where + denotes the Lebesgue measure. We say p # U is a best as functions of : for fixed f. We shall show their continuous dependence on : and differentiability with respect to :.
The Limit of Best Generalized Peak Norm Approximations
β Scribed by Chong Li; G.A. Watson
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 94 KB
- Volume
- 263
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
Norms referred to as generalized peak norms involve a parameter Ξ± which lies between 0 and 1. We consider relationships between the limits of solutions to approximation problems involving these norms and solutions of problems using the norms associated with the limiting values.
π SIMILAR VOLUMES
Monotone approximation relative to peak norms is studied both on an interval and in the discrete case. Existence and some structure results are obtained which demonstrate that peak norm approximation has similar properties to L approxi-1 mation. In particular, sup's and inf's of best approximants ar
## Abstract In view of possible applications in Optimal Control, Differential Games and other fields, we obtain certain invariant characterizations of the limiting Euler trajectories and of the limiting KrassovskiiβSubbotin trajectories of large classes of feedback differential systems defined as p