Dynamical systems, measures, and fractals via domain theory
Information and Computation
Handbook of logic in computer science (vol. 3)
Computable analysis: an introduction
Computable analysis: an introduction
Foundation of a computable solid modelling
Theoretical Computer Science
Domain theory and differential calculus (functions of one variable)
Mathematical Structures in Computer Science
A computational model for multi-variable differential calculus
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Hi-index | 0.00 |
We develop a notion of derivative of a real-valued function on a Banach space, called the L-derivative, which is constructed by introducing a generalization of Lipschitz constant of a map. The values of the L-derivative of a function are non-empty weak* compact and convex subsets of the dual of the Banach space. This is also the case for the Clarke generalised gradient. The L-derivative, however, is shown to be upper semi continuous with respect to the weak* topology, a result which is not known to hold for the Clarke gradient on infinite dimensional Banach spaces. We also formulate the notion of primitive maps dual to the L-derivative, an extension of Fundamental Theorem of Calculus for the L-derivative and a domain for computation of real-valued functions on a Banach space with a corresponding computability theory.