Fitting Smooth Functions to Data

Download or read book Fitting Smooth Functions to Data written by Charles Fefferman and published by American Mathematical Soc.. This book was released on 2020-10-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Hölder and Sobolev spaces in place of Cm. 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.