ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 26, 28, 58 Dudley, Richard, Mass. Inst. of Tech., Cambridge, MA, USA; Norvaiša, Rimas, Inst. of Math. and Informatics, Vilnius, Lithuania Differentiability of six nonlinear operators on nonsmooth functions The six operators considered are composition, convolution, multiplication, and integration (F, G) ↦ ∫ F dG on pairs of functions, and on single functions, the definite or indefinite product integral, and the map F ↦ F^{−1} where F^{−1}(y) = inf{x : F (x) ≥ y}. The operators have been shown to be Fréchet differentiable with respect to some p-variation norms with remainder bounds of optimal order. Integrals are as defined by W. H. and L. C. Young. The product integral is holomorphic for 1 ≤ p < 2, where 2 is sharp. Reference: R. M. Dudley, The order of the remainder in derivatives of composition and inverse operators for p-variation norms, Ann. Statist. 22 (1994), 1-20.