Revista Matemática Iberoamericana

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Volume 33, Issue 1, 2017, pp. 305–324
DOI: 10.4171/RMI/938

Published online: 2017-02-22

Interpolation of data by smooth nonnegative functions

Charles Fefferman[1], Arie Israel[2] and Garving K. Luli[3]

(1) Princeton University, USA
(2) University of Texas at Austin, USA
(3) University of California at Davis, USA

We prove a finiteness principle for interpolation of data by nonnegative $C^m$ and $C^{m−1,1}$ functions. Our result raises the hope that one can start to understand constrained interpolation problems in which, e.g., the interpolating function $F$ is required to be nonnegative.

Keywords: Nonnegative interpolation, constrained interpolation, Whitney extension problem

Fefferman Charles, Israel Arie, Luli Garving: Interpolation of data by smooth nonnegative functions. Rev. Mat. Iberoam. 33 (2017), 305-324. doi: 10.4171/RMI/938