Harmonic analysis and representation theory for groups acting on homogeneous trees /:
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...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1991.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
162. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (ix, 151 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 138-143) and index. |
| ISBN: | 9781107361805 110736180X 9780511662324 0511662327 |
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| 520 | |a 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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| author | Figà-Talamanca, Alessandro, 1938- |
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| contents | 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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| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:16Z |
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| isbn | 9781107361805 110736180X 9780511662324 0511662327 |
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| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Figà-Talamanca, Alessandro, 1938- http://id.loc.gov/authorities/names/n83138273 Harmonic analysis and representation theory for groups acting on homogeneous trees / Alessandro Figà-Talamanca and Claudio Nebbia. Cambridge ; New York : Cambridge University Press, 1991. 1 online resource (ix, 151 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 162 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 Automorphisms. http://id.loc.gov/authorities/subjects/sh85010452 Harmonic analysis. http://id.loc.gov/authorities/subjects/sh85058939 Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Trees (Graph theory) http://id.loc.gov/authorities/subjects/sh85137259 Fourier Analysis https://id.nlm.nih.gov/mesh/D005583 Arbres (Théorie des graphes) Analyse harmonique. Représentations de groupes. Automorphismes. MATHEMATICS Infinity. bisacsh Trees (Graph theory) fast Automorphisms fast Harmonic analysis fast Representations of groups fast Homogener Baum gnd http://d-nb.info/gnd/4160584-6 Automorphismengruppe gnd http://d-nb.info/gnd/4143708-1 Irreduzible Darstellung gnd http://d-nb.info/gnd/4162430-0 Harmonische analyse. gtt Representatie (wiskunde) gtt Automorphismes. ram Analyse harmonique. ram Représentations de groupes. ram Nebbia, Claudio. Print version: Figà-Talamanca, Alessandro, 1938- Harmonic analysis and representation theory for groups acting on homogeneous trees. Cambridge ; New York : Cambridge University Press, 1991 0521424445 (OCoLC)24177045 London Mathematical Society lecture note series ; 162. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552465 Volltext |
| spellingShingle | Figà-Talamanca, Alessandro, 1938- Harmonic analysis and representation theory for groups acting on homogeneous trees / London Mathematical Society lecture note series ; 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 Automorphisms. http://id.loc.gov/authorities/subjects/sh85010452 Harmonic analysis. http://id.loc.gov/authorities/subjects/sh85058939 Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Trees (Graph theory) http://id.loc.gov/authorities/subjects/sh85137259 Fourier Analysis https://id.nlm.nih.gov/mesh/D005583 Arbres (Théorie des graphes) Analyse harmonique. Représentations de groupes. Automorphismes. MATHEMATICS Infinity. bisacsh Trees (Graph theory) fast Automorphisms fast Harmonic analysis fast Representations of groups fast Homogener Baum gnd http://d-nb.info/gnd/4160584-6 Automorphismengruppe gnd http://d-nb.info/gnd/4143708-1 Irreduzible Darstellung gnd http://d-nb.info/gnd/4162430-0 Harmonische analyse. gtt Representatie (wiskunde) gtt Automorphismes. ram Analyse harmonique. ram Représentations de groupes. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85010452 http://id.loc.gov/authorities/subjects/sh85058939 http://id.loc.gov/authorities/subjects/sh85112944 http://id.loc.gov/authorities/subjects/sh85137259 https://id.nlm.nih.gov/mesh/D005583 http://d-nb.info/gnd/4160584-6 http://d-nb.info/gnd/4143708-1 http://d-nb.info/gnd/4162430-0 |
| title | Harmonic analysis and representation theory for groups acting on homogeneous trees / |
| title_auth | Harmonic analysis and representation theory for groups acting on homogeneous trees / |
| title_exact_search | Harmonic analysis and representation theory for groups acting on homogeneous trees / |
| title_full | Harmonic analysis and representation theory for groups acting on homogeneous trees / Alessandro Figà-Talamanca and Claudio Nebbia. |
| title_fullStr | Harmonic analysis and representation theory for groups acting on homogeneous trees / Alessandro Figà-Talamanca and Claudio Nebbia. |
| title_full_unstemmed | Harmonic analysis and representation theory for groups acting on homogeneous trees / Alessandro Figà-Talamanca and Claudio Nebbia. |
| title_short | Harmonic analysis and representation theory for groups acting on homogeneous trees / |
| title_sort | harmonic analysis and representation theory for groups acting on homogeneous trees |
| topic | Automorphisms. http://id.loc.gov/authorities/subjects/sh85010452 Harmonic analysis. http://id.loc.gov/authorities/subjects/sh85058939 Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Trees (Graph theory) http://id.loc.gov/authorities/subjects/sh85137259 Fourier Analysis https://id.nlm.nih.gov/mesh/D005583 Arbres (Théorie des graphes) Analyse harmonique. Représentations de groupes. Automorphismes. MATHEMATICS Infinity. bisacsh Trees (Graph theory) fast Automorphisms fast Harmonic analysis fast Representations of groups fast Homogener Baum gnd http://d-nb.info/gnd/4160584-6 Automorphismengruppe gnd http://d-nb.info/gnd/4143708-1 Irreduzible Darstellung gnd http://d-nb.info/gnd/4162430-0 Harmonische analyse. gtt Representatie (wiskunde) gtt Automorphismes. ram Analyse harmonique. ram Représentations de groupes. ram |
| topic_facet | 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) |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552465 |
| work_keys_str_mv | AT figatalamancaalessandro harmonicanalysisandrepresentationtheoryforgroupsactingonhomogeneoustrees AT nebbiaclaudio harmonicanalysisandrepresentationtheoryforgroupsactingonhomogeneoustrees |