PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Studia Mathematica

2013 | 217 | 3 | 243-263
Tytuł artykułu

### Generators for algebras dense in $L^{p}$-spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For various $L^{p}$-spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in $L^{p}(μ)$. For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates an algebra dense in $L^{p}(M)$. These results are in sharp contrast to the situation when the generators are required to be smooth. For smooth generators we prove a result similar to a known fact about algebras uniformly dense in continuous functions: for M a smooth manifold-with-boundary of dimension n, at least n smooth functions are required in order to generate an algebra dense in $L^{p}(M)$. We also show that on every smooth manifold-with-boundary there exists a bounded continuous real-valued function that is one-to-one on the complement of a set of measure zero.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
243-263
Opis fizyczny
Daty
wydano
2013
Twórcy
autor
• Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, U.S.A.
autor
• Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory