Pregled bibliografske jedinice broj: 1232227
The density of sets containing large similar copies of finite sets
The density of sets containing large similar copies of finite sets // Journal d analyse mathematique, 148 (2022), 339-359 doi:10.1007/s11854-022-0231-6 (međunarodna recenzija, članak, znanstveni)
CROSBI ID: 1232227 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
The density of sets containing large similar copies of finite sets
Autori
Falconer, Kenneth ; Kovač, Vjekoslav ; Yavicoli, Alexia
Izvornik
Journal d analyse mathematique (0021-7670) 148
(2022);
339-359
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
upper density ; point configuration ; discrepancy
Sažetak
We prove that if E⊆R^d (d≥2) is a Lebesgue-measurable set with density larger than (n−2)/(n−1), then E contains similar copies of every n-point set P at all sufficiently large scales. Moreover, 'sufficiently large' can be taken to be uniform over all P with prescribed size, minimum separation and diameter. On the other hand, we construct an example to show that the density required to guarantee all large similar copies of n-point sets tends to 1 at a rate 1−O(n^(−1/5)*log n).
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
HRZZ-UIP-2017-05-4129 - Multilinearna i nelinearna harmonijska analiza i primjene (MUNHANAP) (Kovač, Vjekoslav, HRZZ ) ( CroRIS)
Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb
Profili:
Vjekoslav Kovač
(autor)
Citiraj ovu publikaciju:
Časopis indeksira:
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
