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Density methods and results in approximation theory

100%

Pinkus A.

Banach Center Publications

2004

tom 64

nr 1

173-192

Approximation theory and functional analysis share many common problems and points of contact. One of the areas of mutual interest is that of density results. In this paper we briefly survey various methods and results in this area starting from work of Weierstrass and Riesz, and extending to more recent times.

Extending n-convex functions

63%

Pinkus A., Wulbert D.

Studia Mathematica

2005

tom 171

nr 2

125-152

We are given data α₁,..., αₘ and a set of points E = {x₁,...,xₘ}. We address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions $f(x_{i}) = α_{i}$, i = 1,...,m, that is also n-convex on a set properly containing E. We consider both one-point extensions of E, and extensions to all of ℝ. We also determine bounds on the n-convex functions satisfying the above interpolation conditions.

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Pinkus A.

1 Wulbert D.

1 2005

1 2004

Wyniki wyszukiwania

Density methods and results in approximation theory

Extending n-convex functions