Extending n-convex functions

Allan Pinkus, and Dan Wulbert. "Extending n-convex functions." Studia Mathematica 171.2 (2005): 125-152. <http://eudml.org/doc/285345>.

@article{AllanPinkus2005,
abstract = {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.},
author = {Allan Pinkus, Dan Wulbert},
journal = {Studia Mathematica},
keywords = {-convex function; B-spline; interpolation; weak Chebyshev system},
language = {eng},
number = {2},
pages = {125-152},
title = {Extending n-convex functions},
url = {http://eudml.org/doc/285345},
volume = {171},
year = {2005},
}

TY - JOUR
AU - Allan Pinkus
AU - Dan Wulbert
TI - Extending n-convex functions
JO - Studia Mathematica
PY - 2005
VL - 171
IS - 2
SP - 125
EP - 152
AB - 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.
LA - eng
KW - -convex function; B-spline; interpolation; weak Chebyshev system
UR - http://eudml.org/doc/285345
ER -