amenability properties of the centres of group algebras abstract let g be a locally compact group and zl 1 g be the centre of its group algebra we show that when g is compact zl 1 g is not amenable when g is either non abelian and connected or is a product of infinitely many finite non abelian groups we also study for some non compact groups g some conditions which imply amenability and hyper tauberian property for zl 1 g

weak amenability of banach algebras on locally compact groups abstract recent work by various authors has considered the implications of banach algebra amenability for various algebras defined over locally compact groups one of the basic tools being the fact that a continuous homomorphic image of an amenable algebra is again amenable in the present paper we look at the consequences of weak amenability here the homomorphism property fails in general however it remains true for suitable direct summands it is this technique that we make much use of here

discontinuous galerkin time discretization in elastoplasticity motivation numerical algorithms and applications discontinuous galerkin discretizations promise to become a very flexible tool in hp adaptive space time discretizations this is very attractive for moving interphase problems such as the free boundary between the elastic and plastic phase in elastoplastic time evolution the mathematical model of which involves variational inequalities and so the distributional time derivative is not obviously generalized to discontinuous test functions this paper motivates and introduces a discontinuous galerkin dg time discretization solution algorithms and examples are established which support feasibility and accuracy of the proposed schemes dg 0 and dg 1 the methods are compared with a backward euler and crank nicholson scheme 2002 published by elsevier science b v

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

adaptive numerical analysis in primal elastoplasticity with hardening the quasi static viscoplastic resp elastoplastic evolution problem with isotropic or kinematic hardening is considered with emphasis on optimal convergence and adapted mesh refining in the spatial discretization within one time step of an implicit time discretization the finite element method leads to a minimisation problem for non smooth convex functions on discrete subspaces for piecewise constant resp affine ansatz functions the stress resp displacement approximations are experimentally and theoretically shown to converge linearly an a posteriori error estimate then justifies an automatic adaptive mesh refining algorithm numerical examples support the superiority of the adapted mesh

lipschitz algebras and derivations of von neumann algebras let m be an abelian von neumann algebra andean abelian operator m bimodule then the domain of any ultraweakly closed derivation from m intoeis a lipschitz algebra conversely every lipschitz algebra can be realized as such a domain we discuss the relevance of this result to the theory of noncommutative metric spaces

amenable and weakly amenable banach algebras with compact multiplication abstract we investigate amenable and weakly amenable banach algebras with compact multiplication any amenable banach algebra with compact multiplication is biprojective as a consequence every semisimple such algebra which has the approximation property is a topological direct sum of full matrix algebras in the radical case no such structure theorem is at hand we also investigate banach algebras which have a bounded approximate identity consisting of normalized powers of an element x any such banach algebra is either unital or radical if the algebra is also generated by x it is weakly amenable we construct a radical example with compact multiplication which moreover is an integral domain this furnishes a new example of a commutative weakly amenable non amenable radical banach algebra

reliable and efficient equilibrated a posteriori finite element error control in elastoplasticity and elastoviscoplasticity with hardening this paper establishes the reliability and efficiency of equilibrated a posteriori estimates for l 2 stress error control of conforming displacement finite element approximations of incremental plasticity and viscoplasticity with hardening explicit expressions for upper bounds of the reliability constant that enters the guaranteed upper error bound illustrate its crucial dependence on the hardening material constants numerical experiments show that adaptive finite element solutions with marking strategy based on the max refinement rule and local equilibrated error estimators lead to optimal empirical convergence rates 2005 elsevier b v all rights reserved

weak amenability of fourier algebras and local synthesis of the anti diagonal abstract we show that for a connected lie group g its fourier algebra a g is weakly amenable only if g is abelian our main new idea is to show that weak amenability of a g implies that the anti diagonal g g g 1 g g is a set of local synthesis for a g g we then show that this cannot happen if g is non abelian we conclude for a locally compact group g that a g can be weakly amenable only if it contains no closed connected non abelian lie subgroups in particular for a lie group g a g is weakly amenable if and only if its connected component of the identity g e is abelian

tracking of signal subspace projectors a new subspace tracking approach that directly operates on the projection matrix onto the signal subspace instead of tracking its unitary eigenbasis is proposed therefore the difficulties arising from introducing a calculus on the manifold of projection matrices are overcome by a proper parameterization of the projectors simulation results are presented from the field of angular frequency retrieval in array signal processing

weak amenability of module extensions of banach algebras we start by discussing general necessary and sufficient conditions for a module extension banach algebra to be n weakly amenable for n 0 1 2 then we investigate various special cases all these case studies finally provide us with a way to construct an example of a weakly amenable banach algebra which is not 3 weakly amenable this answers an open question raised by h g dales f ghahramani and n gronbaek

convergence of dg 1 in elastoplastic evolution the discontinuous galerkin dg methodology provides a hierarchy of time discretization schemes for evolutionary problems such as elastoplasticity with the prandtl reus flow rule a dg time discretization has been proposed for a variational inequality in the context of rate independent inelastic material behaviour in alberty and carstensen in cmme 191 4949 4968 2002 with the help of duality in convex analysis to justify certain jump terms this paper establishes the first a priori error analysis for the dg 1 scheme with discontinuous piecewise linear polynomials in the temporal and lowest order finite elements for the spatial discretization compared to a generalized mid point rule the dg 1 formulation distributes the action of the material law in the form of the variational inequality in time and so it introduces an error in the material law this may result in a suboptimal convergence rate for the dg 1 scheme and this paper shows that the stress error in the l infty l 2 norm is merely o h k 3 2 based on a seemingly sharp error analysis the numerical investigation for a benchmark problem with known analytic solution provides empirical evidence of a higher convergence rate of the dg 1 scheme compared to dg 0

the cyclic and simplicial cohomology of l 1 mathbf n let a l 1 z be the unital semigroup algebra of n we show that the cyclic cohomology groups hc n a a vanish when n is odd and are one dimensional when n is even n 2 using connes exact sequence these results are used to show that the simplicial cohomology groups h n a a vanish for n 2 the results obtained are extended to unital algebras l 1 s for some other semigroups of r

weak and cyclic amenability for fourier algebras of connected lie groups abstract using techniques of non abelian harmonic analysis we construct an explicit non zero cyclic derivation on the fourier algebra of the real a x b group in particular this provides the first proof that this algebra is not weakly amenable using the structure theory of lie groups we deduce that the fourier algebras of connected semisimple lie groups also support non zero cyclic derivations and are likewise not weakly amenable our results complement earlier work of johnson 1994 15 plymen 2001 18 and forrest samei and spronk 2009 9 as an additional illustration of our techniques we construct an explicit non zero cyclic derivation on the fourier algebra of the reduced heisenberg group providing the first example of a connected nilpotent group whose fourier algebra is not weakly amenable

the geometry of weighted low rank approximations the low rank approximation problem is to approximate optimally with respect to some norm a matrix by one of the same dimension but smaller rank it is known that under the frobenius norm the best low rank approximation can be found by using the singular value decomposition svd although this is no longer true under weighted norms in general it is demonstrated here that the weighted low rank approximation problem can be solved by finding the subspace that minimizes a particular cost function a number of advantages of this parameterization over the traditional parameterization are elucidated finding the minimizing subspace is equivalent to minimizing a cost function on the grassmann manifold a general framework for constructing optimization algorithms on manifolds is presented and it is shown that existing algorithms in the literature are special cases of this framework within this framework two novel algorithms a steepest descent algorithm and a newton like algorithm are derived for solving the weighted low rank approximation problem they are compared with other algorithms for low rank approximation as well as with other algorithms for minimizing a cost function on a grassmann manifold

the linear model under mixed gaussian inputs designing the transfer matrix suppose a linear model y hx n where inputs x n are independent gaussian mixtures the problem is to design the transfer matrix h so as to minimize the mean square error mse when estimating x from y this problem has important applications but faces at least three hurdles firstly even for a fixed h the minimum mse mmse has no analytical form secondly the mmse is generally not convex in h thirdly derivatives of the mmse w r t h are hard to obtain this paper casts the problem as a stochastic program and invokes gradient methods the study is motivated by two applications in signal processing one concerns the choice of error reducing precoders the other deals with selection of pilot matrices for channel estimation in either setting our numerical results indicate improved estimation accuracy markedly better than those obtained by optimal design based on standard linear estimators some implications of the non convexities of the mmse are noteworthy yet to our knowledge not well known for example there are cases in which more pilot power is detrimental for channel estimation this paper explains why

pilot assisted channel estimation based on second order statistics a survey about linear channel estimation exploiting slowly varying channel properties is given for receivers with multiple antenna elements the slowly varying channel properties are described by the channel s second order statistics first a detailed comparison of classical linear pilot based channel estimators a novel matched filter and reduced rank rr approaches is made in a common framework with respect to the model they assume for the channel their performance mse and complexity the matched filter channel estimator is introduced which exploits second order statistics with quadratic order of complexity for flat correlated rayleigh fading channels an analytical performance comparison of all estimators in terms of the uncoded bit error probability is provided it is a generalization of previous results and shows that the matched filter is a low complexity alternative with good performance at an interesting signal to noise ratio snr range the effects of these approaches on linear equalization are briefly discussed in the context of direct sequence code division multiple access ds cdma where the focus is on a generalization of the rake receiver in space and time which reduces the channel rank based on its second order statistics resulting in a complexity reduction of the equalizer for this discussion a new notation for the generalized rake is presented which allows for its interpretation in the context of channel estimation and reveals alternatives for implementation we conclude that exploiting second order channel statistics results in significant performance gains and rr channel estimation should only be used together with equalization in the reduced signal subspace

error estimates for space time discretizations of a rate independent variational inequality this paper deals with error estimates for space time discretizations in the context of evolutionary variational inequalities of rate independent type after introducing a general abstract evolution problem we address a fully discrete approximation and provide a priori error estimates the application of the abstract theory to a semilinear case is detailed in particular we provide explicit space time convergence rates for classical strain gradient plasticity and the isothermal souza auricchio model for shape memory alloys

quasi static small strain plasticity in the limit of vanishing hardening and its numerical approximation the quasi static rate independent evolution of the prager ziegler type model of plasticity with hardening is shown to converge to the rate independent evolution of the prandtl reuss elastic perfectly plastic model based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coefficients converging to 0 by using the abstract method of gamma convergence for rate independent systems an unconditionally convergent numerical scheme is devised and two and three dimensional numerical experiments are presented a two sided energy inequality is a posteriori verified to document experimental convergence rates

generalized notions of amenability ii this paper continues the investigation of the first two authors begun in part i it is shown that approximate amenability and approximate contractibility are the same properties as are uniform approximate amenability and amenability bounded approximate contractibility and bounded approximate amenability are characterized by the existence of suitable operator bounded approximate identities for the diagonal ideal results are given on banach sequence algebras lipschitz algebras and beurling algebras and on the crucial role of approximate identities a new proof is given for a result due to n gronbaek on characterizing of amenability for beurling algebras

robust precoding with bayesian error modeling for limited feedback mu miso systems we consider the robust precoder design for multiuser multiple input single output mu miso systems where the channel state information csi is fed back from the single antenna receivers to the centralized transmitter equipped with multiple antennas we propose to compress the feedback data by projecting the channel estimates onto a vector basis known at the receivers and the transmitter and quantizing the resulting coefficients the channel estimator and the basis for the rank reduction are jointly optimized by minimizing the mean square error mse between the true and the rank reduced csi expressions for the conditional mean and the conditional covariance of the channel are derived which are necessary for the robust precoder design these expressions take into account the following sources of error channel estimation truncation for rank reduction quantization and feedback channel delay as an example for the robust problem formulation vector precoding vp is designed based on the expectation of the mse conditioned on the fed back csi our results show that robust precoding based on fed back csi clearly outperforms conventional precoding designs which do not take into account the errors in the csi

amenability properties of banach algebra valued continuous functions abstract let x be a compact hausdorff space and a a banach algebra we investigate amenability properties of the algebra c x a of all a valued continuous functions we show that c x a has a bounded approximate diagonal if and only if a has a bounded approximate diagonal if a has a compactly central approximate diagonal unbounded then c x a has a compactly approximate diagonal weak amenability of c x a for commutative a is also considered

the derivation problem for group algebras if g is a locally compact group then for each derivation d from l 1 g into l 1 g there is a bounded measure m g with d a a a for a l 1 g derivation problem of b e johnson

averaging techniques for reliable a posteriori fe error control in elastoplasticity with hardening averaging techniques are popular tools in adaptive finite element methods for numerical simulation in continuum mechanics since they provide efficient a posteriori error control in this paper the reliability of any averaging estimator is shown for low order finite element methods in one time step of elastoplasticity with hardening the constants and higher order terms are effected by the hardening and the smoothness of given right hand sides but are independent of the structure of a shape regular mesh since it involves a different functional analytical framework the case of perfect plasticity is excluded from this paper

optimal reduced rank estimation and filtering this paper provides a unified view of and a further insight into a class of optimal reduced rank estimators and filters an alternating power ap method for computing the optimal reduced rank estimators and filters is derived and analyzed the ap method is a generalization of the conventional power method for subspace computation which is shown to be globally and exponentially convergent under weak conditions when the rank reduction is relatively large the ap method is computationally more efficient than the conventional methods the ap method is useful for adaptive computation of the canonical components of a desired reduced rank estimate which in turn facilitates the detection of a time varying rank the study shown in this paper is particularly useful for applications that involve a large number of sources and a large number of receivers where rank reduction is either inherent in the multivariate system or required to reduce the model complexity and or the computational load

weak amenability for fourier algebras of 1 connected nilpotent lie groups a special case of a conjecture raised by forrest and runde 2005 10 asserts that the fourier algebra of every non abelian connected lie group fails to be weakly amenable this was already known to hold in the non abelian compact cases by earlier work of johnson 1994 13 and plymen unpublished note in recent work choi and ghandehari 2014 4 the authors verified this conjecture for the real ax b group and hence by structure theory for any semisimple lie group in this paper we verify the conjecture for all 1 connected non abelian nilpotent lie groups by reducing the problem to the case of the heisenberg group as in our previous paper an explicit non zero derivation is constructed on a dense subalgebra and then shown to be bounded using harmonic analysis en route we use the known fusion rules for schrodinger representations to give a concrete realization of the dual convolution for this group as a kind of twisted operator valued convolution we also give some partial results for solvable groups which give further evidence to support the general conjecture

numerical analysis of the primal problem of elastoplasticity with hardening the finite element method is a reasonable and frequently utilised tool for the spatial discretization within one time step in an elastoplastic evolution problem in this paper we analyse the finite element discretization and prove a priori and a posteriori error estimates for variational inequalities corresponding to the primal formulation of hencky plasticity the finite element method of lowest order consists in minimising a convex function on a subspace of continuous piecewise linear resp piecewise constant trial functions an a priori error estimate is established for the fully discrete method which shows linear convergence as the mesh size tends to zero provided the exact displacement field u is smooth near the boundary of the plastic domain which is unknown a priori it is most likely that u is non smooth in this situation automatic mesh refinement strategies are believed to improve the quality of the finite element approximation we suggest such an adaptive algorithm on the basis of a computable a posteriori error estimate this estimate is reliable and efficient in the sense that the quotient of the error by the estimate and its inverse are bounded from above the constants depend on the hardening involved and become larger for decreasing hardening

application of the sinc method to a dynamic elasto plastic problem this paper presents the application of sinc bases to simulate numerically the dynamic behavior of a one dimensional elastoplastic problem the numerical methods that are traditionally employed to solve elastoplastic problems include finite difference finite element and spectral methods however more recently biorthogonal wavelet bases have been used to study the dynamic response of a uniaxial elasto plastic rod giovanni f naldi karsten urban paolo venini a wavelet galerkin method for elastoplasticity problems report 181 rwth aachen igpm and math modelling and scient computing vol 10 2000 in this paper the sinc galerkin method is used to solve the straight elasto plastic rod problem due to their exponential convergence rates and their need for a relatively fewer nodal points sinc based methods can significantly outperform traditional numerical methods j lund k l bowers sinc methods for quadrature and differential equations siam philadelphia 1992 however the potential of sinc based methods for solving elastoplasticity problems has not yet been explored the aim of this paper is to demonstrate the possible application of sinc methods through the numerical investigation of the unsteady one dimensional elastic plastic rod problem

numerical analysis of time depending primal elastoplasticity with hardening the quasi static elastoplastic evolution problem with combined isotropic and kinematic hardening is considered with emphasis on optimal convergence of the lowest order scheme in each time step of a generalized midpoint scheme such as the implicit euler or the crank nicolson scheme the spatial discretization consists of minimizing a convex but nonsmooth function on a subspace of continuous piecewise linear resp piecewise constant trial functions an a priori error estimate is established for the fully discrete method which for smooth data and a smooth exact solution proves linear convergence as the mesh size tends to zero strong convergence of the time derivatives is established under mild conditions on the mesh and time step sizes numerical experiments confirm our theoretical predictions on the improved spatial convergence and indicate that the crank nicolson scheme is not always superior over the implicit euler scheme in practice

disjointness preserving operators between little lipschitz algebras abstract given a real number 0 1 and a metric space x d let lip x be the algebra of all scalar valued bounded functions f on x such that p f sup f x f y d x y x y x x y endowed with any one of the norms f max p f f or f p f f the little lipschitz algebra lip x is the closed subalgebra of lip x formed by all those functions f such that f x f y d x y 0 as d x y 0 a linear mapping t lip x lip y is called disjointness preserving if f g 0 in lip x implies t f t g 0 in lip y in this paper we study the representation and the automatic continuity of such maps t in the case in which x and y are compact we prove that t is essentially a weighted composition operator t f h f for some nonvanishing little lipschitz function h and some continuous map if in addition t is bijective we deduce that h is a nonvanishing function in lip y and is a lipschitz homeomorphism from y onto x and in particular we obtain that t is automatically continuous and t 1 is disjointness preserving moreover we show that there exists always a discontinuous disjointness preserving linear functional on lip x provided x is an infinite compact metric space

banach algebra structure and amenability of a class of matrix algebras with applications abstract we introduce a new category of banach algebras l 1 munn algebras which we use as a tool in the study of semigroup algebras then we characterize amenable l 1 munn algebras and also semisimple ones in this category applying these results to the semigroup algebras provides some characterizations of amenable semigroup algebras we also provide a counter example to a conjecture of duncan and paterson

on character amenability of banach algebras abstract we continue our work e kaniuth a t lau j pym on amenability of banach algebras math proc cambridge philos soc 144 2008 85 96 in the study of amenability of a banach algebra a defined with respect to a character of a various necessary and sufficient conditions of a global and a pointwise nature are found for a banach algebra to possess a mean of norm 1 we also completely determine the size of the set of means for a separable weakly sequentially complete banach algebra a with no mean in a itself a number of illustrative examples are discussed

approximate and pseudo amenability of various classes of banach algebras we continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with r j loy it is shown that every boundedly approximately contractible banach algebra has a bounded approximate identity and that the fourier algebra of the free group on two generators is not operator approximately amenable further examples are obtained of l1 semigroup algebras which are approximately amenable but not amenable using these we show that bounded approximate contractibility need not imply sequential approximate amenability results are also given for segal algebras on locally compact groups and algebras of p pseudo functions on discrete groups

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

a duality based path following semismooth newton method for elasto plastic contact problems a fenchel dualization scheme for the one step time discretized contact problem of quasi static elasto plasticity with combined kinematic isotropic hardening is considered the associated path is induced by a coupled moreau yosida tikhonov regularization of the dual problem the sequence of solutions to the regularized problems is shown to converge strongly to the optimal displacement stress strain triple of the original elasto plastic contact problem in the space continuous setting this property relies on the density of the intersection of certain convex sets which is shown as well it is also argued that the mappings associated with the resulting problems are newton or slantly differentiable consequently each regularized subsystem can be solved mesh independently at a local superlinear rate of convergence for efficiency purposes an inexact path following approach is proposed and a numerical validation of the theoretical results is given

analysis of transfer procedures in elastoplasticity based on the error in the constitutive equations theory and numerical illustration the aim of this work is to illustrate a methodology for the assessment of adaptive strategies for the solution of associative rate independent plasticity problems solved by employing the incremental displacement conforming finite element method this is the first step towards a more rational definition of transfer operators in terms of the ensuing error the motivating idea is the observation that change of data and or finite element mesh from one time interval to the other can be both related to a discontinuity jump of the approximate solution across the time instant t n thus reliable a posteriori estimates will have to depend not only on the time step and finite element mesh size but also on the value of the jump a new error estimate based on the error in the constitutive equations is developed which allows characterization of the discontinuity jump

coupling of fem and bem for interface problems in viscoplasticity and plasticity with hardening this paper is concerned with three dimensional interface or transmission problems in solid mechanics which consist of the quasi static equilibrium condition in a bounded lipschitz domain omega a first order evolution inclusion in omega and the homogeneous linear elasticity problem in an unbounded exterior domain omega 2 the evolution problem in omega models viscoplasticity and prandtl reus plasticity with hardening in a former paper siam j math anal 25 1994 pp 1468 1487 the author stated the interface problem as well as an equivalent formulation and proved existence and uniqueness of solutions here the numerical approximation of the solutions is considered via a symmetric coupling of the fem finite element method and bem boundary element method in space and the generalized midpoint rule in time besides existence uniqueness and uniform boundedness of the solutions of the discrete problems error estimates proving strong convergence of the numerical procedure are gi

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

on the weak amenability of a x and its relation with the approximation property abstract we investigate the weak amenability of the algebra a x of approximable operators on a banach space x and its relation with the bounded approximation property in particular it will be shown that the bounded approximation property is neither necessary nor sufficient for the weak amenability of a x

adaptive finite element methods in computational mechanics we present a general approach to adaptivity for finite element methods and give applications to linear elasticity non linear elasto plasticity and nonlinear conservation laws including numerical results

lipschitz algebras and derivations ii exterior differentiation abstract basic aspects of differential geometry can be extended to various non classical settings lipschitz manifolds rectifiable sets sub riemannian manifolds banach manifolds wiener space etc although the constructions differ in each of these cases one can define a module of measurable 1 forms and a first order exterior derivative we give a general construction which applies to any metric space equipped with a finite measure and produces the desired result in all of the above cases it agrees with cheeger s construction when the latter is defined it also applies to an important class of dirichlet spaces where however the known first order differential calculus in general differs from ours although the two are related

minimum energy band limited predictor with dynamic subspace selection for time variant flat fading channels in this paper we develop and analyze the basic methodology for minimum energy me band limited prediction of sampled time variant flat fading channels this predictor is based on a subspace spanned by time concentrated and band limited sequences the time concentration of these sequences is matched to the length of the observation interval and the band limitation is determined by the support of the doppler power spectral density of the fading process slepian showed that discrete prolate spheroidal dps sequences can be used to calculate the me band limited continuation of a finite sequence we utilize this property to perform channel prediction we generalize the concept of time concentrated and band limited sequences to a band limiting region consisting of disjoint intervals for a fading process with constant spectrum over its possibly discontiguous support we prove that the me band limited predictor is identical to a reduced rank maximum likelihood predictor which is a close approximation of a wiener predictor in current cellular communication systems the time selective fading process is highly oversampled the essential dimension of the subspace spanned by time concentrated and band limited sequences is in the order of two to five only the prediction error mainly depends on the support of the doppler spectrum we exploit this fact to propose low complexity time variant flat fading channel predictors using dynamically selected predefined subspaces the subspace selection is based on a probabilistic bound on the reconstruction error we compare the performance of the me band limited predictor with a predictor based on complex exponentials for a prediction horizon of one eights of a wavelength the numerical simulation results show that the me band limited predictor with dynamic subspace selection performs better than or similar to a predictor based on complex exponentials with perfectly known frequencies for a prediction horizons of three eights of a wavelength the performance of the me band limited predictor approaches that of a wiener predictor with perfectly known doppler bandwidth

maximum likelihood parameter and rank estimation in reduced rank multivariate linear regressions this paper considers the problem of maximum likelihood ml estimation for reduced rank linear regression equations with noise of arbitrary covariance the rank reduced matrix of regression coefficients is parameterized as the product of two full rank factor matrices this parameterization is essentially constraint free but it is not unique which renders the associated ml estimation problem rather nonstandard nevertheless the problem turns out to be tractable and the following results are obtained an explicit expression is derived for the ml estimate of the regression matrix in terms of the data covariances and their eigenelements furthermore a detailed analysis of the statistical properties of the ml parameter estimate is performed additionally a generalized likelihood ratio test glrt is proposed for estimating the rank of the regression matrix the paper also presents the results of some simulation exercises which lend empirical support to the theoretical findings

stochastic mv pure estimator robust reduced rank estimator for stochastic linear model this paper proposes a novel linear estimator named stochastic mv pure estimator developed for the stochastic linear model and designed to provide improved performance over the linear minimum mean square error mmse wiener estimator in cases prevailing in practical real world settings where at least some of the second order statistics of the random vectors under consideration are only imperfectly known the proposed estimator shares its main mathematical idea and terminology with the recently introduced minimum variance pseudo unbiased reduced rank estimator mv pure developed for the linear regression model the proposed stochastic mv pure estimator minimizes the mean square error mse of its estimates subject to rank constraint and inducing minimum distortion to the target random vector therefore the stochastic mv pure combines the techniques of the reduced rank wiener filter named in this paper rr mmse and the distortionless constrained estimator named in this paper c mmse in order to achieve greater robustness against noise or model errors than rr mmse and c mmse furthermore to ensure that the stochastic mv pure estimator combines the reduced rank and minimum distortion approaches in the mse optimal way we propose a rank selection criterion which minimizes the mse of the estimates obtained by the stochastic mv pure as a numerical example we employ the stochastic mv pure rr mmse c mmse and mmse estimators as linear receivers in a mimo wireless communication system this example is chosen as a typical signal processing scenario where the statistical information on the data on which the estimates are built is only imperfectly known we verify that the stochastic mv pure achieves the lowest mse and symbol error rate ser in such settings by employing the proposed rank selection criterion

weak amenability and 2 weak amenability of beurling algebras abstract let l 1 g be a beurling algebra on a locally compact abelian group g we look for general conditions on the weight which allows the vanishing of continuous derivations of l 1 g this leads us to introducing vector valued beurling algebras and considering the translation of operators on them this is then used to connect the augmentation ideal to the behavior of the derivation space we apply these results to give examples of various classes of beurling algebras which are weakly amenable 2 weakly amenable or fail to be even 2 weakly amenable

linear transmit processing in mimo communications systems we examine and compare the different types of linear transmit processing for multiple input multiple output systems where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters we can identify three filter types similar to receive processing the transmit matched filter the transmit zero forcing filter and the transmit wiener filter we show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power moreover the transmit wiener filter has similar convergence properties as the receive wiener filter i e it converges to the matched filter and the zero forcing filter for low and high signal to noise ratio respectively we give closed form solutions for all transmit filters and present the fundamental result that their mean square errors are equal to the errors of the respective receive filters if the information symbols and the additive noise are uncorrelated however our simulations reveal that the bit error ratio results of the transmit filters differ from the results for the respective receive filters

amenability and weak amenability of the fourier algebra let g be a locally compact group we show that its fourier algebra a g is amenable if and only if g has an abelian subgroup of finite index and that its fourier stieltjes algebra b g is amenable if and only if g has a compact abelian subgroup of finite index we then show that a g is weakly amenable if the component of the identity of g is abelian and we prove some partial results towards the converse

weak amenability of triangular banach algebras let a and b be unital banach algebras and let m be a banach a b module then t a m 0 b becomes a triangular banach algebra when equipped with the banach space norm a m 0 b a a m m b b a banach algebra t is said to be n weakly amenable if all derivations from t into its n th dual space t n are inner in this paper we investigate arens regularity and n weak amenability of a triangular banach algebra t in relation to that of the algebras a b and their action on the module m

discontinuous maps from lipschitz algebras for an infinite compact metric space x d 0 1 andf c x letp f sup f t f s d t s t s x t s the set lip x d f c x p f