- Tytuł:
- Integral representation of functions of bounded second Φ-variation in the sense of Schramm
- Autorzy:
-
Gimenez, J.
Merentes, N.
Rivas, S. - Powiązania:
- https://bibliotekanauki.pl/articles/256001.pdf
- Data publikacji:
- 2012
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
Young function
phi-variation
second phi-variation of a function - Opis:
- In this article we introduce the concept of second Φ--variation in the sense of Schramm for normed-space valued functions defined on an interval [a; b] ⊂ R. To that end we combine the notion of second variation due to de la Vallée Poussin and the concept of φ-variation in the sense of Schramm for real valued functions. In particular, when the normed space is complete we present a characterization of the functions of the introduced class by means of an integral representation. Indeed, we show that a function [formula] (where X is a reflexive Banach space) is of bounded second Φ-variation in the sense of Schramm if and only if it can be expressed as the Bochner integral of a function of (first) bounded variation in the sense of Schramm.
- Źródło:
-
Opuscula Mathematica; 2012, 32, 1; 137-151
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł