Representations of Real Numbers by Alternating Perron Series and Their Geometry
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912154250117120 |
|---|---|
| author | Moroz, Mykola |
| author_facet | Moroz, Mykola |
| contents | We consider the representation of real numbers by alternating Perron series ($P^-$-representation), which is a generalization of representations of real numbers by Ostrogradsky-Sierpiński-Pierce series (Pierce series), alternating Sylvester series (second Ostrogradsky series), alternating Lüroth series, etc. Namely, we prove the basic topological and metric properties of $P^-$-representation and find the relationship between $P$-representation and $P^-$-representation in some measure theory problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representations of Real Numbers by Alternating Perron Series and Their Geometry Moroz, Mykola General Mathematics 11K55 (Primary) 11A67, 28A12 (Secondary) We consider the representation of real numbers by alternating Perron series ($P^-$-representation), which is a generalization of representations of real numbers by Ostrogradsky-Sierpiński-Pierce series (Pierce series), alternating Sylvester series (second Ostrogradsky series), alternating Lüroth series, etc. Namely, we prove the basic topological and metric properties of $P^-$-representation and find the relationship between $P$-representation and $P^-$-representation in some measure theory problems. |
| title | Representations of Real Numbers by Alternating Perron Series and Their Geometry |
| topic | General Mathematics 11K55 (Primary) 11A67, 28A12 (Secondary) |
| url | https://arxiv.org/abs/2408.01465 |