completely bounded multipliers over locally compact quantum groups in this paper we consider several interesting multiplier algebras associated with a locally compact quantum groupg firstly we study the completely bounded right multiplier algebra m r cb l1 g we show that m r cb l1 g is a dual banach algebra with a natural operator predual q r l1 g and the completely isometric representation of m r cb l1 g on b l2 g studied recently by junge neufang and ruan is actually weak weak continuous secondly we study the left uniformly continuous space luc g and its banach algebra dual luc g we prove that luc g is a unital c subalgebra of l1 g if the quantum groupg is semi regular we show the connection between luc g and the quan tum measure algebra m g as well as their representations on l1 g and b l2 g finally we study the right uniformly complete qotient space ucq r l1 g and its banach algebra dual ucq r l1 g for co amenable quanum groupsg we obtain the weak homeomorphic completely isometric algebra iso morphism m r cb l1 g m g and the completely isometric isomorphism ucq r l1 g luc g

on topological centre problems and sin quantum groups let a be a banach algebra with a faithful multiplication anda a be the quotient banach algebra of a with the left arens product we introduce a natural banach algebra which is a closed subspace of a a but equipped with a distinct multiplication with the help of this banach algebra new characteriza tions of the topological centre zt a a ofa a are obtained and a characterization of zt a a by lau and ulger for a having a bounded approximate identity is extended to all banach algebras the study of this banach algebra motivates us to introduce the notion of sin locally compact quantum groups and the concept of quotient strong arens irregularity we give characterizations of co amenable sin quan tum groups which are even new for locally compact groups our study shows that the sin property is intrinsically related to topological centre problems we also give characterizations of quotient strong arens irregularity for all quantum group algebras within the class of banach algebras introduced recently by the authors we characterize the unital ones generalizing the corresponding result of lau and ulger we study the interrelationships between strong arens irregularity and quotient strong arens irregularity revealing the complex nature of topological centre problems some open questions by lau and ulger on zt a a are also answered

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

decomposition of b g for any locally compact group g let a g and b g be the fourier and the fourier stieltjes algebras of g respectively b g is decomposed as a direct sum of a g and bs g where bs g is a subspace of b g consisting of all elements b e b g that satisfy the property for any e 0 and any compact subset k c g there is an f c l1 g with if llc g libil e a g is characterizecl by the following an element b e b g is in a g if and only if for any e 0 there is a compact subset k c g such that i f b i e for all f e l1 g with llfllc g 1 and supp f c k note that we do not assume the amenability of g consequently we have ili all 1 lall for all a e a g if g is noncompact we will apply this characterization of bs g to investigate the general properties of bs g and we will see that bs g is not a subalgebra of b g even for abelian locally compact groups if g is an amenable locally compact group then bs g is the subspace of b g consisting of all elements b e b g with the property that for any compact subset k c g ll bi sup llabl a e a g supp a c kc and lhall 1

ergodic sequences in the fourier stieltjes algebra and measure algebra of a locally compact group let g be a locally compact group blum and eisenberg proved that if g is abelian then a sequence of probability measures on g is strongly ergodic if and only if the sequence converges weakly to the haar measure on the bohr compactification of g in this paper we shall prove an extension of blum and eisenberg s theorem for ergodic sequences in the fourier stieltjes algebra of g we shall also give an improvement to milnes and paterson s more recent generalization of blum and eisenberg s result to general locally compact groups and we answer a question of theirs on the existence of strongly or weakly ergodic sequences of measures on g

similarity degree of fourier algebras we show that for a locally compact group g amongst a class which contains amenable and small invariant neighbourhood groups its fourier algebra a g satisfies a completely bounded version pisier s similarity property with similarity degree at most 2 specifically any completely bounded homomorphism a g b h admits an invertible s in b h for which s s 1 cb2 and s 1 s extends to a representation of the c algebra c0 g this significantly improves some results due to brannan and samei 2010 5 and brannan daws and samei 2013 4 we also note that a g has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if g is finite

spectral theory of fourier stieltjes algebras abstract in this paper we start studying spectral properties of the fourier stieltjes algebras largely following zafran s work on the algebra of measures on a locally compact group we show that for a large class of discrete groups the wiener pitt phenomenon occurs i e the spectrum of an element of the fourier stieltjes algebra is not captured by its range we also investigate the notions of absolute continuity and mutual singularity in this setting non commutativity forces upon us two distinct versions of support of an element indicating a crucial difference between this setup and the realm of abelian groups in spite of these difficulties we also show that one can introduce and use generalised characters to prove a criterion on belonging of a multiplicative linear functional to the shilov boundary of the fourier stieltjes algebra

lebesgue type decomposition of subspaces of fourier stieltjes algebras let g be a locally compact group and let a g and b g be the fourier algebra and the fourier stieltjes algebra of g respectively for any unitary representation of g let b g denote the w closed linear subspace of b g generated by all coefficient functions of and b 0 g the closure of b g a c g where a c g consists of all functions in a g with compact support in this paper we present descriptions of b 0 g and its orthogonal complement b s g in b g generalizing a recent result of t miao we show that for some classes of locally compact groups g there is a dichotomy in the sense that for arbitrary either b 0 g 0 or b 0 g a g we also characterize functions in b 0 g a c g b 0 g and study the question of whether b 0 g a g implies that weakly contains the regular representation

iterative solution of high order boundary element method for acoustic impedance boundary value problems abstract a high order boundary element method for time harmonic acoustic impedance boundary value problems is presented the method is based on the galerkin type formulation of the burton miller integral equation bmie with high order polynomial basis and testing functions this formulation has several important advantages it is free of the interior resonance problem the hypersingular integral operator of the traditional bmie formulation can be avoided it leads to faster convergence in terms of the number of unknowns than the low order methods and it shows a good performance with iterative solvers to avoid the numerical difficulties associated to the implementation of the singular surface integral equations the singularity extraction technique is applied to evaluate the integrals in the singular and near singular cases the resulting matrix equation is solved iteratively with the generalized minimal residual method gmres and a simple preconditioner based on the incomplete lu factorization is applied to expedite the convergence numerical results indicate that the bmie formulation with galerkin method and high order basis functions has good convergence properties for various geometries and boundary conditions on a wide frequency range when the gmres method is applied to solve the matrix equation iteratively this in turn indicates that the formulation is well suited for an efficient application of fast solution procedures such as the fast multipole method

a unified boundary element method for the analysis of sound and shell like structure interactions i formulation and verification a unified boundary element method bem is developed in this paper to model both the exterior acoustic field and the elastic shell like structure in a coupled analysis the conventional boundary integral equation bie for three dimensional 3d elastodynamics is applied to thin shell like structures which can have arbitrary shapes and small thicknesses the nearly singular integrals existing in the bie when applied to thin bodies are transformed to nonsingular line integrals and are evaluated accurately and efficiently for the exterior 3d acoustic domain the burton and miller composite bie formulation is employed to overcome the fictitious eigenfrequency difficulty fed and the thin shape breakdown tsb conforming c0 quadratic elements are employed in the discretization of the two sets of bies the developed bie formulations are valid for both radiation and scattering problems and for all wave numbers numerical examples using spherical and cylindrical shells including nonuniform thickness and nond

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

homomorphisms of convolution algebras abstract we establish an explicit algebraic one to one correspondence between the homomorphisms l 1 f m g of group and measure algebras over locally compact groups f and g and group homomorphisms f m where m is a semi topological subgroup of m g w we show how to extend any such homomorphism to a larger convolution algebra to obtain nicer continuity properties we augment greenleaf s characterization of the contractive subgroups of m g greenleaf 1965 17 by completing the description of their topological structures we show that not every contractive homomorphism has the dual form of cohen s factorization in the abelian case thus answering a question posed by kerlin and pepe 1975 in 27 we obtain an alternative factorization of any contractive homomorphism l 1 f m g into four homomorphisms where each of the four factors is one of the natural types appearing in the cohen factorization

solution of 3d laplace and helmholtz equations in exterior domains using hp infinite elements abstract this work is devoted to a convergence study for infinite element discretizations for laplace and helmholtz equations in exterior domains the proposed approximation applies to separable geometries only combining an hp fe discretization on the boundary of the domain with a spectral like representation resulting from the separation of variables in the radial direction the presentation includes a convergence proof for the laplace equation and a stability analysis for the variational formulation of the helmholtz equation in weighted sobolev spaces the theoretical investigations are verified and illustrated with numerical examples for the exterior spherical domain

on the density of the fourier stieltjes algebra abstract let g be a locally compact group and 1 p let a p g denote the figa talamanca herz algebra and ma p g its pointwise multiplier algebra in this paper we shall introduce two new spaces of multipliers of a p g defined as coefficient functions of certain representations of g on some interpolation couples then we shall show that in the amenable case the fourier stieltjes algebra b g is dense in ma p g and that ma p g as an ordered space is a complete invariant for g

a new form of the hypersingular boundary integral equation for 3 d acoustics and its implementation with c0 boundary elements abstract an improved weakly singular form of the hypersingular boundary integral equation hbie for 3 d acoustic wave problems is presented in this paper compared with the weakly singular form of the hbie published earlier y j liu and f j rizzo a weakly singular form of the hypersingular boundary integral equation applied to 3 d acoustic wave problems comput methods appl mech engrg 96 1992 271 287 this new form involves only tangential derivatives of the density function and thus its discretization using the boundary element method bem is easier to perform instead of using nonconforming and c1 continuous boundary elements advocated earlier c0 continuous conforming quadratic elements are employed in the discretization of this weakly singular form of the hbie some justifications on using c0 elements for hbies are provided to reflect the current views on this crucial issue for hbies it is postulated that the original c1 continuity requirement for the density function in the analytical hbie formulation can be relaxed to piecewise c1 continuity in the numerical implementation of the weakly singular forms of the hbie numerical examples of both scattering and radiation problems clearly demonstrate the accuracy and versatility of the new weakly singular form of the hbie for 3 d acoustics

module homomorphisms and multipliers on locally compact quantum groups abstract for a banach algebra a with a bounded approximate identity we investigate the a module homomorphisms of certain introverted subspaces of a and show that all a module homomorphisms of a are normal if and only if a is an ideal of a we obtain some characterizations of compactness and discreteness for a locally compact quantum group g furthermore in the co amenable case we prove that the multiplier algebra of l 1 g can be identified with m g as a consequence we prove that g is compact if and only if luc g wap g and m g z luc g which partially answer a problem raised by volker runde

an ultra weak method for acoustic fluid solid interaction we introduce the ultra weak variational formulation uwvf for fluid solid vibration problems in particular we consider the scattering of time harmonic acoustic pressure waves from solid elastic objects the problem is modeled using a coupled system of the helmholtz and navier equations the transmission conditions on the fluid solid interface are represented in an impedance type form after which we can employ the well known ultra weak formulations for the helmholtz and navier equations the uwvf approximation for both equations is computed using a superposition of propagating plane waves a condition number based criterion is used to define the plane wave basis dimension for each element as a model problem we investigate the scattering of sound from an infinite elastic cylinder immersed in a fluid a comparison of the uwvf approximation with the analytical solution shows that the method provides a means for solving wave problems on relatively coarse meshes however particular care is needed when the method is used for problems at frequencies near the resonance frequencies of the fluid solid system

asymptotic convergence in finite and boundary element methods part 2 the lbb constant for rigid and elastic scattering problems abstract the paper is a continuation of 1 and contains the evaluation of the exact lbb constant in terms of the wave number for typical problems all with spherical geometry in elastic scattering solutions to the problem of scattering of a plane wave on an elastic spherical shell for different wave numbers illustrate the dramatic effect of the magnitude of the lbb constant on the convergence

on the ideal structure of some banach algebras related to convolution operators on lp g keywords generalized fourier algebras p convolution operators maximal regular ideals minimal ideals amenability reference cahru article 2004 002doi 10 1016 j jfa 2004 02 011 record created on 2008 12 10 modified on 2016 08 08

a near subtraction result in metric spaces the locally closed graph case abstract this paper concerns a near subtraction result for multifunctions with locally closed graph in metric spaces

extension of fourier algebra homomorphisms to duals of algebras of uniformly continuous functionals for a locally compact group g let xg be one of the following introverted subspaces of vn g ucb g the c algebra of uniformly continuous functionals on a g w g the space of weakly almost periodic functionals on a g or m g the c algebra generated by the left regular representation on the measure algebra of g we discuss the extension of homomorphisms of reduced fourier stieltjes algebras on g and h to cb norm preserving weak weak continuous homomorphisms of xg into xh where xg xh is one of the pairs ucb g ucb h w g w h or m g m h when g is amenable these extensions are characterized in terms of piecewise affine maps

convergence adaptive refinement and scaling in 1d peridynamics we introduce here adaptive refinement algorithms for the non local method peridynamics which was proposed in j mech phys solids 2000 48 175 209 as a reformulation of classical elasticity for discontinuities and long range forces we use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected we discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1d in the limit of the horizon going to zero continuous micromoduli lead to optimal rates of convergence independent of the grid used while discontinuous micromoduli produce optimal rates of convergence only for uniform grids examples for static and dynamic elasticity problems in 1d are shown the relative error for the static and dynamic solutions obtained using adaptive refinement are significantly lower than those obtained using uniform refinement for the same number of nodes copyright 2008 john wiley sons ltd

module maps on duals of banach algebras and topological centre problems we study various spaces of module maps on the dual of a banach algebra a and relate them to topological centres we introduce an auxiliary topological centre zt a a for the left quotient banach algebra a a of a our results indicate that zt a a is indispensable for investigating properties of module maps over a and for understanding some asymmetry phenomena in topological centre problems as well as the interrelationships between different arens irregularity properties for the class of banach algebras of type m introduced recently by the authors we show that strong arens irregularity can be expressed both in terms of automatic normality of a module maps on a and through certain commutation relations this in particular generalizes the earlier work on group algebras by ghahramani and mcclure 1992 13 and by ghahramani and lau 1997 12 we link a module map property over a to the space wap a of weakly almost periodic functionals on a generalizing a result by lau and ulger 1996 34 for banach algebras with a bounded approximate identity we also show that for a locally compact quantum group g the quotient strong arens irregularity of l1 g can be obtained from that of m g and can be characterized via the canonical c0 g module structure on luc g

finite dimensional invariant subspace property and amenability for a class of banach algebras anthony to ming lau and yong zhangabstract motivated by a result of ky fan in 1965 we establish a charac terization of a left amenable f algebra which includes the group algebra andthe fourier algebra of a locally compact group and quantum group algebras or more generally the predual algebra of a hopf von neumann algebra interms of a nite dimensional invariant subspace property this is done by rstrevealing a xed point property for the semigroup of norm one positive lin ear functionals in the algebra our result answers an open question posted intokyo in 1993 by the rst author see 25 problem 5 we also show that theleft amenability of an ideal in an f algebra may determine the left amenabilityof the algebra

module homomorphisms and topological centres associated with weakly sequentially complete banach algebras abstract this paper is a contribution to the theory of weakly sequentially complete banach algebras a we require them to have bounded approximate identities and for the most part to be ideals in their second duals so that examples are the group algebras l 1 g for compact groups g or the fourier algebras a g for discrete amenable groups g in section 2 we present our main result that the topological centre or set of weak bicontinuous elements of a is identifiable with a as a corollary we deduce in section 3 that each left a module homomorphism from a to a a can be realized as right translation by an element of a these conclusions generalise recent advances in the subject in section 4 we take a special algebra l 1 s for a commutative discrete semigroup s and show that if its second dual has an identity then that identity must lie in l 1 s

on a conjecture by ghahramani lau and related problems concerning topological centres abstract let a be a banach algebra and consider a equipped with the first arens product we establish a general criterion which ensures that a is left strongly arens irregular i e the first topological centre of a is reduced to a itself using this criterion we prove that for a very large class of locally compact groups ghahramani lau s conjecture cf lau 94 and gha lau 95 stating the left strong arens irregularity of the measure algebra m g holds true our methods obviously yield as well the right strong arens irregularity in the situation considered furthermore the same condition used above implies that every linear left a module homomorphism on a is automatically bounded and w continuous we finally show that our criterion also yields a partial answer to a question raised by lau ulger trans amer math soc 348 3 1996 1191 on the topological centre of the algebra a a for a having a right approximate identity bounded by 1

discontinuous galerkin methods with staggered hybridization for linear elastodynamics abstract in this paper we will develop a new staggered hybridization technique for discontinuous galerkin methods to discretize linear elastodynamic equations the idea of hybridization is used extensively in many discontinuous galerkin methods but the idea of staggered hybridization is new our new approach offers several advantages namely energy conservation high order optimal convergence preservation of symmetry for the stress tensor block diagonal mass matrices as well as low dispersion error the key idea is to use two staggered hybrid variables to enforce the continuity of the velocity and the continuity of the normal component of the stress tensor on a staggered mesh we prove the stability and the convergence of the proposed scheme in both the semi discrete and the fully discrete settings numerical results confirm the optimal rate of convergence and show that the method has a superconvergent property for dispersion furthermore an application of this method to rayleigh wave propagation is presented

the drop theorem the petal theorem and ekeland s variational principle on montre que le principe variationnel d ekeland ou plus precisement une forme legerement modifiee est une consequence d un resultat geometrique connu sous le terme de theoreme de la goutte

characterisations of fourier and fourier stieltjes algebras on locally compact groups abstract motivated by the beautiful work of m a rieffel 1965 and of m e walter 1974 we obtain characterisations of the fourier algebra a g of a locally compact group g in terms of the class of f algebras i e a banach algebra a such that its dual a is a w algebra whose identity is multiplicative on a for example we show that the fourier algebras are precisely those commutative semisimple f algebras that are tauberian contain a nonzero real element and possess a dual semigroup that acts transitively on their spectrums our characterisations fall into three flavours where the first one will be the basis of the other two the first flavour also implies a simple characterisation of when the predual of a hopf von neumann algebra is the fourier algebra of a locally compact group we also obtain similar characterisations of the fourier stieltjes algebras of g en route we prove some new results on the problem of when a subalgebra of a g is the whole algebra and on representations of discrete groups

the c algebra generated by operators with compact support on a locally compact group abstract let g be a locally compact group and vn g be the von neumann algebra generated by the left regular representation of g let ucb denote the c subalgebra generated by operators in vn g with compact support when g is abelian ucb corresponds to the space of bounded uniformly continuous functions on the dual group of g in this paper we prove among other things that for a large class of locally compact groups which include the heisenberg group the ax b group and the motion group the centre of the banach algebra ucb is the fourier stieltjes algebra b g

on ideals in the bidual of the fourier algebra and related algebras let g be a compact nonmetrizable topological group whose local weight b g has uncountable cofinality let h be an amenable locally compact group a g h the fourier algebra of g h and uc2 g h the space of uniformly continuous functionals in vn g h a g h we use weak factorization of operators in the group von neumann algebra vn g h to prove that there exist at least 22b g left ideals of dimensions at least 22b g in a g h and in uc2 g h we show that every nontrivial right ideal in a g h and in uc2 g h has dimension at least 22b g

application of hp adaptive be fe methods to elastic scattering abstract the investigation focuses on the development of hp adaptive methods for simulation of acoustical scattering problems the present formulation is based on steady state linear elasticity equations coupled with the burton miller integral equation representing the behavior of a surrounding acoustical medium the highlights of the proposed approach include a mathematically consistent variational formulation of the problem an hp adaptive fe be approximation based on standard galerkin methods an element by element solver a residual based a posteriori error estimate an hp adaptive strategy particular attention is given to asymptotic convergence and to a comparison of theory and numerical simulations

error analysis in numerical solution of acoustic integral equations we present an analysis of both first and second kind integral equaitons of prototype dirichlet and neumann problems in particular we will treat boundary integral equations for acoustic scattering from bounded impenetrable objects and the corresponding potential zero frequency equations specifically we will show how residual error may be employed to obtain useful error estimates without ever knowing the exact solution

some geometric properties on the fourier and fourier stieltjes algebras of locally compact groups arens regularity and related problems let g be a locally compact topological group and a g b g be respectively the fourier and fourier stieltjes algebras of g it is one of the purposes of this paper to investigate the rnp radon nikodym property and some other geometric properties such as weak rnp the dunford pettis property and the schur property on the algebras a g and b g and to relate these properties to the properties of the multiplication operator on the group c algebra c g we also investigate the problem of arens regularity of the projective tensor products c g a when b g c g has the rnp and a is any c algebra some related problems on the measure algebra the group algebra and the algebras a p g pf p g pm p g 1 p are also discussed

adaptive hpq finite element methods for the analysis of 3d based models of complex structures part 1 hierarchical modeling and approximations this is a paper out of a series of three papers devoted to model and hpq adaptive finite element methods assigned for modeling and analysis of complex structures in this paper we focus our attention on hierarchical models and hierarchical approximations while the issues of error estimation and adaptivity control will be presented in the next papers of the series in all the papers we consider the elastic structures of complex mechanical description we apply 3d or 3d based mechanical models hierarchical modeling and hierarchical approximations within our finite element formulation in the proposed approach the mechanical model and discretization parameters such as the size h of the element and the longitudinal and transverse approximation orders p and q can vary locally i e they can be different in each finite element the a posteriori error estimation is based on the residual equilibration methods applied to the assessment of the modeling and approximation errors the error controlled adaptive procedures are derived from a four step strategy with possible iterations on h and p steps

on an h type mesh refinement strategy based on minimization of interpolation errors abstract an adaptive finite element method is proposed which involves an automatic mesh refinement in areas of the mesh where local errors are determined to exceed a pre assigned limit the estimation of local errors is based on interpolation error bounds and extraction formulas for highly accurate estimates of second derivatives applications to several two dimensional model problems are discussed the results indicate that the method can be very effective for both regular problems and problems with strong singularities

solution of elastic scattering problems in linear acoustics using h p boundary element method abstract the work is a continuation of 1 a simplified 3d model problem reduced from the general class of elastic scattering problems is analyzed focusing attention on such practical details of the 3d implementation as a triangles based h p approximation and corresponding data structure integration of singular integrals and its effect on theoretically optimal rates of convergence a posteriori error estimation and sample adaptive strategies

solution of elastic scattering problems in linear acoustics using h p boundary element methods abstract a simplified model problem reduced from the general class of elastic scattering problems is analyzed both classical helmholtz and hypersingular formulations are discussed and a general h p boundary element method based on the burton miller combination of both approaches is formulated a simple l 2 residual a posteriori error estimate is discussed as a basis of adaptive h or p refinements

the p and h p versions of the finite element method basic principles and properties in the classical form of the finite element method called the hversion piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy in this paper we discuss the fundamental theoretical ideas behind the relatively recent p version and h p version in the p version a fixed mesh is used and p is allowed to increase the h p version combines both approaches the authors describe and explain the basic properties and characteristics of these newer versions especially in areas where their behavior is significantly different from that of the h version simplified proofs of key concepts are included and computational illustrations of several results are provided a benchmark comparison between the various versions in included

weak factorizations of operators in the group von neumann algebras of certain amenable groups and applications let g be a compact group whose local weight b g has uncountable cofinality let h be an amenable locally compact group and a g h be the fourier algebra of g h we prove that the group von neumann algebra vn g h a g h has the weak uniform a g h factorization property of level b g as a corollary we show that a g h is strongly arens irregular and the topological centre of uc2 g h is equal to the fourier stieltjes algebra b g h

dual banach algebras associated to the coset space of a locally compact group abstract for h a closed group of a locally compact group g b forrest 4 has defined the fourier and fourier stieltjes algebras associated to the coset space g h a g h and b g h respectively he proved that when h is compact it is possible to extend many classical results to this new setting we continue this investigation with the study of the dual space of a g h showing that it can be identified with a particular type of w closed ideal of v n g determined by h we obtain a characterization of all w closed left ideals of v n g that are of this particular form we introduce and study the analogs of some of the classical subspaces of v n g u b c g w g and a p g in the new setting we obtain results similar to those of d e ramirez 2 e granirer 6 and a t lau 9 obtained for these spaces in the group setting

recent progress on application of hp adaptive be fe methods to elastic scattering summary several new issues related to the projcct described in references 1 3 are reported the presented problems include i sensitivity of p convergence results to geometric parametrizations and an idea of a new mesh generation for lip approximations 2 a posteriori error estimation for the coupled problem 3 a better understanding of the meaning of the asymptotic convergence a few typical numerical examples conclude the presentation

a unified approach to a posteriori error estimation using element residual methods this paper deals with the problem of obtaining numerical estimates of the accuracy of approximations to solutions of elliptic partial differential equations it is shown that by solving appropriate local residual type problems one can obtain upper bounds on the error in the energy norm moreover in the special case of adaptiveh p finite element analysis the estimator will also give a realistic estimate of the error a key feature of this is the development of a systematic approach to the determination of boundary conditions for the local problems the work extends and combines several existing methods to the case of fullh p finite element approximation on possibly irregular meshes with elements of non uniform degree as a special case the analysis proves a conjecture made by bank and weiser some a posteriori error estimators for elliptic partial differential equations math comput 44 283 301 1985