Author: Emil AxelgaardPublisher:
ISBN:
Category :
Languages : en
Pages : 121
Book Description
Infinite Dimensional Spherical Analysis and Harmonic Analysis for Groups Acting on Homogeneous Trees
Author: Emil AxelgaardHarmonic Analysis for Anisotropic Random Walks on Homogeneous Trees
Author: Alessandro Figà-TalamancaPublisher: American Mathematical Soc.
ISBN: 0821825941
Category : Mathematics
Languages : en
Pages : 86
Book Description
This work presents a detailed study of the anisotropic series representations of the free product group Z/2Z*...*Z/2Z. These representations are infinite dimensional, irreducible, and unitary and can be divided into principal and complementary series. Anisotropic series representations are interesting because, while they are not restricted from any larger continuous group in which the discrete group is a lattice, they nonetheless share many properties of such restrictions. The results of this work are also valid for nonabelian free groups on finitely many generators.
Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees
Author: Alessandro Figá-TalamancaPublisher: Cambridge University Press
ISBN: 0521424445
Category : Mathematics
Languages : en
Pages : 165
Book Description
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.
Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees
Author: Publisher:
ISBN: 9781107366718
Category : Trees (Graph theory)
Languages : en
Pages : 164
Book Description
These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree.
On Spherical Analysis on Groups of Isometries of Homogeneous Trees
Author: M. G. CowlingPublisher:
ISBN:
Category : Spherical harmonics
Languages : en
Pages : 26
Book Description
Harmonic Functions on Trees and Buildings
Author: Adam KornyiPublisher: American Mathematical Soc.
ISBN: 9780821855423
Category : Mathematics
Languages : en
Pages : 196
Book Description
This volume presents the proceedings of the workshop ``Harmonic Functions on Graphs'' held at the Graduate Center of CUNY in the fall of 1995. The main papers present material from four minicourses given by leading experts: D. Cartwright, A. Figa-Talamanca, S. Sawyer and T. Steger. These minicourses are introductions which gradually progress to deeper and less known branches of the subject. One of the topics treated is buildings, which are discrete analogues of symmetric spaces of arbitrary rank; buildings of rank are trees. Harmonic analysis on buildings is a fairly new and important field of research. One of the minicourses discusses buildings from the combinatorial perspective and another examines them from the $p$-adic perspective. The third minicourse deals with the connections of trees with $p$-adic analysis. And the fourth deals with random walks, i.e., with the probabilistic side of harmonic functions on trees. The book also contains the extended abstracts of 19 of the 20 lectures given by the participants on their recent results. These abstracts, well detailed and clearly understandable, give a good cross-section of the present state of research in the field.
Topics in Probability and Lie Groups: Boundary Theory
Author: John Christopher TaylorPublisher: American Mathematical Soc.
ISBN: 0821802755
Category : Mathematics
Languages : en
Pages : 214
Book Description
This volume is comprised of two parts: the first contains articles by S. N. Evans, F. Ledrappier, and Figa-Talomanaca. These articles arose from a Centre de Recherches de Mathematiques (CRM) seminar entitiled, ``Topics in Probability on Lie Groups: Boundary Theory''. Evans gives a synthesis of his pre-1992 work on Gaussian measures on vector spaces over a local field. Ledrappier uses the freegroup on $d$ generators as a paradigm for results on the asymptotic properties of random walks and harmonic measures on the Martin boundary. These articles are followed by a case study by Figa-Talamanca using Gelfand pairs to study a diffusion on a compact ultrametric space. The second part of the book is an appendix to the book Compactifications of Symmetric Spaces (Birkhauser) by Y. Guivarc'h and J. C. Taylor. This appendix consists of an article by each author and presents the contents of this book in a more algebraic way. L. Ji and J.-P. Anker simplifies some of their results on the asymptotics of the Green function that were used to compute Martin boundaries. And Taylor gives a self-contained account of Martin boundary theory for manifolds using the theory of second order strictly elliptic partial differential operators.
Representations of Lie Groups, Kyoto, Hiroshima, 1986
Author: K. OkamotoPublisher: Academic Press
ISBN: 1483257576
Category : Mathematics
Languages : en
Pages : 673
Book Description
Representations of Lie Groups, Kyoto, Hiroshima, 1986 contains the proceedings of a symposium on "Analysis on Homogeneous Spaces and Representations of Lie Groups" held on September 1-6, 1986 in Japan. The symposium provided a forum for discussing Lie groups and covered topics ranging from geometric constructions of representations to the irreducibility of discrete series representations for semisimple symmetric spaces. A classification theory of prehomogeneous vector spaces is also described. Comprised of 22 chapters, this volume first considers the characteristic varieties of certain modules over the enveloping algebra of a semisimple Lie algebra, such as highest weight modules and primitive quotients. The reader is then introduced to multiplicity one theorems for generalized Gelfand-Graev representations of semisimple Lie groups and Whittaker models for the discrete series. Subsequent chapters focus on Lie algebra cohomology and holomorphic continuation of generalized Jacquet integrals; the generalized Geroch conjecture; algebraic structures on virtual characters of a semisimple Lie group; and fundamental groups of semisimple symmetric spaces. The book concludes with an analysis of the boundedness of certain unitarizable Harish-Chandra modules. This monograph will appeal to students, specialists, and researchers in the field of pure mathematics.
Representation Theory and Noncommutative Harmonic Analysis II
Author: A.A. KirillovPublisher: Springer Science & Business Media
ISBN: 3662097567
Category : Mathematics
Languages : en
Pages : 274
Book Description
Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.
Author: Jean-Philippe Anker