Spectral Analysis on Standard Locally Homogeneous Spaces
A groundbreaking theory has emerged for spectral analysis of pseudo-Riemannian locally symmetric spaces, extending beyond the traditional Riemannian framework. The theory introduces innovative approaches to global analysis of locally symmetric spaces endowed with an indefinite metric. Breakthrough m...
محفوظ في:
| المؤلفون الرئيسيون: | , |
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| مؤلف مشترك: | |
| التنسيق: | الكتروني كتاب الكتروني |
| اللغة: | الإنجليزية |
| منشور في: |
Singapore :
Springer Nature Singapore : Imprint: Springer,
2025.
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| الطبعة: | 1st ed. 2025. |
| سلاسل: | FJ-LMI Subseries,
2367 |
| الموضوعات: | |
| الوصول للمادة أونلاين: | https://doi.org/10.1007/978-981-96-1957-3 |
| الوسوم: |
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جدول المحتويات:
- 1 Introduction
- 2 Method of proof
- Part I Generalities
- 3 Reminders: spectral analysis on spherical homogeneous spaces
- 4 Discrete spectrum of type I and II
- 5 Differential operators coming from 𝑳 and from the fiber 𝑭
- Part II Proof of the theorems of Chapter 1
- 6 Essential self-adjointness of the Laplacian
- 7 Transfer of Riemannian eigenfunctions and spectral decomposition
- 8 Consequences of conditions (A) and (B) on representations of G and 𝑳
- 9 The maps i𝝉,𝚪 and p𝝉,𝚪 preserve type I and type II
- 10 Infinite discrete spectrum of type II
- Part III Representation-theoretic description of the discrete spectrum
- 11 A conjectural picture
- 12 The discrete spectrum in terms of group representations.