Harmonic analysis and representation theory for groups acting on homogeneous trees / Alessandro Figà-Talamanca and Claudio Nebbia.
Material type: TextSeries: London Mathematical Society lecture note series ; 162.Publication details: Cambridge ; New York : Cambridge University Press, 1991.Description: 1 online resource (ix, 151 pages) : illustrationsContent type:- text
- computer
- online resource
- 9781107361805
- 110736180X
- 9780511662324
- 0511662327
- Automorphisms
- Harmonic analysis
- Representations of groups
- Trees (Graph theory)
- Fourier Analysis
- Arbres (Théorie des graphes)
- Analyse harmonique
- Représentations de groupes
- Automorphismes
- MATHEMATICS -- Infinity
- Automorphisms
- Harmonic analysis
- Representations of groups
- Homogener Baum
- Automorphismengruppe
- Irreduzible Darstellung
- Harmonische analyse
- Representatie (wiskunde)
- Automorphismes
- Analyse harmonique
- Représentations de groupes
- 515.2433 22
- QA166.2 .F43 1991eb
- 31.30
- 31.21
- *22D12
- 20E08
- 22-02
- 22E50
- 43-02
- 43A85
- 43A90
- 57M07
- SI 320
- SK 260
- SK 450
Item type | Home library | Collection | Call number | Materials specified | Status | Date due | Barcode | |
---|---|---|---|---|---|---|---|---|
Electronic-Books | OPJGU Sonepat- Campus | E-Books EBSCO | Available |
Includes bibliographical references (pages 138-143) and index.
Print version record.
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.
Cover; Title; Copyright; Contents; Preface; Chapter I; 1) Graphs and trees; 2) The free group as a tree; 3) Automorphisms of a tree; 4) The group of automorphisms Aut(X); 5) Compact maximal subgroups; 6) Discrete subgroups; 7) Cayley graphs which are trees; 8) Amenable subgroups; 9) Orbits of amenable subgroups; 10) Groups with transitive action on the boundary; 11) Notes and remarks; Chapter II; 1) Eigenfunctions of the Laplace operator; 2) Spherical functions; 3) Intertwining operators; 4) The Gelfand pair (G, K); 5) Spherical representations
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