a class of superrigid group von neumann algebras we prove that for any group g in a fairly large class of generalized wreath product groups the associated von neumann algebra lg completely remembers the group g more precisely if lg is isomorphic to the von neumann algebra l of an arbitrary countable group then must be isomorphic to g this represents the rst superrigidity result pertaining to group von neumann algebras

a characterization of the l2 range of the poisson transform related to strichartz conjecture on symmetric spaces of noncompact type abstract the main purpose of this paper is to solve strichartz conjecture concerning an image characterization of the poisson transform in the l 2 theory on symmetric spaces of noncompact type we prove that the poisson transform provides an isomorphism between the l 2 space on the boundary and a certain weighted l 2 space consisting of joint eigenfunctions on symmetric spaces of noncompact type our approach is based on the scattering theory for the schrodinger operator moreover we give a fourier restriction estimate and an asymptotic formula for the poisson transform

on the poisson transform on symmetric spaces of real rank one abstract in this paper we investigate l 2 boundedness properties of the poisson transform associated to a symmetric space of real rank one and prove a related plancherel type theorem

an efficient algorithm for the computation of the utd t transition function we present an efficient algorithm for the numerical calculation of the t canonical transition function which is encountered in the uniform geometrical theory of diffraction utd such a transition function allows the uniform ray field description of various high frequency diffraction mechanisms such as double wedge or vertex diffraction the proposed algorithm is valid for both real and imaginary arguments as required to deal with the general case in utd applications

on the operator homology of the fourier algebra and its cb multiplier completion abstract we study various operator homological properties of the fourier algebra a g of a locally compact group g establishing the converse of two results of ruan and xu 35 we show that a g is relatively operator 1 projective if and only if g is in and that a g is relatively operator 1 flat if and only if g is inner amenable we also exhibit the first known class of groups for which a g is not relatively operator c flat for any c 1 as applications of our techniques we establish a hereditary property of inner amenability answer an open question of lau and paterson 24 and answer an open question of anantharaman delaroche 1 on the equivalence of inner amenability and property w in the bimodule setting we show that relative operator 1 biflatness of a g is equivalent to the existence of a contractive approximate indicator for the diagonal g in the fourier stieltjes algebra b g g thereby establishing the converse to a result of aristov runde and spronk 3 we conjecture that relative 1 biflatness of a g is equivalent to the existence of a quasi central bounded approximate identity in l 1 g that is g is qsin and verify the conjecture in many special cases we finish with an application to the operator homology of a c b g giving examples of weakly amenable groups for which a c b g is not operator amenable

some oe and w rigidity results for actions by wreath product groups we use deformation rigidity theory in the von neumann algebra framework to study probability measure preserving actions by wreath product groups in particular we single out large families of wreath product groups satisfying various types of orbit equivalence oe rigidity for instance we show that whenever h k are icc property t groups such that h and k admit stably orbit equivalent action and such that h and k are ergodic then automatically is stably orbit equivalent to and h is stably orbit equivalent to k rigidity results for von neumann algebras arising from certain actions of such groups i e w rigidity results are also obtained

the role of restriction theorems in harmonic analysis on harmonic na groups we shall obtain inequalities for fourier transform via moduli of continuity on na groups these results in particular settle the conjecture posed in a recent paper by w o bray and m pinsky in the context of noncompact rank one symmetric spaces these problems naturally demand versions of fourier restriction theorem on these spaces which we shall prove we shall also elaborate on the connection between the restriction theorem and the kunze stein phenomena on na groups for noncompact riemannian symmetric spaces of rank one analogues of all the results follow the same way

algorithm for the computation of the generalized fresnel integral the generalized fresnel integral appears as a canonical function in the uniform ray field representation of several high frequency diffraction mechanisms such as double wedge or vertex diffraction here we propose an algorithm for its calculation which is valid both for real and imaginary arguments as required for treating the general case in the uniform geometrical theory of diffraction framework

wiener tauberian type theorems for radial sections of homogenous vector bundles on certain rank one riemannian symmetric spaces of noncompact type we will show that an uniform treatment yields wiener tauberian type results for various banach algebras and modules consisting of radial sections of some homogenous vector bundles on rank one riemannian symmetric spaces g k of noncompact type one example of such a vector bundle is the spinor bundle the algebras and modules we consider are natural generalizations of the commutative banach algebra of integrable radial functions on g k the first set of them are beurling algebras with analytic weights while the second set arises due to kunze stein phenomenon for noncompact semisimple lie groups

an endpoint estimate for the kunze stein phenomenon and related maximal operators one of the purposes of this paper is to prove that if g is a noncompact connected semisimple lie group of real rank one with flnite center then l 2 1 g l 2 1 g l 2 1 g let k be a maximal compact subgroup of g and x g k a symmetric space of real rank one we will also prove that the noncentered maximal operator m2f z sup2b 1 jbj z b jf z 0 jdz 0 is bounded from l 2 1 x t ol 2 1 x and from l p x t ol p x in the sharp range of exponents p2 2 1 the supremum in the deflnition ofm2f z i s taken over all balls containing the point z

stability for impulsive differential systems in terms of two measures stability properties of impulsive differential systems are investigated using two different measures and employing piecewise continuous lyapunov functions

h type groups and iwasawa decompositions since their introduction by a kaplan kpl some ten years ago generalised heisenberg groups also known as groups of heisenberg type or h type groups have provided a framework in which to construct interesting examples in geometry and analysis see for instance c2 kp2 kp3 kpr k2 rl r2 tl tv the iwasawa n groups associated to all the real rank one simple lie groups are h type so one has a convenient vehicle for studying these in a unified way many problems on these simple lie groups can be reduced to a problem on h type groups via the so called noncompact picture and often problems on h type groups can be solved on all the groups of the family in one fell swoop as in for example ch ck dr out of this approach to studying simple lie groups several problems arise such as why only some h type groups correspond to simple lie groups of real rank one in this paper we discuss various features of iwasawa n groups which distinguish them in the class of all h type groups we shall show that all h type groups which possess certain geometric properties clearly possessed by iwasawa n groups satisfy a lie algebraic condition implicit in the work of b kostant kt2 that we shall call the j condition we shall also use elementary clifford algebra to classify the

on quasi stability for impulsive differential systems on developpe une theorie de la stabilite relativement a une solution donnee de systemes differentiels impulsifs une telle etude conduit a un mecanisme complique et les notions de stabilite doivent etre modifiees

singular integrals on symmetric spaces ii we extend some of our earlier results on boundedness of singular integrals on symmetric spaces of real rank one to arbitrary noncompact symmetric spaces our main theorem is a transference principle for operators defined by k bi invariant kernels with certain large scale cancellation properties as an application we prove l p boundedness of operators defined by fourier multipliers that satisfy singular differential inequalities of the hormandermichlin type

characterization of eigenfunctions of the laplace beltrami operator using fourier multipliers abstract let x be a rank one riemannian symmetric space of noncompact type and be the laplace beltrami operator of x the space x can be identified with the quotient space g k where g is a connected noncompact semisimple lie group of real rank one with finite center and k is a maximal compact subgroup of g thus g acts naturally on x by left translations through this identification a function or measure on x is radial i e depends only on the distance from ek when it is invariant under the left action of k we consider right convolution operators on functions f on x defined by f f where is a radial possibly complex measure on x these operators will be called multipliers in particular is a radial average when is a radial probability measure notable examples of radial averages are ball sphere and annular averages and the heat operator in this paper we address problems of the following type fix a multiplier in particular an averaging operator suppose that f k k z is a bi infinite sequence of functions on x such that for all k z f k a f k 1 and f k m for some constants a c m 0 and a suitable norm from this hypothesis we try to infer that f 0 hence every f k is an eigenfunction of

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

on p approximation properties for p operator spaces abstract this paper has a two fold purpose let 1 p we first introduce the p operator space injective tensor product and study various properties related to this tensor product including the p operator space approximation property for p operator spaces on l p spaces we then apply these properties to the study of the pseudofunction algebra pf p g the pseudomeasure algebra pm p g and the figa talamanca herz algebra a p g of a locally compact group g we show that if g is a discrete group then most of approximation properties for the reduced group c algebra c g the group von neumann algebra vn g and the fourier algebra a g related to amenability weak amenability and approximation property of g have the natural p analogues for pf p g pm p g and a p g respectively the p completely bounded multiplier algebra m cb a p g plays an important role in this work

a general uniform double wedge diffraction coefficient the uniform theory of diffraction utd is extended to include double diffraction by an arbitrary configuration of two wedges a scalar double diffraction coefficient is defined which is uniform throughout space while reducing to the product of single diffraction coefficients outside overlapping transition regions the result is formulated in terms of double fresnel integrals which can be rapidly evaluated

on the connection between sets of operator synthesis and sets of spectral synthesis for locally compact groups we extend the results by froelich and spronk and turowska on the connection between operator synthesis and spectral synthesis for a g to second countable locally compact groups g this gives us another proof that one point subset of g is a set of spectral synthesis and that any closed subgroup is a set of local spectral synthesis furthermore we show that non triangular sets are strong operator ditkin sets and we establish a connection between operator ditkin sets and ditkin sets these results are applied to prove that any closed subgroup of g is a local ditkin set

strong rigidity of generalized bernoulli actions and computations of their symmetry groups abstract we study equivalence relations and ii 1 factors associated with quotients of generalized bernoulli actions of kazhdan groups specific families of these actions are entirely classified up to isomorphism of ii 1 factors this yields explicit computations of outer automorphism and fundamental groups in particular every finitely presented group is concretely realized as the outer automorphism group of a continuous family of non stably isomorphic ii 1 factors

strongly solid group factors which are not interpolated free group factors we give examples of non amenable infinite conjugacy classes groups with the haagerup property weakly amenable with constant cb 1 for which we show that the associated ii1 factors l are strongly solid i e the normalizer of any diffuse amenable subalgebra p subset l gamma generates an amenable von neumann algebra nevertheless for these examples of groups l is not isomorphic to any interpolated free group factor l ft for 1 t

bimodules in crossed products of von neumann algebras abstract in this paper we study bimodules over a von neumann algebra m in the context of an inclusion m m g where g is a discrete group acting on a factor m by outer automorphisms we characterize the m bimodules x m g that are closed in the bures topology in terms of the subsets of g we show that this characterization also holds for w closed bimodules when g has the approximation property ap a class of groups that includes all amenable and weakly amenable ones as an application we prove a version of mercer s extension theorem for certain w continuous surjective isometric maps on x

on the asymptotic stability by nondecrescent ljapunov function on donne des conditions suffisantes pour la stabilite asymptotique partielle de la solution nulle d un systeme non autonome en utilisant une fonction auxiliaire additionnelle au lieu de la decrescence de la fonction de ljapunov

hnn extensions of von neumann algebras abstract reduced hnn extensions of von neumann algebras as well as c algebras will be introduced and their modular theory factoriality and ultraproducts will be discussed in several concrete settings detailed analysis on them will be also carried out

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

some function spaces on symmetric spaces related to convolution operators soit g un groupe de lie semi simple connexe non compact de rang 1 une mesure positive k droite invariante a support compact soit 1 p 2 alors definit un operateur de convolution borne sur l p g si et seulement si il y a une fonction h dans l p 1 g telle que pour toute fonction c sur g k u avec u 4p 2 pp u g u g o d g g u g o h g dg la norme convolution de est equivalente a la norme l p 1 de h

perturbing families of lyapunov functions and stability in terms of two measures on considere les proprietes de stabilite non uniforme en termes de deux mesures en employant des familles perturbantes de fonctions de lyapunov

an lp fourier analysis on symmetric spaces spherical fourier transforms of lp 1 p 2 functions on a riemannian symmetric space are studied it is proved that the spherical transform of such a function extends holomorphically to the same domain of the dual space as the one where the spherical transform of a schwartz function of lp type extends holomorphically and is rapidly decreasing cf 11 and also it is proved that a hausdorff young inequality and a riemann lebesgue lemma hold in the domain

a note on double edge diffraction for parallel wedges an extended spectral theory of the diffraction approach is used in the investigation of double edge diffraction in the near field region of a parallel wedge geometry illuminated by a cylindrical wave a high frequency approximation can be formulated in terms of a canonical double stationary phase integral a uniform asymptotic reduction of the latter using the method of d s jones 1971 results in a compact representation involving the generalized fresnel integral with certain advantages in numerical applications over past representations

on paley wiener and hardy theorems for na groups let n be a h type group and let s na be an one dimensional solvable extension of n for the helgason fourier transform on s we prove the following analogue of hardy s theorem let hat f y z stand for the helgason fourier transform of f and let h denote the heat kernel associated to the laplace beltrami operator suppose a function f on s satisfies the conditions f x ch x and int limits n hat f lambda y z 2 1 z 2 gamma dy dz leq c e 2 beta lambda 2 for all x s where gamma frac k 1 2 k being the dimension of the centre of n then f 0 or f ch depending on whether or we also establish a stronger version of hardy s theorem and a paley wiener theorem these are generalisations of the corresponding results for rank one symmetric spaces of noncompact type

a bozejko picardello type inequality for finite dimensional cat 0 cube complexes abstract we prove a bozejko picardello type inequality for finite dimensional cat 0 cube complexes and as a consequence we obtain that a group acting properly on a finite dimensional cat 0 cube complex is weakly amenable with the cowling haagerup constant 1

growth properties of fourier transforms via moduli of continuity abstract we obtain new inequalities for the fourier transform both on euclidean space and on non compact rank one symmetric spaces in both cases these are expressed as a gauge on the size of the transform in terms of a suitable integral modulus of continuity of the function in all settings the results present a natural corollary a quantitative form of the riemann lebesgue lemma a prototype is given in one dimensional fourier analysis

fourier restriction theorem and characterization of weak l2 eigenfunctions of the laplace beltrami operator abstract in this paper we prove that for r 0 the poisson transform p f of f l 2 k m belongs to l 2 g k this complements an earlier result of lohoue and rychener using this we then prove an analogue of tomas stein restriction theorem for riemannian symmetric spaces of noncompact type with real rank one by using this estimate of the poisson transform we also characterize all weak l 2 eigenfunction of the laplace beltrami operator of riemannian symmetric spaces of noncompact type with real rank one and eigenvalue 2 2 for r 0

rigidity for von neumann algebras given by locally compact groups and their crossed products we prove the first rigidity and classification theorems for crossed product von neumann algebras given by actions of non discrete locally compact groups we prove that for arbitrary free probability measure preserving actions of connected simple lie groups of real rank one the crossed product has a unique cartan subalgebra up to unitary conjugacy we then deduce a w strong rigidity theorem for irreducible actions of products of such groups more generally our results hold for products of locally compact groups that are nonamenable weakly amenable and that belong to ozawa s class mathcal s

fourier and radon transform on harmonic na groups in this article we study the fourier and the horocyclic radon transform on harmonic n a groups also known as damek ricci spaces we consider the geometric fourier transform for functions on l p spaces and prove an analogue of the l 2 restriction theorem we also prove some mixed norm estimates for the fourier transform generalizing the hausdorff young and hardy littlewood paley inequalities unlike euclidean spaces the domains of the fourier transforms are various strips in the complex plane all the theorems are considered on these entire domains of the fourier transforms finally we deal with the existence of the radon transform on l p spaces and obtain its continuity property

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

stability criteria for impulsive differential equations in terms of two measures in general the stability notions of a given solution d t of an impulsive differential system cannot be transferred to the stability notions of the trivial solution by change of variables this is because of the fact that moments of impulse effects of 4 t need not be the same as that of a different solution x t and therefore demanding that the difference lx t d t 1 be small for all future time seems unnatural see 4 73 as a result the definitions of stability require suitable changes in the general situations and the corresponding theory has not yet been developed however in the case of impulsive differential systems with fixed moments of impulse effects such a problem does not arise and hence the standard definitions of stability will suffice employing suitable discontinuous lyapunov functions stability theory has recently been developed for such systems 1 2 3 51 in this paper we shall discuss stabiliy theory of impulsive differential systems with fixed moments of impulse effects in terms of two measures since such a theory enables us to unify a variety of stability results found in the literature we shall employ theory of impulsive differential inequalities as well as a direct approach to bring out the advantages of each approach

strong solidity of group factors from lattices in so n 1 and su n 1 abstract we show that the group factors l where is an icc lattice in either so n 1 or su n 1 n 2 are strongly solid in the sense of ozawa and popa 2010 13 this strengthens a result of ozawa and popa 2010 14 showing that these factors do not have cartan subalgebras

a hardy littlewood theorem for spherical fourier transforms on symmetric spaces let q 2 if f is a measurable function on rn such that f x x n 1 2q lq rn then its fourier transform f can be defined and there exists a constant aq such that the inequality f q f n 1 2q q holds this result is called the hardy littlewood theorem this paper studies what the corresponding function to x n is for the spherical fourier transform on riemannian symmetric spaces and gives an analogue of this theorem also it is shown that the spherical fourier transform of function f having the corresponding property on gk extends holomorphically to a tube domain and that an analogue of riemann lebesgue lemma holds there the following three cases are treated the riemannian symmetric spaces of the noncompact type those of the compact type and the symmetric spaces on which the cartan motion groups are acting