Book contents
- Frontmatter
- Contents
- Foreword
- Symbols
- Preface
- 1 Introduction
- Part One Historical and Theoretical Background
- Part Two Statistics and Applications to Data Analysis
- Part Three Complementary Topics
- 8 Further Applications
- 9 Transforms of Christoffel–Darboux Kernels
- 10 Spectral Characterization and Extensions of the Christoffel Function
- References
- Index
10 - Spectral Characterization and Extensions of the Christoffel Function
from Part Three - Complementary Topics
Published online by Cambridge University Press: 31 March 2022
Book contents
- Frontmatter
- Contents
- Foreword
- Symbols
- Preface
- 1 Introduction
- Part One Historical and Theoretical Background
- Part Two Statistics and Applications to Data Analysis
- Part Three Complementary Topics
- 8 Further Applications
- 9 Transforms of Christoffel–Darboux Kernels
- 10 Spectral Characterization and Extensions of the Christoffel Function
- References
- Index
Summary
A spectral characterization of the Christoffel function is provided via its associated moment matrix, and that of Dirac measures. A first (Hahn-Banach) extension of the Christoffel function to Lp spaces is characterized. A second extension is also provided and analyzed where squares of polynomials (hence positive everywhere) are replaced by larger convex cones of polynomials positive on the support of the underlying measure, in particular polynomials in a certain associated quadratic module.
Keywords
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- Chapter
- Information
- The Christoffel–Darboux Kernel for Data Analysis , pp. 136 - 154Publisher: Cambridge University PressPrint publication year: 2022