The circle theorem and related theorems for Gauss-type quadrature rules.
The Convergence and Saturation of Iterations of Positive Linear Operators.
The Convergence Rates of Expansions in Jacobi Polynomials.
The convex interpolation of histogram by polynomial splines: The existence theorem
The degenerate B-splines as a basis in the space of algebraic polynomials
The Derivation of Cubic Splines with Obstacles by Methods of Optimization and Optimal Control.
The direct and converse inequalities for Jackson-type operators on spherical cap.
The discrete Fourier-Transform an Lp approximation of functions.
The distribution of extremal points for Kergin interpolations : real case
We show that a convex totally real compact set in admits an extremal array for Kergin interpolation if and only if it is a totally real ellipse. (An array is said to be extremal for when the corresponding sequence of Kergin interpolation polynomials converges uniformly (on ) to the interpolated function as soon as it is holomorphic on a neighborhood of .). Extremal arrays on these ellipses are characterized in terms of the distribution of the points and the rate of convergence is investigated....
The distribution of the break points by the approximation of a square root by means of a broken line
The e-Algorithm and Multivariate Pade-Approximants
The Error Norm of Gaussian Quadrature Formulae for Weight Functions of Bernstein-Szegö Type.
The error norm of Gauss-Lobatto quadrature formulae for weight functions of Bernstein-Szegö type.
The Euler Maclaurin Expansion for the Cauchy Principal Value Integral.
The Euler-Maclaurin sum formula for an inner derivation.
The evaluation of the remainders in approximation formulas by linear positive operators of interpolatory type.
The fractional transport equation: an analytical solution and a spectral approximation by Chebyshev polynomials.
The "Full Clarkson-Erdős-Schwartz Theorem" on the closure of non-dense Müntz spaces
Denote by spanf₁,f₂,... the collection of all finite linear combinations of the functions f₁,f₂,... over ℝ. The principal result of the paper is the following. Theorem (Full Clarkson-Erdős-Schwartz Theorem). Suppose is a sequence of distinct positive numbers. Then is dense in C[0,1] if and only if . Moreover, if , then every function from the C[0,1] closure of can be represented as an analytic function on z ∈ ℂ ∖ (-∞, 0]: |z| < 1 restricted to (0,1). This result improves an earlier result...
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...