Tchebyshev Systems That Cannot be Transformed Into Markov Systems.
The approximation of functions in the sense of Tchebychev. II
The approximation of functions in the sense of Tchebychev. I
The approximation property of order p in locally convex spaces.
The discrete Fourier-Transform an Lp approximation of functions.
The fundamentality of sets of ridge functions.
The general complex case of the Bernstein-Nachbin approximation problem
We present a solution to the (strict) Bernstein-Nachbin approximation problem in the general complex case. As a corollary, we get proofs of the analytic, the quasi-analytic, and the bounded criteria for localizability in the general complex case. This generalizes the known results of the real or self-adjoint complex cases, in the same way that Bishop’s Theorem generalizes the Weierstrass-Stone Theorem. However, even in the real or self-adjoint complex cases, the results that we obtain are stronger...
The Haar Condition and Multiplicity of Zeros.
The Marcinkiewicz interpolation theorem extends to weighted spaces
The operation of infimal convolution [Book]
The operator remainder in the Euler-Maclaurin formula.
The space of all bounded operators on Hilbert space does not have the approximation property
The strong unicity constant and its applications
In this report we discuss the applications of the strong unicity constant and highlight its use in the minimal projection problem.
The strong unicity constant for projections.
Tractability of multivariate problems for weighted spaces of functions
We survey recent results on tractability of multivariate problems. We mainly restrict ourselves to linear multivariate problems studied in the worst case setting. Typical examples include multivariate integration and function approximation for weighted spaces of smooth functions.
Transitivity of proximinality and norm attaining functionals
We study the question of when the set of norm attaining functionals on a Banach space is a linear space. We show that this property is preserved by factor reflexive proximinal subspaces in spaces and generally by taking quotients by proximinal subspaces. We show, for (ℓ₂) and c₀-direct sums of families of reflexive spaces, the transitivity of proximinality for factor reflexive subspaces. We also investigate the linear structure of the set of norm attaining functionals on hyperplanes of c₀ and...
Tres teoremas de aproximación en el espacio Lp mediante polinomios de coeficientes enteros.
Two-dimensional real symmetric spaces with maximal projection constant
Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that where is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that for any two-dimensional real symmetric space V.