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A Santalo-type Inequality for the J Transform Florentin, Dan
Description
n recent years, it was proven that there exist precisely four order isomorphisms acting in the class of geometric convex functions. These are the Legendre transform ${\cal L}$, the geometric duality transform ${\cal A}$, their composition ${\cal J}$, and the identity. It is known that ${\cal L}$ and ${\cal A}$ satisfy Santal\'{o}-type inequalities, e.g. the quantity $M(f) = {\rm Vol}(f)\cdot{\rm Vol}({\cal L}f)$ is bounded from above and below (here ${\rm Vol}(f)$ stands for the integral over ${\mathbb R}^n$ of $e^{-f}$). We prove similar (asymptotically sharp) bounds for the quantity $M^{\cal J} (f) = {\rm Vol}( {\cal J} f) / {\rm Vol}(f)$, and describe the extremal functions.
Item Metadata
Title |
A Santalo-type Inequality for the J Transform
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-03-28T10:41
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Description |
n recent years, it was proven that there exist precisely four order isomorphisms acting in the class of geometric convex functions. These are the Legendre transform ${\cal L}$, the geometric duality transform ${\cal A}$, their composition ${\cal J}$, and the identity. It is known that ${\cal L}$ and ${\cal A}$ satisfy Santal\'{o}-type inequalities, e.g. the quantity $M(f) = {\rm Vol}(f)\cdot{\rm Vol}({\cal L}f)$ is bounded from above and below (here ${\rm Vol}(f)$ stands for the integral over ${\mathbb R}^n$ of $e^{-f}$). We prove similar (asymptotically sharp) bounds for the quantity $M^{\cal J} (f) = {\rm Vol}( {\cal J} f) / {\rm Vol}(f)$, and describe the extremal functions.
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Extent |
23.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Kent State University
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Series | |
Date Available |
2019-03-18
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0377069
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International