On Polynomial Interpolation on the Unit Ball

Analysis on the Unit Ball and on the Simplex

Many results on the unit ball and those on the simplex can be deduced from each other or from the corresponding results on the unit sphere. The areas in which such a connection appears include orthogonal polynomials, approximation, cubature formulas and polynomial interpolation. We explain this phenomenon in some detail.

Polynomial Interpolation on the Unit Sphere and on the Unit Ball

Predicting the Efficiency of Decision-Making Unit by Using Piecewise Polynomial Extrapolation in Different Times

In this article, we will estimate efficiency amountof decision-making unit by offering the continuous piecewise polynomialextrapolation and interpolation by CCR model input-oriented on the assumptionthat it is constant returns to scale in different times. And finally, we willestimate efficiency amount of decision-making unit indifferent times byoffering an example.

Multivariate Markov Polynomial Inequalities and Chebyshev Nodes

This article considers the extension of V. A. Markov’s theorem for polynomial derivatives to polynomials with unit bound on the closed unit ball of any real normed linear space. We show that this extension is equivalent to an inequality for certain directional derivatives of polynomials in two variables that have unit bound on the Chebyshev nodes. We obtain a sharpening of the Markov inequality...

Duality, Convexity and Peak Interpolation in the Drury-arveson Space

We consider the closed algebra Ad generated by the polynomial multipliers on the Drury-Arveson space. We identify Ad as a direct sum of the preduals of the full multiplier algebra and of a commutative von Neumann algebra, and establish analogues of many classical results concerning the dual space of the ball algebra. These developments are deeply intertwined with the problem of peak interpolati...