This book is an introductory text that charts the recent
developments in the area of Whitney-type extension problems and the
mathematical aspects of interpolation of data. It provides a
detailed tour of a new and active area of mathematical research. In
each section, the authors focus on a different key insight in the
theory. The book motivates the more technical aspects of the theory
through a set of illustrative examples. The results include the
solution of Whitney's problem, an efficient algorithm for a finite
version, and analogues for Hoelder and Sobolev spaces in place of C
m . The target audience consists of graduate students and junior
faculty in mathematics and computer science who are familiar with
point set topology, as well as measure and integration theory. The
book is based on lectures presented at the CBMS regional workshop
held at the University of Texas at Austin in the summer of 2019.
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