Multivalued superposition operators in ideal spaces of vector functions III
✍ Scribed by Jürgen Appell; Nguyêñ Hôǹg Thái; Petr P. Zabrejko
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 539 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0019-3577
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract Let __I__, __J__ ⊂ ℝ be intervals. The main result says that if a superposition operator __H__ generated by a function of two variables __h__: __I__ × __J__ → ℝ, __H__ (__φ__)(__x__) ≔ __h__ (__x__, __φ__ (__x__)), maps the set __BV__ (__I__, __J__) of all bounded variation functions,
It is proved that a C 0 -semigroup T=[T(t)] t 0 of linear operators on a Banach space X is uniformly exponentially stable if and only if it acts boundedly on one of the spaces L p (R + , X) or C 0 (R + , X) by convolution. As an application, it is shown that T is uniformly exponentially stable if an