Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.04357 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929736965423104 |
|---|---|
| author | Bernád, J. Z. Frigyik, A. B. |
| author_facet | Bernád, J. Z. Frigyik, A. B. |
| contents | Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff's results in this direction provide us with a general approximation scheme. There are situations when we need to break the interval into uneven pieces. In this paper, we explore alternative conditions to the one found by Smolyanov et al. such that Chernoff's original result can be extended to unevenly distributed time intervals. Two applications concerning the foundations of quantum mechanics and the central limit theorem are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chernoff's product formula: Semigroup approximations with non-uniform time intervals Bernád, J. Z. Frigyik, A. B. Mathematical Physics Functional Analysis 47D06, 47N50, 47N30 Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff's results in this direction provide us with a general approximation scheme. There are situations when we need to break the interval into uneven pieces. In this paper, we explore alternative conditions to the one found by Smolyanov et al. such that Chernoff's original result can be extended to unevenly distributed time intervals. Two applications concerning the foundations of quantum mechanics and the central limit theorem are presented. |
| title | Chernoff's product formula: Semigroup approximations with non-uniform time intervals |
| topic | Mathematical Physics Functional Analysis 47D06, 47N50, 47N30 |
| url | https://arxiv.org/abs/2407.04357 |