Schauder Type Theorems for Differentiable and Holomorphic Mappings.
Second order differentiability and Lipschitz smooth points of convex functionals
Second order differentiability of integral functionals on Sobolev spaces and L2-spaces.
Semidifferential calculus.
Semireflexive Spaces In Which The Theorem On The Derivative-Of-The-Inverse Fails For Frechet Derivatives.
Separating polynomials on Banach spaces.
In this paper we survey some recent results concerning separating polynomials on real Banach spaces. By this we mean a polynomial which separates the origin from the unit sphere of the space, thus providing an analog of the separating quadratic form on Hilbert space.
Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces
Smooth approximations without critical points
In any separable Banach space containing c 0 which admits a C k-smooth bump, every continuous function can be approximated by a C k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points). On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains a set...
Smooth measures, the Malliavin calculus and approximations in infinitedimensional spaces
Smooth partitions of unity in preduals of WCG spaces.
Smoothness in Banach spaces. Selected problems.
This is a short survey on some recent as well as classical results and open problems in smoothness and renormings of Banach spaces. Applications in general topology and nonlinear analysis are considered. A few new results and new proofs are included. An effort has been made that a young researcher may enjoy going through it without any special pre-requisites and get a feeling about this area of Banach space theory. Many open problems of different level of difficulty are discussed. For the reader...
Smoothness of a typical convex function
Sobolev type inequalities for p>0
Sobolev's and local derivatives
Some convexity questions arising in statistical mechanics.
Some more recent results concerning weak Asplund spaces.
Some properties on the closed subsets in Banach spaces
It is shown that under natural assumptions, there exists a linear functional does not have supremum on a closed bounded subset. That is the James Theorem for non-convex bodies. Also, a non-linear version of the Bishop-Phelps Theorem and a geometrical version of the formula of the subdifferential of the sum of two functions are obtained.
Some recent results concerning weak Asplund spaces
Some Relations Between Additive Functions - II
Some remarks on nonlinear functionals