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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.16245 |
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| _version_ | 1866909588866990080 |
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| author | Sababe, S. Hashemi Baghban, Amir |
| author_facet | Sababe, S. Hashemi Baghban, Amir |
| contents | We extend the classical Heisenberg uncertainty principle to a fractional $L^p$ setting by investigating a novel class of uncertainty inequalities derived from the fractional Schrödinger equation. In this work, we establish the existence of extremal functions for these inequalities, characterize their structure as fractional analogues of Gaussian functions, and determine the sharp constants involved. Moreover, we prove a quantitative stability result showing that functions nearly attaining the equality in the uncertainty inequality must be close -- in an appropriate norm -- to the set of extremizers. Our results provide new insights into the fractional analytic framework and have potential applications in the analysis of fractional partial differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extremizers and Stability for Fractional $L^p$ Uncertainty Principles Sababe, S. Hashemi Baghban, Amir Classical Analysis and ODEs Differential Geometry Functional Analysis 35Q55, 35R11, 42B10, 26D15, 35A23 We extend the classical Heisenberg uncertainty principle to a fractional $L^p$ setting by investigating a novel class of uncertainty inequalities derived from the fractional Schrödinger equation. In this work, we establish the existence of extremal functions for these inequalities, characterize their structure as fractional analogues of Gaussian functions, and determine the sharp constants involved. Moreover, we prove a quantitative stability result showing that functions nearly attaining the equality in the uncertainty inequality must be close -- in an appropriate norm -- to the set of extremizers. Our results provide new insights into the fractional analytic framework and have potential applications in the analysis of fractional partial differential equations. |
| title | Extremizers and Stability for Fractional $L^p$ Uncertainty Principles |
| topic | Classical Analysis and ODEs Differential Geometry Functional Analysis 35Q55, 35R11, 42B10, 26D15, 35A23 |
| url | https://arxiv.org/abs/2504.16245 |