On Spectral Means And Some Of Their Applications
On spectral properties of the Laplace operator via boundary perturbation.
On ℒ-spline interpolation and approximation on the whole real line
On Spline Systems: Lm-Splines.
On superadditive rates of convergence
On the analogue of the division polynomials for hyperelliptic curves.
On the approximate values of an implicitly given function
On the approximation by compositions of fixed multivariate functions with univariate functions
The approximation in the uniform norm of a continuous function f(x) = f(x₁,...,xₙ) by continuous sums g₁(h₁(x)) + g₂(h₂(x)), where the functions h₁ and h₂ are fixed, is considered. A Chebyshev type criterion for best approximation is established in terms of paths with respect to the functions h₁ and h₂.
On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions
AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.The paper is concerned with establishing direct estimates for convolution operators on homogeneous Banach spaces of periodic functions by means of appropriately defined Kfunctional. The differential operator in the K-functional is defined by means of strong limit and described explicitly in terms of its Fourier coefficients. The description is simple and independent of the homogeneous Banach space. Saturation of such...
On the approximation of analytic functions by the -Bernstein polynomials in the case .
On the approximation of continuosly diffentialble functions in Hilbert spaces
On the approximation of continuous functions.
On the approximation of functions by matrix means in the generalized Hölder metric
Under some assumptions on the matrix of a summability method, whose rows are sequences of bounded variation, we obtain a generalization and an improvement of some results of Xie-Hua Sun and L. Leindler.
On the approximation of functions on locally compact abelian groups.
On the approximation of locally bounded functions by operators of Bleimann, Butzer and Hahn.
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 approximation properties of Bernstein polynomials via probabilistic tools.
On the behavior of algebraic polynomials in regions with piecewise smooth boundary without cusps
We continue studying the estimation of Bernstein-Walsh type for algebraic polynomials in regions with piecewise smooth boundary.
On the Bernstein-Walsh-Siciak theorem
By the Oka-Weil theorem, each holomorphic function f in a neighbourhood of a compact polynomially convex set can be approximated uniformly on K by complex polynomials. The famous Bernstein-Walsh-Siciak theorem specifies the Oka-Weil result: it states that the distance (in the supremum norm on K) of f to the space of complex polynomials of degree at most n tends to zero not slower than the sequence M(f)ρ(f)ⁿ for some M(f) > 0 and ρ(f) ∈ (0,1). The aim of this note is to deduce the uniform version,...
On the best approximation properties of -smooth functions on an interval of the real axis (to the phenomenon of unsaturated numerical methods).