Abstract
This paper deals with an analog of the Mahler volume product related to the ℑ transform acting in the class of geometric convex functions Cvx0(ℝn). We provide asymptotically sharp bounds for the quantity sJ(f) = ∫e-ℑf ∫e-f and characterize all the extremal functions.
| Original language | English |
|---|---|
| Article number | 1950090 |
| Journal | Communications in Contemporary Mathematics |
| Volume | 23 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Feb 2021 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2021 World Scientific Publishing Company.
Funding
The first named author was partially supported by the U.S. National Science Foundation Grant DMS-1101636, and also partially supported by the AMSSimons Travel Grant, which is administered by the American Mathematical Society with support from the Simons Foundation. The authors would like to thank Fedor Nazarov and Shiri Artstein-Avidan for useful discussions. The first named author was partially supported by the U.S. National Science Foundation Grant DMS-1101636, and also partially supported by the AMS-Simons Travel Grant, which is administered by the American Mathematical Society with support from the Simons Foundation.
| Funders | Funder number |
|---|---|
| U.S. National Science Foundation | |
| National Science Foundation | DMS-1101636 |
| Simons Foundation | |
| American Mathematical Society |
Keywords
- Convex
- Legendre
- Mahler
- Santaló
- functional