bias in slope estimates for the linear errors in variables model by the variance ratio method slope estimates for linear measurement error errors in variables models based on assumed knowledge of the ratio of measurement error variances are biased if the underlying linear relationship is anything other than a completely deterministic law like relationship this paper describes an eight parameter linear measurement error model of general applicability that includes an optional errors in equations term malinvaud e 1980 statistical methods of econometrics that allows the explicit characterization of the asymptotic bias of such slope estimates when the assumption of a law like relationship does not hold this bias may be large underscoring the importance of recognizing the potential influence of errors in equations in measurement error models

on scalar extensions and spectral decompositions of complex symmetric operators abstract in this paper we prove that a complex symmetric operator with property is subscalar as a corollary we get that such operators with rich spectra have nontrivial invariant subspaces we also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints

efficient estimation in the errors in variables model we consider efficient estimation of the slope in the errors in variables model with normal error when either the ratio of error variances is known and the distribution of the independent is arbitrary and unknown or the distribution of the independent variable is not gaussian or degenerate we calculate information bounds and exhibit estimates achieving these bounds using an initial minimum distance estimate and suitable estimates of the efficient score function

effective properties of linear viscoelastic heterogeneous media internal variables formulation and extension to ageing behaviours abstract the laplace carson transform classically used for homogenization of linear viscoelastic heterogeneous media yields integral formulations of effective behaviours these are far less convenient than internal variables formulations with respect to computational aspects as well as to theoretical extensions to closely related problems such as ageing viscoelasticity noticing that the collocation method is usually adopted to invert the laplace carson transforms we first remark that this approximation is equivalent to an internal variables formulation which is exact in some specific situations this result is illustrated for a two phase composite with phases obeying a compressible maxwellian behaviour next an incremental formulation allows to extend at each time step the previous general framework to ageing viscoelasticity finally with the help of a creep test of a porous viscoelastic matrix reinforced with elastic inclusions it is shown that the method yields accurate predictions comparing to reference results provided by periodic cell finite element computations

some new classes of complex symmetric operators we say that an operator t e b h is complex symmetric if there exists a conjugate linear isometric involution c so that t ct c we prove that binormal operators operators that are algebraic of degree two including all idempotents and large classes of rank one perturbations of normal operators are complex symmetric from an abstract viewpoint these results explain why the compressed shift and volterra integration operator are complex symmetric finally we attempt to describe all complex symmetric partial isometries obtaining the sharpest possible statement given only the data dim ker t dim ker t

effective behavior of linear viscoelastic composites a time integration approach a new method for determining the overall behavior of composite materials comprised of linear viscoelastic constituents is presented unlike classical methods which are based on the laplace transform the present method operates directly in the time domain upon use of an implicit time discretization scheme the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function this minimization problem is rigorously equivalent to a linear thermoelastic problem with a transformation strain which is a nonuniform field not even uniform within the phases the variational technique of ponte castaneda is used to approximate the nonuniform eigenstrains by piecewise uniform eigenstrains the latter problem is amenable to simpler calculations and analytical results for appropriate microstructures can be obtained the accuracy of the proposed scheme is assessed by comparison of the method with exact results obtained either by full finite element simulations in time domain or by available analytical results obtained by the laplace transform

growth conditions compact perturbations and operator subdecomposability with applications to generalized cesaro operators abstract we adapt recent results of albrecht and ricker to obtain conditions under which growth constraints on the left resolvent of a banach space operator are preserved under suitable perturbations as an application we establish bishop s property for certain generalized cesaro operators on the classical hardy spaces h p 1 p our methods also apply to unilateral weighted shifts whose weight sequence converges sufficiently rapidly as well as to perturbations of restrictions of a class of generalized scalar operators

points d evaluation pour les operateurs cycliques ayant la propriete de bishop β abstract let t be a linear bounded cyclic operator in a separable complex hilbert space h let b t and ba t denote respectively the set of bounded point evaluation and the set of analytic point evaluation of t we show that if t has the bishop property then ba t b t ap t where ap t is the approximate spectrum of t in the particular case when t is an operator of multiplication by z in a hardy space this was proved by trent pacific j math 80 1979 279 on the other hand using the generalized and the local spectral theory we obtain sufficient conditions on ba t under which the spectrum of t and the local spectrum of t at any y 0 in h coincide at the end results involving the spectral picture of quasi similar cyclic operators are given

operators which do not have the single valued extension property abstract in this paper we shall consider the relationships between a local version of the single valued extension property of a bounded operator t l x on a banach space x and some quantities associated with t which play an important role in fredholm theory in particular we shall consider some conditions for which t does not have the single valued extension property at a point o c

cesaro averaging operators on hardy spaces it is shown that the cesaro averaging operator 1 satisfies an inequality which immediately implies that it is bounded on certain hardy spaces including h p 0 p h p 0 p 2 for 0 the operator which is conjugate to on h 2 is also shown to be bounded on h p for 1 p p and 0

solid extensions of the cesaro operator on the hardy space h2 d abstract we introduce and study the largest banach space of analytic functions on the unit disc which is solid for the coefficient wise order and to which the classical cesaro operator c h 2 h 2 can be continuously extended while still maintaining its values in h 2 properties of this banach space h c e s 2 as well as a characterization of individual analytic functions which belong to h c e s 2 are presented in addition both the multiplier space of h c e s 2 and the spectrum of c h c e s 2 h c e s 2 are determined

on local spectral properties of complex symmetric operators abstract in this paper we study properties of complex symmetric operators in particular we prove that every complex symmetric operator having property or is decomposable moreover we show that complex symmetric operator t has dunford s property c and it satisfies weyl s theorem if and only if its adjoint does

a simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials in this paper a numerical multiscale method is proposed for computing the response of structures made of linearly non aging viscoelastic and highly heterogeneous materials in contrast with most of the approaches reported in the literature the present one operates directly in the time domain and avoids both defining macroscopic internal variables and concurrent computations at micro and macro scales the macroscopic constitutive law takes the form of a convolution integral containing an effective relaxation tensor to numerically identify this tensor a representative volume element rve for the microstructure is first chosen relaxation tests are then numerically performed on the rve correspondingly the components of the effective relaxation tensor are determined and stored for different snapshots in time at the macroscopic scale a continuous representation of the effective relaxation tensor is obtained in the time domain by interpolating the data with the help of spline functions the convolution integral characterizing the time dependent macroscopic stress strain relation is evaluated numerically arbitrary local linear viscoelastic laws and microstructure morphologies can be dealt with implicit algorithms are provided to compute the time dependent response of a structure at the macroscopic scale by the finite element method accuracy and efficiency of the proposed approach are demonstrated through 2d and 3d numerical examples and applied to estimate the creep of structures made of concrete

on complex symmetric operator matrices abstract an operator t l h is said to be complex symmetric if there exists a conjugation j on h such that t j t j in this paper we find several kinds of complex symmetric operator matrices and examine decomposability of such complex symmetric operator matrices and their applications in particular we consider the operator matrix of the form t a b 0 j a j where j is a conjugation on h we show that if a is complex symmetric then t is decomposable if and only if a is furthermore we provide some conditions so that a weyl s theorem holds for the operator matrix t

a differential homogenization method for estimating the macroscopic response and field statistics of particulate viscoelastic composites abstract this work provides an analytical method for determining the time dependent effective constitutive response of linear viscoelastic composites with particulate microstructures by means of a differential algebraic system das of equations by making use of differential equations instead of difference equations and utilizing as primary variables the variances of the field fluctuations instead of the properties of fictitious linear comparison composites the new formulation is found to be more robust and to alleviate some of the issues associated with earlier incremental approaches remarkably the new formulation can be shown to recover the exact results of the correspondence principle for isotropic incompressible composites subjected to proportional loading as well as for isotropic compressible composites subjected to purely hydrostatic loading more generally the proposed formulation is not exact but still delivers reasonably accurate estimates in most cases lastly a generalization of the das formulation is provided for nonlinear viscoelastic composites with incompressible phases and also found to be more robust than earlier approaches

on the generalized resolvent in banach spaces abstract we construct for a closed densely defined operator a on a banach space x a generalized resolvent on the domain of fredholm regularity of a meromorphic in the fredholm domain a of a

characterizations of perturbations of spectra of 2 2 upper triangular operator matrices abstract when a b h and b b k are given we denote by m c the operator acting on the infinite dimensional separable hilbert space h k of the form m c a c 0 b in this paper we first give some necessary and sufficient conditions for m c to be a left invertible operator an upper semi weyl upper semi fredholm operator for some c b k h which extend the corresponding results in cao et al 2006 4 cao and meng 2005 5 hwang and lee 2001 12 and li and du 2006 15 then we present some counter examples

wave propagation and reflection transmission in a stratified viscoelastic solid abstract the paper investigates time harmonic wave propagation in continuously stratified solids and provides the results of a reflection transmission process generated by a layer sandwiched between homogeneous half spaces the layer is continuously stratified and allows for jump discontinuities at a finite number of planes the dissipative effects are accounted for through the classical boltzmann law of viscoelasticity by using displacement and traction as convenient vector variables the governing equations are considered in a vector volterra integral equation and the solution is determined by means of a matricant next the matricant is applied to determine the reflection and transmission coefficients of a layer with a generic piecewise continuous profile of the material properties the reflection transmission process produced by an obliquely incident wave is considered for horizontally polarized waves the low frequency approximation is derived for the reflection and transmission coefficients next the high frequency approximation is investigated by a wkb like procedure which involves a complex valued frequency dependent shear modulus the displacement solution is obtained for the forward and the backward propagating waves in the layer along with the reflection and transmission coefficients

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

means of unitaries conjugations and the friedrichs operator abstract if c is a conjugation an isometric conjugate linear involution on a separable complex hilbert space h then t b h is called c symmetric if t c t c in this note we prove that each c symmetric contraction t is the mean of two c symmetric unitary operators we discuss several corollaries and an application to the friedrichs operator of a planar domain

some effects of ignoring correlated measurement errors in straight line regression and prediction instructive expressions are developed for expected values of the least squares regression coefficient sample residual mean squared error and squared sample correlation coefficient in terms of a general measurement error model allowing for correlated measurement errors these expressions are useful in assessing the importance of measurement error in given applications and can be inverted to give simple estimators of measurement error model parameters based on the usual least squares estimates they show that in certain circumstances the correlation of variables contaminated with measurement errors can be greater than that of the uncontaminated variables these simple expressions should be useful in promoting the use of measurement error models in applications an example demonstrates that even in some cases where the least squares regression coefficient is affected little by measurement error valid estimation of the standard error of prediction may require the use of a measurement error model

essential point spectra of operator matrices trough local spectral theory abstract for a b x b b y and c b y x let m c be the operator defined on x y by a c 0 b in this paper we study defect set a b m c where is the browder spectrum the essential approximate point spectrum and browder essential approximate point spectrum we then give application for weyl s and browder s theorems

complex symmetric partial isometries an operator t b h is complex symmetric if there exists a conjugate linear isometric involution c h h so that t ct c we provide a concrete description of all complex symmetric partial isometries in particular we prove that any partial isometry on a hilbert space of dimension 4 is complex symmetric

resolvant generalise et separation des points singuliers quasi fredholm c apostol et k clancey trans amer math soc 215 1976 293 300 ont introduit la notion de projection spectrale generalisee cette notion permet en particulier de separer les ensembles finis de points singuliers dans le domaine semi fredholm s a d un operateur a borne dans un hilbert h dans ce travail on se propose de generaliser ce resultat au domaine quasi fredholm de a q a et pour cela nous donnons une nouvelle representation triangulaire du type d apostol

consistent invertibility of upper triangular operator matrices abstract let h and k be separable infinite dimensional hilbert spaces and let a b h and b b k be given operators a necessary and sufficient condition is obtained for a c 0 b to be a ci operator for some respectively every c b k h furthermore some related results are obtained

resolvent estimates and decomposable extensions of generalized cesaro operators we determine the spectrum of generalized cesaro operators with essentially rational symbols acting on various spaces of analytic functions including hardy spaces weighted bergman and dirichlet spaces then we show that in all cases these operators are subdecomposable c 2009 elsevier inc all rights reserved

weyl type theorems of 2 2 upper triangular operator matrices abstract let m c a c 0 b be an upper triangular operator matrix on the hilbert space h h where h is a hilbert space in this paper necessary and sufficient conditions for m c a b are obtained where is the essential spectrum the weyl spectrum the browder spectrum the essential approximate point spectrum and the browder essential approximate point spectrum for m c we further investigate the relationship among weyl type theorems such as weyl s a weyl s browder s and a browder s theorems

self adjoint perturbations of spectra for upper triangular operator matrices abstract this paper is concerned with the self adjoint perturbations of the spectra for the upper triangular partial operator matrix with given diagonal entries a necessary and sufficient condition is given under which such operator matrix admits a weyl fredholm operator completion by choosing some bounded self adjoint operator it is shown that the self adjoint perturbation of the weyl essential spectrum can be the proper set of the general perturbation combining the spectral properties we further characterize the perturbation of the weyl essential spectrum for hamiltonian operators

invertible composition operators on hp abstract the weakly closed algebras generated by certain sets of composition operators are shown to be reflexive a structure theorem for invertible composition operators on h2 is obtained and used to show that such operators are reflexive the structure theorem shows that invertible hyperbolic composition operators are similar to cosubnormal operators built up from bilateral weighted shifts another consequence of the structure theorem is that the composition operators induced by hyperbolic disc automorphisms are universal thus the general invariant subspace problem for hilbert space operators is contained in the problem of determining the invariant subspace lattices of these operators

the semi fredholmness of 2 2 operator matrices abstract let h 1 and h 2 be separable infinite dimensional hilbert spaces and let a b h 1 b b h 2 and c b h 2 h 1 be given operators a necessary and sufficient condition is obtained for a c x b to be a right left fredholm operator for some x b h 1 h 2

on the spectrum of the cesaro operator on spaces of analytic functions this paper concerns the cesaro operator acting on various spaces of analytic functions on the unit disc the remarkable fact that this operator is subnormal when acting on the hardy space h2 has lead to extensive studies of its spectral picture on other spaces of this type we present some of the methods that have been used to obtain information about the spectrum of the cesaro operator acting on hardy and bergman spaces and give a unified approach to these problems which also yields new results in this direction in particular we prove that the cesaro operator is subdecomposable on h1 and on the standard weighted bergman spaces 0

the classes of local spectral theory in this paper we consider several classes of operators on a complex hilbert space which appear in local spectral theory a complete description in terms of properties of various parts of the spectrum is obtained for the operators in the closure and for the operators in the interior of each of these classes

estimation of parameters in linear structural relationships sensitivity to the choice of the ratio of error variances summary maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available the most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known this paper investigates the use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error variance ratio

a class of integral operators on spaces of analytic functions abstract we determine the spectrum and essential spectrum as well as resolvent estimates for a class of integral operators t f z z 1 1 z 0 z f 1 1 d acting on either the analytic besov spaces or other banach spaces of analytic functions on the unit disc including the classical hardy and weighted bergman spaces as well as certain dirichlet spaces and generalized bloch spaces our results unify and extend recent work by aleman and persson 2 the current authors 4 and albrecht and miller 1

estimation of the linear relationship between the measurements of two methods with proportional errors the linear relationship between the measurements of two methods is estimated on the basis of a weighted errors in variables regression model that takes into account a proportional relationship between standard deviations of error distributions and true variable levels weights are estimated by an interative procedure as shown by simulations the regression procedure yields practically unbiased slope estimates in realistic situations standard errors of slope and location difference estimations are derived by the jackknife principle for illustration the linear relationship is estimated between the measurements of two albumin methods with proportional errors

on the closure of the complex symmetric operators compact operators and weighted shifts abstract we study the closure cso of the set cso of all complex symmetric operators on a separable infinite dimensional complex hilbert space among other things we prove that every compact operator in cso is complex symmetric using a construction of kakutani as motivation we also describe many properties of weighted shifts in cso cso in particular we show that weighted shifts which demonstrate a type of approximate self similarity belong to cso cso as a byproduct of our treatment of weighted shifts we explain several ways in which our result on compact operators is optimal

spectral properties of cesaro like operators on weighted bergman spaces abstract we determine spectral pictures and resolvent estimates for a class of integral operators on the weighted bergman spaces l a p d m for p 1 1 and show in particular these operators are subdecomposable moreover in the case that p 2 we show that some of these operators are subnormal some are normaloid and some are subscalar

continuity of spectrum and approximate point spectrum on operator matrices abstract let x and y be given banach spaces for a b x b b y and c b y x let m c be the operator defined on x y by m c a c 0 b in this paper we give conditions for continuity of at m c through continuity of at a and b where can be equal to the spectrum or approximate point spectrum

perturbation of spectra of operator matrices and local spectral theory abstract for a l x b l y and c l y x we denote by m c the operator defined on x y by a c 0 b in this article we study defect set d a b m c for different spectra including the spectrum the essential spectrum weyl spectrum and the approximate point spectrum we then apply the obtained results to the stability of such spectra d and the classes of operators c for which stability holds of m c using local spectral theory