Generalized upper and lower Legendre conjugates for weight functions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915884601180160 |
|---|---|
| author | Schindl, Gerhard |
| author_facet | Schindl, Gerhard |
| contents | We introduce and study new transformations between two functions satisfying some basic growth properties and generalize the known lower and upper Legendre conjugate (or envelope). We also investigate how these transformations modify recently defined growth indices for weight functions. A special but important and useful situation, to which the knowledge is then applied, is when considering associated weight functions which are expressed in terms of an underlying weight sequence. In this case these transformations precisely correspond to the point-wise product resp. point-wise division of the given sequences. Therefore, the new approach studied in this work illustrates the genuineness and importance and suggests applications for weighted spaces in different directions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized upper and lower Legendre conjugates for weight functions Schindl, Gerhard Classical Analysis and ODEs 26A12, 26A48, 26A51 We introduce and study new transformations between two functions satisfying some basic growth properties and generalize the known lower and upper Legendre conjugate (or envelope). We also investigate how these transformations modify recently defined growth indices for weight functions. A special but important and useful situation, to which the knowledge is then applied, is when considering associated weight functions which are expressed in terms of an underlying weight sequence. In this case these transformations precisely correspond to the point-wise product resp. point-wise division of the given sequences. Therefore, the new approach studied in this work illustrates the genuineness and importance and suggests applications for weighted spaces in different directions. |
| title | Generalized upper and lower Legendre conjugates for weight functions |
| topic | Classical Analysis and ODEs 26A12, 26A48, 26A51 |
| url | https://arxiv.org/abs/2505.07497 |