symmetric polynomials and their ratios Sra, Suvrit © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. We prove ‘power’ generalizations of Marcus–Lopes style (including McLeod and Bullen) concavity inequalities for elementary symmetric polynomials, and similar generalizations to convexity inequalities of McLeod and Baston for complete homogeneous symmetric polynomials. We also present additional concavity results for elementary symmetric polynomials, of which the main result is a concavity theorem that yields a well-known log-convexity 1972 result of Muir for positive definite matrices as a corollary. 2021-10-27T20:35:05Z 2021-10-27T20:35:05Z 2020 2021-04-14T14:41:55Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136374 en 10.1080/03081087.2018.1527891 Linear and Multilinear Algebra Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Informa UK Limited arXiv
spellingShingle Sra, Suvrit
New concavity and convexity results for symmetric polynomials and their ratios
title New concavity and convexity results for symmetric polynomials and their ratios
title_full New concavity and convexity results for symmetric polynomials and their ratios
title_fullStr New concavity and convexity results for symmetric polynomials and their ratios
title_full_unstemmed New concavity and convexity results for symmetric polynomials and their ratios
title_short New concavity and convexity results for symmetric polynomials and their ratios
title_sort new concavity and convexity results for symmetric polynomials and their ratios
url https://hdl.handle.net/1721.1/136374
work_keys_str_mv AT srasuvrit newconcavityandconvexityresultsforsymmetricpolynomialsandtheirratios