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Quadratic vector equations on complex upper half-plane /
The authors consider the nonlinear equation -\frac 1m=z+Sm with a parameter z in the complex upper half plane \mathbb H, where S is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values in \mathbb H is unique and its z-dependence is conveniently desc...
| Cote: | Libro Electrónico |
|---|---|
| Auteurs principaux: | , , |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Providence :
American Mathematical Society,
[2019].
|
| Collection: | Memoirs of the American Mathematical Society ;
no. 1261. |
| Sujets: | |
| Accès en ligne: | Texto completo |
Table des matières:
- Cover
- Title page
- Chapter 1. Introduction
- Chapter 2. Set-up and main results
- 2.1. Generating density
- 2.2. Stability
- 2.3. Relationship between Theorem 2.6 and Theorem 2.6 of [AEK16b]
- 2.4. Outline of proofs
- Chapter 3. Local laws for large random matrices
- 3.1. Proof of local law inside bulk of the spectrum
- Chapter 4. Existence, uniqueness and \Lp{2}-bound
- 4.1. Stieltjes transform representation
- 4.2. Operator and structural \Lp{2}-bound
- Chapter 5. Properties of solution
- 5.1. Relations between components of and
- 5.2. Stability and operator
- Chapter 6. Uniform bounds
- 6.1. Uniform bounds from \Lp{2}-estimates
- 6.2. Uniform bound around =0 when =0
- Chapter 7. Regularity of solution
- Chapter 8. Perturbations when generating density is small
- 8.1. Expansion of operator
- 8.2. Cubic equation
- Chapter 9. Behavior of generating density where it is small
- 9.1. Expansion around non-zero minima of generating density
- 9.2. Expansions around minima where generating density vanishes
- 9.3. Proofs of Theorems 2.6 and 2.11
- Chapter 10. Stability around small minima of generating density
- Chapter 11. Examples
- A.6. Cubic roots and associated auxiliary functions
- Bibliography
- Back Cover