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Author :
Publisher :
Page : 164 pages
File Size : 36,94 MB
Release : 1991
Category : Trees (Graph theory)
ISBN : 9781107366718
These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree.
Author : Alessandro Figá-Talamanca
Publisher : Cambridge University Press
Page : 165 pages
File Size : 29,74 MB
Release : 1991-06-28
Category : Mathematics
ISBN : 0521424445
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
Publisher :
Page : 163 pages
File Size : 34,43 MB
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 9781107361805
These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree.
Author : Alessandro Figá-Talamanca
Publisher : Cambridge University Press
Page : 0 pages
File Size : 47,17 MB
Release : 1991-06-28
Category : Mathematics
ISBN : 9780521424448
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 :
Publisher :
Page : 176 pages
File Size : 39,60 MB
Release : 1955
Category :
ISBN :
Author : Alex Lubotzky
Publisher : Springer Science & Business Media
Page : 201 pages
File Size : 29,33 MB
Release : 2010-02-17
Category : Mathematics
ISBN : 3034603320
In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.
Author : Alessandro Figà-Talamanca
Publisher : American Mathematical Soc.
Page : 86 pages
File Size : 35,71 MB
Release : 1994
Category : Mathematics
ISBN : 0821825941
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.
Author : Charles V. Benton
Publisher : Nova Publishers
Page : 256 pages
File Size : 13,21 MB
Release : 2004
Category : Mathematics
ISBN : 9781590339138
Physics and mathematics have always been closely intertwined, with developments in one field frequently inspiring the other. Currently, there are many unsolved problems in physics which will likely require new innovations in mathematical physics. Mathematical physics is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory, and, in general, with the mathematical foundations of theoretical physics. This includes such subjects as scattering theory for n bodies, quantum mechanics (both non-relativistic and relativistic), atomic and molecular physics, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models), and mathematical developments in functional analysis and algebra to which such subjects lead. This book presents leading-edge research in this fast-moving field.
Author : Emil Axelgaard
Publisher :
Page : 121 pages
File Size : 25,55 MB
Release : 2012
Category :
ISBN :
Author : Elias M. Stein
Publisher : Princeton University Press
Page : 168 pages
File Size : 31,48 MB
Release : 1970-02-21
Category : Mathematics
ISBN : 9780691080673
This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, such as those arising in the study of the expansions coming from second order elliptic operators. A review of background material in Lie groups and martingale theory is included to make the monograph more accessible to the student.