MATRIX POWER MEANS AND PÓLYA--SZEGÖ TYPE INEQUALITIES
t has been shown that if μ is a compactly supported probability measure on Mn+, then for every unit vector η∈ℂn, there exists a compactly supported probability measure (denoted by <μ η,η> on ℝ+ so that the inequality <Pt(μ)η,η>≤ Pt(<μ η,η>) (t∈(0,1]) holds. In particular, we...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2020-03-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | http://www.utgjiu.ro/math/sma/v15/p15_11.pdf |
| Summary: | t has been shown that if μ is a compactly supported probability measure on Mn+, then for every unit vector η∈ℂn, there exists a compactly supported probability measure (denoted by <μ η,η> on ℝ+ so that the inequality
<Pt(μ)η,η>≤ Pt(<μ η,η>) (t∈(0,1])
holds. In particular, we consider a reverse of the above inequality and present some Pólya--Szegö type inequalities for power means of probability measures on positive matrices. |
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| ISSN: | 1843-7265 1842-6298 |