Functions of bounded variation and polarization
β Scribed by Angela Alberico; Adele Ferone; Roberta Volpicelli
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 146 KB
- Volume
- 282
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
It is known that, if u is a real valued function on β^N^ of bounded variation, then its total variation decreases under polarization. In this paper we identify the difference between the total variation of u and that one of its polar u~Ξ ~ (Β© 2009 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
π SIMILAR VOLUMES
~t ~s i ## I l -i s n R arbitrary The function 11./1 is a norm on the set V , of all functions f wit,h f ( 0 ) = 0. supplied with this norm I ; , is a BAXACH space. For p=-1 set ct,(f) = Iim sup ( lf(ti) -/(ti -,) i p)i 'p
Complementary spaces for Fourier series were introduced by G. Goes and generalized by M. Tynnov. In this paper we investigate a notion of complementary space for double Fourier series of functions of bounded variation. Various applications are given.
## Abstract Let __I__, __J__ β β be intervals. The main result says that if a superposition operator __H__ generated by a function of two variables __h__: __I__ Γ __J__ β β, __H__ (__Ο__)(__x__) β __h__ (__x__, __Ο__ (__x__)), maps the set __BV__ (__I__, __J__) of all bounded variation functions,
## Abstract The set of unary functions of complexity classes defined by using bounded primitive recursion is inductively characterized by means of bounded iteration. Elementary unary functions, linear space computable unary functions and polynomial space computable unary functions are then inductiv