Differentiability of convex functions on a Banach space with smooth bump function.
Differentiability of distributions at a single point
Differentiability of Lipschitzian mappings between Banach spaces
Differentiability of mappings in the geometry of Carnot manifolds.
Differentiability of Minima of Non-Differentiable Functionals.
Differentiability of Musielak-Orlicz sequence spaces
Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space
Differentiability of the mappings of Carnot-Carathéodory spaces in the Sobolev and -topologies.
Differentiability points of a distance function
Differentiable mappings on topological vector spaces
Differentiable structure in a conjugate vector bundle of infinite dimension [Book]
Differential calculi over quantum groups
An exposition is given of recent work of the author and others on the differential calculi that occur in the setting of compact quantum groups. The principal topics covered are twisted graded traces, an extension of Connes' cyclic cohomology, invariant linear functionals on covariant calculi and the Hodge, Dirac and Laplace operators in this setting. Some new results extending the classical de Rham theorem and Poincaré duality are also discussed.
Differential calculus on 'non-standard' (h-deformed) Minkowski spaces
The differential calculus on 'non-standard' h-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.
Differential geometrical relations for a class of formal series
An extension of the category of local manifolds is considered. Instead of smooth mappings of neighbourhoods of linear spaces as morphisms we deal with formal operator power series (or formal maps). Analogues of the objects appearing on smooth manifolds and vector bundles (vector fields, sections of a bundle, exterior forms, the de Rham complex, connection, etc.) are considered in this way. All the examinations are carried out in algebraic language, for we do not care about the convergence of formal...
Differential geometry in the space of positive operators.
Differential independence via an associative product of infinitely many linear functionals
We generalize the infinitesimal independence appearing in free probability of type B in two directions: to higher order derivatives and other natural independences: tensor, monotone and Boolean. Such generalized infinitesimal independences can be defined by using associative products of infinitely many linear functionals, and therefore the associated cumulants can be defined. These products can be seen as the usual natural products of linear maps with values in formal power series.
Differentialble paths in topological vector spaces
Differentially closed ideals in rings of analytic functions.
Differentialoperatoren ganzer Funktionen.
Differentiation bases for Sobolev functions on metric spaces.
We study Lebesgue points for Sobolev functions over other collections of sets than balls. Our main result gives several conditions for a differentiation basis, which characterize the existence of Lebesgue points outside a set of capacity zero.