Induced representations of C∗-algebras

Locally compact groups Dynamical systems and crossed products Special cases and basic constructions Imprimitivity theorems Induced representations and induced ideals Orbits and quasi-orbits Properties of crossed products Ideal structure The proof of the Gootman-Rosenberg-Sauvageot theorem Amenable groups The Banach *-algebra $L^1(G,A)$ Bundles of $C*$-algebras Groups Representations of $C*$-algebras Direct integrals Effros's ideal center decomposition The Fell topology Miscellany Notation and Symbol Index Index Bibliography.

/pdf/crossed-products-of-c-algebras-citugfufjv.pdf

Crossed products of C*-algebras

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 1. CAS DU GROUPE D'HEISENBERG 1.1. N o t a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 1.2. D i f f u s i o n a s s o c i 6 e a u l a p l a c i e n de K o h n e t 6 q u a t i o n d e l a c h a l e u r . . . . . . . . . 98 1.3. S o l u t i o n s f o n d a m e n t a l e d e A• . . . . . . . . . . . . . . . . . . . . . . . 101 1.4. S i n g u l a r i t 6 s p o u r r h y p o e l l i p t i c i t ~ . . . . . . . . . . . . . . . . . . . . . . 102

/pdf/principe-de-moindre-action-propagation-de-la-chaleur-et-bmrklrahc4.pdf

Principe de moindre action, propagation de la chaleur et estimees sous elliptiques sur certains groupes nilpotents

This paper gives a negative solution to the problem of Milnor concerning the degrees of growth of groups. The construction also answers a question of Day concerning amenable groups. A number of other results are obtained on residually finite finitely generated infinite 2-groups. Bibliography: 51 titles.

http://iopscience.iop.org/article/10.1070/IM1985v025n02ABEH001281/pdf

Degrees of Growth of Finitely Generated Groups, and the Theory of Invariant Means

Let $X_1, X_2,\cdots, X_k, X_{k+1},\cdots, X_n$ be exchangeable random variables taking values in the set $S$. The variation distance between the distribution of $X_1, X_2,\cdots, X_k$ and the closest mixture of independent, identically distributed random variables is shown to be at most $2 ck/n$, where $c$ is the cardinality of $S$. If $c$ is infinite, the bound $k(k - 1)/n$ is obtained. These results imply the most general known forms of de Finetti's theorem. Examples are given to show that the rates $k/n$ and $k(k - 1)/n$ cannot be improved. The main tool is a bound on the variation distance between sampling with and without replacement. For instance, suppose an urn contains $n$ balls, each marked with some element of the set $S$, whose cardinality $c$ is finite. Now $k$ draws are made at random from this urn, either with or without replacement. This generates two probability distributions on the set of $k$-tuples, and the variation distance between them is at most $2 ck/n$.

/pdf/finite-exchangeable-sequences-ficmmp7lyh.pdf

Finite Exchangeable Sequences

The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group

/pdf/a-functional-calculus-for-rockland-operators-on-nilpotent-34dxwowfrp.pdf

A functional calculus for Rockland operators on nilpotent Lie groups

We consider a stochastic recursion X
 n+1 = M
 n+1
 X
 n
  + Q
 n+1, (
 $${n\in \mathbb {N}}$$
 ), where (Q
 n
 , M
 n
 ) are i.i.d. random variables such that Q
 n
 are translations, M
 n
 are similarities of the Euclidean space $${\mathbb {R}^d}$$
 and $${X_n\in \mathbb {R}^d}$$
 . In the present paper we show that if the recursion has a unique stationary measure ν with unbounded support then the weak limit of properly dilated ν exists and defines a homogeneous tail measure Λ. The structure of Λ is studied and the supports of ν and Λ are compared. In particular, we obtain a product formula for Λ.

/pdf/tail-homogeneity-of-stationary-measures-for-some-5ddh4u9t0f.pdf

Tail-homogeneity of stationary measures for some multidimensional stochastic recursions

Let G be a locally compact group. To every LI(G ) function f=f* on G corresponds a hermitian operator T I acting on L 2 (G) by convolution. In this paper we consider the relation between the spectrum off as an element of the Banach *-algebra L~(G) and the spectrum of the operator T s. To be specific, we consider the problem under what condition on G and f=f* the equality SPLI~6~ f= Sp T I (0) holds. Since the inclusion SPLI~G~ .fD Sp Ty is valid for all G and f, equality (0) can be rephrased as for a regular value 2 of Tj, one has (21 - T/)- t = 2-1 I + Tg with some

On the spectrum of convolution operators on groups with polynomial growth

/pdf/means-and-folner-condition-on-locally-compact-groups-36lcgdlgyz.pdf

Andrzej Hulanicki

Papers

The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group

A functional calculus for Rockland operators on nilpotent Lie groups

Tail-homogeneity of stationary measures for some multidimensional stochastic recursions

On the spectrum of convolution operators on groups with polynomial growth

Means and Følner condition on locally compact groups