Book contents
- Frontmatter
- Dedication
- Contents
- Foreword
- Preface
- Part One Preliminaries: Entrywise Powers Preserving Positivity in a Fixed Dimension
- Part Two Entrywise Functions Preserving Positivity in all Dimensions
- 11 History – Schoenberg, Rudin, Vasudeva, and Metric Geometry
- 12 Loewner’s Determinant Calculation in Horn’s Thesis
- 13 The Stronger Horn–Loewner Theorem via Mollifiers
- 14 Stronger Vasudeva and Schoenberg Theorems via Bernstein’s Theorem
- 15 Proof of the Stronger Schoenberg Theorem (Part I) – Positivity Certificates
- 16 Proof of the Stronger Schoenberg Theorem (Part II) – Real Analyticity
- 17 Proof of the Stronger Schoenberg Theorem (Part III) – Complex Analysis
- 18 Preservers of Loewner Positivity on Kernels
- 19 Preservers of Loewner Monotonicity and Convexity on Kernels
- 20 Functions Acting Outside Forbidden Diagonal Blocks
- 21 The Boas–Widder Theorem on Functions with Positive Differences
- 22 Menger’s Results and Euclidean Distance Geometry
- 23 Exercises
- Part Three Entrywise Polynomials Preserving Positivity in a Fixed Dimension
- Part I: Bibliographic Notes and References
- Part II: Bibliographic Notes and References
- Part III: Bibliographic Notes and References
- References
- Index
This chapter is part of a book that is no longer available to purchase from Cambridge Core
18 - Preservers of Loewner Positivity on Kernels
from Part Two - Entrywise Functions Preserving Positivity in all Dimensions
Book contents
- Frontmatter
- Dedication
- Contents
- Foreword
- Preface
- Part One Preliminaries: Entrywise Powers Preserving Positivity in a Fixed Dimension
- Part Two Entrywise Functions Preserving Positivity in all Dimensions
- 11 History – Schoenberg, Rudin, Vasudeva, and Metric Geometry
- 12 Loewner’s Determinant Calculation in Horn’s Thesis
- 13 The Stronger Horn–Loewner Theorem via Mollifiers
- 14 Stronger Vasudeva and Schoenberg Theorems via Bernstein’s Theorem
- 15 Proof of the Stronger Schoenberg Theorem (Part I) – Positivity Certificates
- 16 Proof of the Stronger Schoenberg Theorem (Part II) – Real Analyticity
- 17 Proof of the Stronger Schoenberg Theorem (Part III) – Complex Analysis
- 18 Preservers of Loewner Positivity on Kernels
- 19 Preservers of Loewner Monotonicity and Convexity on Kernels
- 20 Functions Acting Outside Forbidden Diagonal Blocks
- 21 The Boas–Widder Theorem on Functions with Positive Differences
- 22 Menger’s Results and Euclidean Distance Geometry
- 23 Exercises
- Part Three Entrywise Polynomials Preserving Positivity in a Fixed Dimension
- Part I: Bibliographic Notes and References
- Part II: Bibliographic Notes and References
- Part III: Bibliographic Notes and References
- References
- Index
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- Matrix Analysis and Entrywise Positivity Preservers , pp. 155 - 158Publisher: Cambridge University PressPrint publication year: 2022