Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Overview
- Part One Background Material
- Part Two The Laplace and Schrödinger Operators
- Part Three Sharp Constants in Lieb–Thirring Inequalities
- 5 Sharp Lieb–Thirring Inequalities
- 6 Sharp Lieb–Thirring Inequalities in Higher Dimensions
- 7 More on Sharp Lieb–Thirring Inequalities
- 8 More on the Lieb–Thirring Constants
- References
- Index
8 - More on the Lieb–Thirring Constants
from Part Three - Sharp Constants in Lieb–Thirring Inequalities
Published online by Cambridge University Press: 03 November 2022
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Overview
- Part One Background Material
- Part Two The Laplace and Schrödinger Operators
- Part Three Sharp Constants in Lieb–Thirring Inequalities
- 5 Sharp Lieb–Thirring Inequalities
- 6 Sharp Lieb–Thirring Inequalities in Higher Dimensions
- 7 More on Sharp Lieb–Thirring Inequalities
- 8 More on the Lieb–Thirring Constants
- References
- Index
Summary
In this chapter, we derive the currently best known bounds on the constants in the Lieb–Thirring inequality following Hundertman–Laptev–Weidl and Frank–Hundertmark–Jex–Nam. These arguments proceed by proving bounds for one-dimensional Schrödinger operators with matrix-valued potentials and then using the method of "lifting in dimension." In the final section, we summarize the results in the book and provide an overview of what is known about the sharp constants in the Lieb–Thirring and Cwikel–Lieb–Rozenblum inequalities.
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- Publisher: Cambridge University PressPrint publication year: 2022