# Mathematics Colloquia and Seminars

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### INTERPOLATION OF DATA BY NONNEGATIVE \(C^2\) FUNCTIONS

**PDE and Applied Math Seminar**

Speaker: | Black Jiang, UC Davis |

Location: | 2112 |

Start time: | Fri, Mar 15 2019, 4:10PM |

This is a repeat of the talk given on Feb 8 to a small audience due to the QMAC colloqium scheduled at the same time.In this talk, we consider the following extension problem of Whitney-type: given a finite set on the plane with prescribed nonnegative values, how do we decide the minimal \(C^2\) norm of all the globally nonnegative functions that interpolate the data?

There is a twofold solution to the problem, namely, an algorithm which allows us to compute the minimal norm, and a bounded extension operator which recovers an interpolant witnessing the minimal norm.

The idea of the proof relies on the observation that any finite set on the plane lies on a curve on a sufficiently small scale, so the local problem is essentially one-dimensional and readily solvable. We will look at some key objects that will allow us to control these scales so that the local solutions are compatible with each other.

This is joint work with Kevin Luli.

A repeat of the same talk by Black scheduled on Feb 8 but conflicted with the QMAC Colloqium.