Interpolation of Weighted Extremal Functions

Zeros of Extremal Functions in Weighted Bergman Spaces

For −1 < α ≤ 0 and 0 < p < ∞, the solutions of certain extremal problems are known to act as contractive zerodivisors in the weighted Bergman space Aα. We show that for 0 < α ≤ 1 and 0 < p < ∞, the analogous extremal functions do not have any extra zeros in the unit disk and, hence, have the potential to act as zero-divisors. As a corollary, we find that certain families of hypergeometric funct...

Extremal Problems of Interpolation Theory

We consider problems where one seeks m×m matrix valued H∞ functions w(ξ) which satisfy interpolation constraints and a bound (0.1) w∗(ξ)w(ξ) ≤ ρmin, |ξ| < 1, where the m×m positive semi-definite matrix ρmin is minimal (no smaller than) any other matrix ρ producing such a bound. That is, if (0.2) w∗(ξ)w(ξ) ≤ ρ, |ξ| < 1, and if ρmin − ρ is positive semi-definite, then ρmin = ρ. This is an example...

On a Weighted Interpolation of Functions with Circular Majorant

Denote by Ln the projection operator obtained by applying the Lagrange interpolation method, weighted by (1 − x), at the zeros of the Chebyshev polynomial of the second kind of degree n + 1. The norm ‖Ln‖ = max ‖f‖∞≤1 ‖Lnf‖∞, where ‖ · ‖∞ denotes the supremum norm on [−1, 1], is known to be asymptotically the same as the minimum possible norm over all choices of interpolation nodes for unweight...

About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities

INTERPOLATION BY HYPERBOLIC B-SPLINE FUNCTIONS

In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.