On the singular support of distributions and Fourier transforms on symmetric spaces
On the singular support of the distributional determinant
On the size of approximately convex sets in normed spaces
Let X be a normed space. A set A ⊆ X is approximately convexif d(ta+(1-t)b,A)≤1 for all a,b ∈ A and t ∈ [0,1]. We prove that every n-dimensional normed space contains approximately convex sets A with and , where ℋ denotes the Hausdorff distance. These estimates are reasonably sharp. For every D>0, we construct worst possible approximately convex sets in C[0,1] such that ℋ(A,Co(A))=(A)=D. Several results pertaining to the Hyers-Ulam stability theorem are also proved.
On the Size of Balls Covered by Analytic Transformations.
On the size of the sets of gradients of bump functions and starlike bodies on the Hilbert space
We study the size of the sets of gradients of bump functions on the Hilbert space , and the related question as to how small the set of tangent hyperplanes to a smooth bounded starlike body in can be. We find that those sets can be quite small. On the one hand, the usual norm of the Hilbert space can be uniformly approximated by smooth Lipschitz functions so that the cones generated by the ranges of its derivatives have empty interior. This implies that there are smooth Lipschitz bumps...
On the smoothness of Orlicz sequence spaces equipped with Orlicz norm.
We give a criterion of smoothness of Orlicz sequence spaces with Orlicz norm.
On the Sobolev class and quasiregularity.
On the Sobolev spaces I.
On the solubility of transcendental equations in commutative C*-algebras.
On the solution -dimensional of the product operator and diamond Bessel operator.
On the solution of distributional Abel integral equation by distributional Sumudu transform.
On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces.
On the solvability of nonlocal pluriparabolic problems.
On the Souslin-graph theorem
On the Space C(X,E) with the Topology of Simple Convergence.
On the space D'(l) of sequential distributions.
On the space of Bloch harmonic functions and interpolation of spaces of harmonic and holomorphic functions
On the space of integral Dirichlet functions of several complex variables
On the space of -summable sequences
On the space of vector-valued functions integrable with respect to the white noise