On Projections and monotony in Lp-spaces.
On the approximation of continuosly diffentialble functions in Hilbert spaces
On the approximation of functions on locally compact abelian groups.
On the approximation of real continuous functions by series of solutions of a single system of partial differential equations
We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function can be approximated with arbitrary accuracy by an infinite sum of analytic functions , each solving the same system of universal partial differential equations, namely (σ = 1,..., s).
On the Chebyshev alternation theorem.
On the closure of modules of continuously differentiable mappings
On the Convergence and Approximation of Cosine Functions.
On the existence and characterization of minimal projections.
On the existence of almost greedy bases in Banach spaces
We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy bases begun in [3]. We show that almost greedy bases are essentially optimal for n-term approximation when the TGA is modified to include a Chebyshev approximation. We prove that if a Banach space X has a basis and contains a complemented subspace with a symmetric basis and finite cotype then X has an...
On the Fast Convergence of a Galerkin-Like Method for Equations of the Second Kind.
On the Fréchet differentiability of distance functions
On the interpolation in linear spaces.
On the Kaczmarz algorithm of approximation in infinite-dimensional spaces
The Kaczmarz algorithm of successive projections suggests the following concept. A sequence of unit vectors in a Hilbert space is said to be effective if for each vector x in the space the sequence (xₙ) converges to x where (xₙ) is defined inductively: x₀ = 0 and , where . We prove the effectivity of some sequences in Hilbert spaces. We generalize the concept of effectivity to sequences of vectors in Banach spaces and we prove some results for this more general concept.
On the lower semi-continuity of the set valued metric projection.
On the Minimum Norm Projection on Closed Subspaces of L^p[0, 2*pi] and an Application
On the Number of Zeros of Functions in a Weak Tchebyshev-Space.
On the points of multivaluedness of metric projections in separable Banach spaces
On the points of multivaluedness of monotone operators
On the randomized complexity of Banach space valued integration
We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the nth minimal errors are bounded by if and only if X is of equal norm type p.
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.