**CBMS Regional Conference Series in Mathematics**

Volume: 135;
2020;
160 pp;
Softcover

MSC: Primary 41; 42; 52; 65;

**Print ISBN: 978-1-4704-6130-0
Product Code: CBMS/135**

List Price: $59.00

AMS Member Price: $47.20

MAA Member Price: $53.10

**Electronic ISBN: 978-1-4704-6263-5
Product Code: CBMS/135.E**

List Price: $59.00

AMS Member Price: $47.20

MAA Member Price: $53.10

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#### Supplemental Materials

# Fitting Smooth Functions to Data

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*Charles Fefferman; Arie Israel*

A co-publication of the AMS and CBMS

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 \(C^{m}\).

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.

#### Readership

Graduate students and researchers interested in Whitney extension and interpolation problems.

#### Table of Contents

# Table of Contents

## Fitting Smooth Functions to Data

- Cover Cover11
- Title page iii4
- Preface ix10
- Chapter 1. Overview 112
- Chapter 2. Whitneyโs Extension Theorem 1526
- Chapter 3. ๐ถ^{๐} Interpolation for Finite Data 3142
- Chapter 4. The Classical Whitney Extension Problem 7384
- Chapter 5. Extension and Interpolation in Sobolev Spaces 99110
- Chapter 6. Vector-Valued Functions 135146
- Chapter 7. Open Problems 151162
- 7.1. (1+๐)-Optimal Interpolation 151162
- 7.2. Interpolants of Minimal Norm 151162
- 7.3. Practical Algorithms 152163
- 7.4. Continuous Semialgebraic Sections 152163
- 7.5. ๐ถ^{๐} Semialgebraic Sections 152163
- 7.6. Sobolev Interpolation 152163
- 7.7. Computing Selections 153164
- 7.8. Interpolation with Constraints 153164
- 7.9. Sobolev Extension Domains 154165
- 7.10. ๐ถ^{โ} extension 154165
- 7.11. Fitting a Manifold to Data 154165

- Bibliography 155166
- Index 159170
- Back Cover Back Cover1173