Harmonic Analysis and Representation Theory for Groups Acting on Homogeneous Trees
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"Harmonic Analysis and Representation Theory for Groups Acting on Homogeneous Trees" by Alessandro Figà-Talamanca, Claudio Nebbia is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G.I. Ol'shiankii. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.
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"Harmonic Analysis and Representation Theory for Groups Acting on Homogeneous Trees" by Alessandro Figà-Talamanca, Claudio Nebbia is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Topic: Core Mathematics
Author: Alessandro Figà-Talamanca, Claudio Nebbia
Who this is for:
- Teachers and classroom instructors
- Students building subject mastery
- Readers looking for practical learning support
Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.
These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G.I. Ol'shiankii. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.
| Author | Alessandro Figà-Talamanca, Claudio Nebbia |
| Publisher | Cambridge University Press |
| Published | 1991 |
| ISBN-13 | 9780521424448 |
| Binding | Paperback |
| Pages | 165 |
| Language | English |
| Subjects | Mathematics |
| Topic | Core Mathematics |
| Series | London Mathematical Society Lecture Note |
Format: Paperback
Length: 165 pages
Language: English
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