The Jordan decomposition states that a function f: R → R is of bounded variation if and only if it can be written as the dierence of two monotone increasing functions. In this paper we generalize this property to real valued BV functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa. A counterexample is given which prevents further extensions.
A decomposition theorem for BV functions / Bianchini, S.; Tonon, D.. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 10:6(2011), pp. 1549-1566. [10.3934/cpaa.2011.10.1549]
A decomposition theorem for BV functions
Bianchini, S.;Tonon, D.
2011-01-01
Abstract
The Jordan decomposition states that a function f: R → R is of bounded variation if and only if it can be written as the dierence of two monotone increasing functions. In this paper we generalize this property to real valued BV functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa. A counterexample is given which prevents further extensions.| File | Dimensione | Formato | |
|---|---|---|---|
|
Bianchini-Tonon.pdf
Open Access dal 01/07/2012
Tipologia:
Documento in Post-print
Licenza:
Non specificato
Dimensione
160.54 kB
Formato
Adobe PDF
|
160.54 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
