Hardy-type inequalities for fractional powers of the Dunkl--Hermite operator
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| Description: |
Roncal, L
Monday 8th April 2019 - 15:00 to 16:00 |
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| Created: | 2019-04-17 11:31 |
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| Collection: | Approximation, sampling and compression in data science |
| Publisher: | Isaac Newton Institute |
| Copyright: | Roncal, L |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | We prove Hardy-type inequalities for the conformally invariant fractional powers of the Dunkl--Hermite operator. Consequently, we also obtain Hardy inequalities for the fractional harmonic oscillator as well.
The strategy is as follows: first, by introducing suitable polar coordinates, we reduce the problem to the Laguerre setting. Then, we push forward an argument developed by R. L. Frank, E. H. Lieb and R. Seiringer, initially developed in the Euclidean setting, to get a Hardy inequality for the fractional-type Laguerre operator. Such argument is based on two facts: first, to get an integral representation for the corresponding fractional operator, and second, to write a proper ground state representation. This is joint work with \'O. Ciaurri (Universidad de La Rioja, Spain) and S. Thangavelu (Indian Institute of Science of Bangalore, India). |
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