The oriented derivative
Functional Analysis
2023-07-20 v1
Abstract
We show that the derivatives in the sense of Fr\'echet and G\^ateaux can be viewed as derivatives oriented towards a star convex set with the origin as center. The resulting oriented differential calculus extends the mean value theorem, the chain rule and the Taylor formula in Banach spaces. Moreover, the oriented derivative decomposes additively along countably infinite orthogonal sums in Hilbert spaces.
Keywords
Cite
@article{arxiv.2307.10104,
title = {The oriented derivative},
author = {Alexander Kalinin},
journal= {arXiv preprint arXiv:2307.10104},
year = {2023}
}