Fréchet differentiability of Lipschitz functions via a variational principle
Fréchet differentiability, strict differentiability and subdifferentiability
Fréchet differentiability via partial Fréchet differentiability
Let be Banach spaces and a real function on . Let be the set of all points at which is partially Fréchet differentiable but is not Fréchet differentiable. Our results imply that if are Asplund spaces and is continuous (respectively Lipschitz) on , then is a first category set (respectively a -upper porous set). We also prove that if , are separable Banach spaces and is a Lipschitz mapping, then there exists a -upper porous set such that is Fréchet differentiable at every...
Fréchet directional differentiability and Fréchet differentiability
Zaj’ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any real-valued function on a normed linear space, the set of points where the function is Fréchet directionally differentiable but not Fréchet differentiable...
Fréchet-spaces-valued measures and the AL-property.
Associated with every vector measure m taking its values in a Fréchet space X is the space L1(m) of all m-integrable functions. It turns out that L1(m) is always a Fréchet lattice. We show that possession of the AL-property for the lattice L1(m) has some remarkable consequences for both the underlying Fréchet space X and the integration operator f → ∫ f dm.
Fréchet-valued analytic functions and linear topological invariants.
Fubini theorems for bornological measures
Fully absolutely summing and Hilbert-Schmidt multilinear mappings.
The space of the fully absolutely (r;r1,...,rn)-summing n-linear mappings between Banach spaces is introduced along with a natural (quasi-)norm on it. If r,rk C [1,+infinite], k=1,...,n, this space is characterized as the topological dual of a space of virtually nuclear mappings. Other examples and properties are considered and a relationship with a topological tensor product is stablished. For Hilbert spaces and r = r1 = ... = rn C [2,+infinite[ this space is isomorphic to the space of the Hilbert-Schmidt...
Fully summing mappings between Banach spaces
We introduce and investigate the non-n-linear concept of fully summing mappings; if n = 1 this concept coincides with the notion of nonlinear absolutely summing mappings and in this sense this article unifies these two theories. We also introduce a non-n-linear definition of Hilbert-Schmidt mappings and sketch connections between this concept and fully summing mappings.
Functional Banach spaces of holomorphic functions on Reinhardt domains
Functional integration for euclidean Dirac fields
Functions of finite fractional variation and their applications to fractional impulsive equations
We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a -additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures.
Fundamental theorem of Wiener calculus.
Funktionalanalytische Fassung des Satzes von Radon-Nikodym. I.
Further results on integral representations