linear preservers of weak majorization on l1 i when i is an infinite set abstract the necessary and sufficient conditions that a bounded linear map on the banach space l 1 i may be considered as a linear preserver of weak majorization on l 1 i where i is an arbitrary infinite set are given also we prove that the set of all linear preservers of weak majorization is closed under the norm topology

a tower of coverings of quasi projective varieties abstract the main goal of this article is to relate asymptotic geometric properties on a tower of coverings of a non compact kahler manifold of finite volume with reasonable geometric assumptions to its universal covering examples to which our findings are applicable include moduli spaces of hyperbolic punctured riemann surfaces and hermitian locally symmetric spaces of finite volume

a new proof of the howe conjecture let j q denote the space of g invariant distributions supported on ad g9 q if g e g set ad g f z f f g zg if q is a locally constant compactly supported function on g resp g define tq q to be the linear functional on j q defined by tq o t t 0 the set q will be fixed throughout the paper so we will abbreviate tq to t the g invariance of the distributions in j q means t ad g f t f if l is a compact open subgroup of g denote as c g l the space of compactly supported functions on g which are right l invariant similary if l is an open compact lattice in g let c g l be the space of compactly supported functions on g which are l invariant in hol howe conjectured that if q is a compact subset of g resp 9 then the restriction of the distributions in j q to c b l resp c g l is finite dimensional a more common formulation of the group version of the howe conjecture replaces the space c g l with the hecke algebra 7 g l of compactly supported l biinvariant functions on g since 7 g l c c g l apriori our formulation with c g l implies the hecke algebra formulation it is a simple matter to show that in fact the two formulations are equivalent if f e c 9 l then the function f g lf kgk 1 dk belongs to the hecke algebra and the map f 1 f is a surjection the linear functional on j q induced by f is a positive multiple of the linear functional induced by f thus the two spaces of linear functionals are equal and so the two formulations are equivalent

poincare series for non riemannian locally symmetric spaces abstract we initiate the spectral analysis of pseudo riemannian locally symmetric spaces g h beyond the classical cases where h is compact automorphic forms or is trivial analysis on symmetric spaces for any non riemannian reductive symmetric space x g h on which the discrete spectrum of the laplacian is nonempty and for any discrete group of isometries whose action on x is sufficiently proper we construct l 2 eigenfunctions of the laplacian on x x for an infinite set of eigenvalues these eigenfunctions are obtained as generalized poincare series i e as projections to x of sums over the orbits of eigenfunctions of the laplacian on x we prove that the poincare series we construct still converge and define nonzero l 2 functions after any small deformation of inside g for a large class of groups thus the infinite set of eigenvalues we construct is stable under small deformations this contrasts with the classical setting where the nonzero discrete spectrum varies on the teichmuller space of a compact riemann surface we actually construct joint l 2 eigenfunctions for the whole commutative algebra of invariant differential operators on x

isotonic linear operators on the space of all convergent real sequences abstract in this work we consider a natural preorder on c the banach space of all convergent real sequences which is called convex majorization we find a large class of bounded linear operators t c c which preserve convex majorization and denote this class by i then some interesting properties of each t i are obtained

parabolic transfer for real groups this paper is the second of two articles in real harmonic analysis in the first paper a14 we established asymptotic formulas for some natural distributions on a real group in this paper we shall establish important relationships among the distributions as the group varies the group is the set of real points of a connected reductive group g over r the distributions are weighted orbital integrals jm f on g r and their invariant counterparts im f here m g is a levi subgroup of g while mg reg r is a strongly g regular conjugacy class in m r the relationships are defined by the invariant transfer of functions on g r to functions attached to endoscopic groups of g this necessitates our working with the invariant distributions im f we refer the reader to the introduction of a14 for some general remarks on these objects the distributions im f are the generic archimedean terms in the invariant trace formula we cannot review the trace formula here the reader might consult the introductions to a13 and its two predecessors for a brief summary the purpose of the paper a13 was to stabilize the invariant trace formula subject to a condition on the fundamental lemma that has been established in some special cases the stable trace formula is a milestone of sorts it is expected to lead to reciprocity laws which relate fundamental arithmetic data attached to automorphic representations on different groups the stable trace formula of a13 relies upon the results of this paper as well as a paper a16 in preparation this has been our guiding motivation the relevant identities among the nonarchimedean forms of the distributions im f were actually established in a13 they were a part of the global argument that culminated in the stable trace formula as such they are subject to the condition on the fundamental lemma mentioned above our goal here is to establish the outstanding archimedean identities we shall do so by purely local means which are independent of the fundamental lemma to simplify the introducton we assume that the derived group of g is simply connected the identities then relate the invariant distributions ong r with stable distributions on endoscopic groups g r we recall that a stable distribution on g r depends only on the average values assumed by a test function over strongly regular stable conjugacy classes in greg r which is to say intersections of g reg r

extending a characterization of majorization to infinite dimensions abstract we consider recent work linking majorization and trumping two partial orders that have proven useful with respect to the entanglement transformation problem in quantum information with general dirichlet polynomials mellin transforms and completely monotone sequences we extend a basic majorization result to the more physically realistic infinite dimensional setting through the use of generalized dirichlet series and riemann stieltjes integrals

irreducible cuspidal representations with prescribed local behavior let g be a simple algebraic group defined over the global field k in this paper we use the simple trace formula to determine the sum of the multiplicities of the irreducible representations in the cuspidal spectrum of g with specified local behavior at a finite set of places of k and unramified elsewhere this sum is expressed as the product of the values of modified artin l functions at negative integers

on distinguished square integrable representations for galois pairs and a conjecture of prasad we prove an integral formula computing multiplicities of square integrable representations relative to galois pairs over p adic fields and we apply this formula to verify two consequences of a conjecture of dipendra prasad one concerns the exact computation of the multiplicity of the steinberg representation and the other the invariance of multiplicities by transfer among inner forms

invariants nilpotent orbits and prehomogeneous vector spaces provisionally in the introduction we call such a triple g o ad g i i 0 a prehomogeneous vector space of vinberg type abbreviated pv of v type the purpose of this paper is to construct relative invariants of pv of v type in a unified way let us explain the way of construction of invariants we may assume that the original graded lie algebra g is zh graded i e g ie 2l g i we may also assume that i 2 without loss of generality cf 1 2 4 let p v be a representation of g and

active classification for pomdps a kalman like state estimator author s zois ds levorato m mitra u abstract 1991 2012 ieee the problem of state tracking with active observation control is considered for a system modeled by a discrete time finite state markov chain observed through conditionally gaussian measurement vectors the measurement model statistics are shaped by the underlying state and an exogenous control input which influence the observations quality exploiting an innovations approach an approximate minimum mean squared error mmse filter is derived to estimate the markov chain system state to optimize the control strategy the associated mean squared error is used as an optimization criterion in a partially observable markov decision process formulation a stochastic dynamic programming algorithm is proposed to solve for the optimal solution to enhance the quality of system state estimates approximate mmse smoothing estimators are also derived finally the performance of the proposed framework is illustrated on the problem of physical activity detection in wireless body sensing networks the power of the proposed framework lies within its ability to accommodate a broad spectrum of active classification applications including sensor management for object classification and tracking estimation of sparse signals and radar scheduling

an infinite dimensional schur horn theorem and majorization theory the main result of this paper is the extension of the schur horn theorem to infinite sequences for two nonincreasing nonsummable sequences and that converge to 0 there exists a positive compact operator a with eigenvalue list and diagonal sequence if and only if j 1n j j 1n j for every n if and only if q for some orthostochastic matrix q when and are summable requiring additionally equality of their infinite series obtains the same conclusion extending a theorem by arveson and kadison our proof depends on the construction and analysis of an infinite product of t transform matrices

generalized orbital integrals of some euler poincare functions of a reductive p adic group abstract schneider and stuhler have defined euler poincare functions of irreducible representations of reductive p adic groups and calculated their orbital integrals orbital integrals belong to a larger family of invariant distributions appearing in the geometric side of the arthur selberg trace formula we calculate the value of these distributions on the euler poincare functions of tempered representations using the arthur local trace formula

the dimensions of spaces of siegel cusp forms of general degree abstract in this paper we give a dimension formula for spaces of siegel cusp forms of general degree with respect to neat arithmetic subgroups the formula was conjectured before by several researchers cf 40 43 45 75 the dimensions are expressed by special values of shintani zeta functions for spaces of symmetric matrices at non positive integers this formula was given by shintani for only a small part of the geometric side of the trace formula see 64 to be precise it is the contribution of unipotent elements corresponding to the partitions 2 j 1 2 n 2 j where n denotes the degree and 0 j n hence our work is to show that all the other contributions vanish therefore one finds that shintani s formula means the dimension itself combining our formula and an explicit formula of the shintani zeta functions which was discovered by ibukiyama and saito cf 44 42 61 we can derive an explicit dimension formula for the principal congruence subgroups of level greater than two cf 43 45 in this explicit dimension formula the dimensions are described by degree n weight k level n and the bernoulli numbers b m

asymptotique des nombres de betti des varietes arithmetiques we study the question of the growth of betti numbers of certain arithmetic varieties in tower of congruence coverings in fact our results are about siegel varieties and varieties associated to orthogonal groups we explain how a theorem of waldspurger can be used to obtain lower and upper bound our results are in the direction of conjectures made by sarnak and xue

complete signal processing bases and the jacobi group the continuous windowed fourier and wavelet transforms are created from the actions of the heisenberg and affine groups respectively both wavelet and windowed fourier bases are known to be complete that is the only signal which is orthogonal to every element of each basis is the zero signal the jacobi group is a group which contains both the heisenberg and affine groups and it can also be used to produce bases for signal processing this paper investigates completeness for bases of one and two real variables which are produced by the jacobi group

discrete series characters and the lefschetz formula for hecke operators this paper consists of three independent but related parts in the rst part xx1 6 we give a combinatorial formula for the constants appearing in the numerators of characters of stable discrete series representations of real groups see x3 as well as an analogous formula for individual discrete series representations see x6 moreover we give an explicit formula theorem 5 1 for certain stable virtual characters on real groups by theorem 5 2 these include the stable discrete series characters and thus we recover the results of x3 in a more natural way in the second part x7 we use the character formula given in theorem 5 1 to rewrite the lefschetz formula of gm for the local contribution at a single xed point component to the trace of a hecke operator on weighted cohomology in the same spirit as that of arthur s lefschetz formula a in terms of stable virtual characters on real groups see theorem 7 14 b we then sum the contributions of the various xed point components and show that in the case of middle weighted cohomology the resulting global lefschetz xed point formula agrees with arthur s lefschetz formula this gives a topological proof of arthur s formula

l2 index and the selberg trace formula abstract a method is developed for computing the l 2 index of a locally symmetric elliptic differential operator d acting on a locally symmetric manifold m g k with g semisimple of real rank one and of finite co volume based on applying the selberg trace formula to the difference of the two heat kernels associated to d the applications include an extension of the osborne warner multiplicity formula to certain non integrable discrete series derived from the l 2 spinor formula and showing the existence in some cases of non invariant l 2 cohomology classes in the middle dimension via the l 2 signature formula

asymptotically optimal nonlinear mmse multiuser detection based on multivariate gaussian approximation in this paper a class of nonlinear minimum mean squared error multiuser detectors is derived based on a multivariate gaussian approximation of the multiple access interference for large systems this approach leads to expressions identical to those describing the probabilistic data association pda detector thus providing an alternative analytical justification for this structure a simplification to the pda detector based on approximating the covariance matrix of the multivariate gaussian distribution is suggested resulting in a soft interference cancellation scheme corresponding multiuser soft input soft output detectors delivering extrinsic log likelihood ratios are derived for application in iterative multiuser decoders finally a large system performance analysis is conducted for the simplified pda showing that the bit error rate ber performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector methods from statistical neurodynamics are shown to provide a closely related alternative large system prediction numerical results demonstrate that for large systems the ber is accurately predicted by the analysis and found to be close to optimal performance

majorization doubly stochastic matrices and comparison of eigenvalues abstract 1 basic properties of majorization 2 isotone maps and algebraic operations 3 double sub and superstochasticity 4 doubly stochastic matrices 5 doubly stochastic matrices with minimum permanent 6 comparison of eigenvalues 7 doubly stochastic maps

on a theorem of osborne and warner multiplicities in the cuspidal spectrum osborne and warner have given a formula for the multiplicity of an integrable discrete series representation in l2 g when g is real rank one semi simple lie group and is a discrete subgroup of co finite volume we simplify and evaluate this formula to show that for most g as above the multiplicity is the formal degree of the representation times the volume of g when it is not we give a simple interpretation of the difference

intertwining operators and residues i weighted characters operateurs d entrelacement normalisation groupes reels groupes p adiques representations standard les distributions j m la distribution j m x residus changements de contour les espaces 7b h ac g f s et 7b f ac g f s l application m

the dimension of the space of siegel eisenstein series of weight one in general it is difficult to determine the dimension of the space of siegel modular forms of low weights in particular the dimensions of the spaces of cusp forms are known in only a few cases in this paper we calculate the dimension of the space of siegel eisenstein series of weight 1 which is a certain subspace of a complement of the space of cusp forms

a new family of soft output adaptive receivers exploiting nonlinear mmse estimates for tdma based wireless links decision directed adaptive receivers suffer performance degradation on time varying and intersymbol interference impaired links because of two major problems the use of predicted channel estimates due to the unavoidable decision delay of any detector and the unreliability of hard decisions used for channel estimation and tracking it is shown here that combining a recursive nonlinear symbol estimator with a channel estimator with a low prediction order may alleviate this performance degradation in particular it is here proposed to employ the nonlinear minimum mean square error nl mmse filtered and fixed lag smoothed estimates of the transmitted symbols in place of the usual hard decisions for channel estimation and tracking it is also shown that these nl mmse estimates can be recursively computed on the basis of a linear transformation of the vector of the a posteriori probabilities apps of the states of the channel this approach allows the prediction order of the channel estimates to be limited and at the same time limits the performance degradation due to erroneous hard decisions another result presented here is that the use of nl mmse estimates in place of hard decisions is not based on mere intuition only but is a straightforward consequence of the statement of the problem of mmse channel estimation when the overly optimistic assumption of correct decisions is dropped on the basis of this novel approach a new family of soft output adaptive receivers is presented for time division multiple access based radio communications the proposed family of adaptive receivers is based on an app computer and exploits the apps for both channel estimation and detection the versatility of the apps ensures that the architecture of the proposed receiver is flexible so that several estimators and detectors can be embedded in it

smooth cuspidal automorphic forms and integrable discrete series in this paper we construct smooth cuspidal automorphic forms related to integrable discrete series of a connected semisimple lie group with finite center for classical and adelic situation as an application of the theory of schwartz spaces for automorphic forms developed by casselman in the classical situation smooth cuspidal automorphic forms are constructed via an explicit continuous map from the frechet space of smooth vectors of a banach realization inside l 1 g of an integrable discrete series into the space of smooth vectors of a strong topological dual of an appropriate schwartz space

on limit multiplicites of discrete series representations in spaces of automorphic forms of course the groups f are then arithmetic subgroups of g in this situation it seems natural to assume that as n the spectral decomposition of l2 f g will approximate that of g in particular let 3 be a discrete series representation of g if f is a subgroup of g let re f 6 be the multiplicity of 3 in the representation of g by right translations on l2 f g choose a haar measure dg on g if f is arithmetic let v f g be the finite volume of f g for the measure induced by dg let d 3 be the formal degree of 3 for the measure dg

asymptotic behavior of supercuspidal representations and sato tate equidistribution for families abstract we establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes for the tame supercuspidals constructed by j k yu we prove the limit multiplicity property with error terms thereby we obtain a sato tate equidistribution for the hecke eigenvalues of these families the main new ingredient is to show that the orbital integrals of matrix coefficients of tame supercuspidal representations with increasing formal degree on a connected reductive p adic group tend to zero uniformly for every noncentral semisimple element

convex majorization on discrete lp spaces abstract in this paper for p 1 and a nonempty set i we consider a natural preorder on l p i which is said to be convex majorization then some interesting properties of all bounded linear operators t l p i l p i preserving the convex majorization are given we also characterize these operators and assert one of the important properties of them that is the rows of matrix form of such an operator belongs to l 1 i

on the differential equations satisfied by weighted orbital integrals weighted orbital integrals are distributions on reductive groups over local fields appearing both in the local and global trace formulas there are associated invariant distributions which play the same role in the invariant trace formulas in the case of real groups the fourier transforms of these distributions satisfy a system of differential equations as a step towards determining those fourier transforms we show that this system is holonomic and has a simple singularity at infinity we deduce that any solution has a series expansion and is a linear combination of certain canonical solutions for some groups of small rank we solve the recursion formula for the coefficients explicitly

weak majorization and doubly substochastic operators on lp i abstract we extend the notion of weak majorization on the banach space l p i where i is a non empty set and p 1 using doubly substochastic operators on l p i the close relationship between weak majorization and these operators are presented among others we show that f w g and g w f iff there is a partial permutation p such that g p f using the specific type of positive increasing convex functions a necessary and sufficient condition for f w g and g w f is given

weak supermajorization and families as doubly superstochastic operators on lp i abstract we present necessary and sufficient conditions that a family a a i j i j i of real numbers may be considered as a bounded linear operator on banach spaces l 1 i and l i where i is an arbitrary non empty set moreover we get that these conditions are sufficient for a family to be a bounded linear operator on l p i for each p 1 within this class of operators the notion of doubly superstochastic operator is introduced as an extension of the doubly superstochastic matrix and some of its essentially properties are presented in the second part we extend the notion of weak supermajorization relation on the banach space l p i using doubly superstochastic operators and present close relationship between this relation and superstochastic operators as generalisation well known results in the theory of majorization among others for two functions f g l 1 i we show that relations f w s g and g w s f hold if and only if there exist a permutation p such that g p f

a stable trace formula iii proof of the main theorems this paper is the last of three articles designed to stabilize the trace formula our goal is to stabilize the global trace formula for a general connected group subject to a condition on the fundamental lemma that has been established in some special cases in the first article i we laid out the foundations of the process we also stated a series of local and global theorems which together amount to a stabilization of each of the terms in the trace formula in the second paper ii we established a key reduction in the proof of one of the global theorems in this paper we shall complete the proof of the theorems we shall combine the global reduction of ii with the expansions that were established in section 10 of i we refer the reader to the introduction of i for a general discussion of the problem of stabilization the introduction of ii contains further discussion of the trace formula with emphasis on the elliptic coefficients agll s these objects are basic ingredients of the geometric side of the trace formula

the l2 lefschetz numbers of hecke operators introduction 5 1 hecke operators and l2 cohomology 52 the spectral decomposition of cohomology 6 3 application of the trace formula 54 the functions pa t 5 5 proof of theorem 5 1 6 the main formula appendix bibliography

linear preservers of majorization on lp i abstract in this paper we use doubly stochastic operators to extend the notion of majorization on l p where i is assumed to be an infinite set and p 1 and then characterize the structure of all bounded linear maps on this space which preserve majorization we will see that the two cases p 1 and p 1 lead to different structures