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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
[2019].
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1261. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 050 | 4 | |a QA3 |b .Am35 no.1261 | |
| 082 | 0 | 4 | |a 515.63 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Ajanki, Oskari Heikki, |e author. | |
| 245 | 1 | 0 | |a Quadratic vector equations on complex upper half-plane / |c Oskari Heikki Ajanki, László Erdős, Torben Krüger. |
| 264 | 1 | |a Providence : |b American Mathematical Society, |c [2019]. | |
| 264 | 4 | |c © 2019 | |
| 300 | |a 1 online resource (v, 133 pages ): |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |2 rdamedia | ||
| 338 | |a online resource |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society ; |v number 1261 | |
| 500 | |a "September 2019; Volume 261; number 1261 (fifth of 7 numbers)" -- cover. | ||
| 504 | |a Includes bibliographical references. | ||
| 588 | |a Description based on print version record. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a A.6. Cubic roots and associated auxiliary functions -- Bibliography -- Back Cover | |
| 520 | |a 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 described as the Stieltjes transforms of a family of measures v on \mathbb R. In a previous paper the authors qualitatively identified the possible singular behaviors of v: under suitable conditions on S we showed that in the density of v only algebraic singularities of degree two or three may occur. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Vector algebra. | |
| 650 | 6 | |a Algèbre vectorielle. | |
| 650 | 7 | |a Álgebra vectorial |2 embne | |
| 650 | 7 | |a Vector algebra |2 fast | |
| 700 | 1 | |a Erdős, László, |d 1966- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJfRH8VCjq9dR6xFdvdJDq | |
| 700 | 1 | |a Krüger, Torben, |e author. | |
| 776 | 0 | 8 | |i Print version: Ajanki, Oskari Heikki. |t Quadratic vector equations on complex upper half-plane. |d Providence, RI : American Mathematical Society, 2019 |z 9781470436834 |w (DLC) 2020023144 |w (OCoLC)1164819680 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1261. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5990829 |z Texto completo |
| 938 | |a YBP Library Services |b YANK |n 301000554 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37445301 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5990829 | ||
| 994 | |a 92 |b IZTAP | ||