fourth order canonical forms of singular self adjoint boundary conditions abstract canonical forms of self adjoint boundary conditions are well known in the second order sturm liouville case for both regular and singular problems these are critical for the theoretical investigation of the eigenvalues as well as their numerical computation recently canonical forms have been found for fourth order regular problems these are much more complicated than the second order ones here we find canonical forms for fourth order singular problems with one or both endpoints of the domain interval singular and with arbitrary deficiency index d in the regular fourth order case d 4 in the singular case d can assume any value between 0 and 4 and moreover depends on the nature of the singularities at the two endpoints these different values of d and their dependence on the endpoints introduces serious additional complications

symplectic geometry and dissipative differential operators abstract everitt and markus characterized the domains of self adjoint differential operators in terms of lagrangian subspaces of complex symplectic spaces in this paper we define dissipative and strictly dissipative subspaces for complex symplectic spaces and characterize the domains of dissipative and strictly dissipative differential operators in terms of these subspaces

symmetric positive solutions to singular system with multi point coupled boundary conditions in this paper we study the existence and multiplicity of symmetric positive solutions for a nonlinear system with multi point coupled boundary conditions the arguments are based upon a specially constructed cone and the fixed point index theorem in cones an example is then given to demonstrate the applicability of our results

matrix representations of fourth order boundary value problems with periodic boundary conditions we show that a class of regular self adjoint fourth order boundary value problems bvps is equivalent to a certain class of matrix problems conversely for any given matrix problem in this class there exist fourth order self adjoint bvps which are equivalent to the given matrix problem equivalent here means that they have exactly the same eigenvalues such an equivalence is considered with the special coupled boundary conditions i e periodic boundary conditions

fourth order boundary value problems with finite spectrum abstract for every positive integer m we construct a class of regular self adjoint and non self adjoint fourth order boundary value problems with at most 3 m 1 eigenvalues counting multiplicity

linear preserver problems a brief introduction and some special techniques abstract linear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions subsets relations etc invariant the earliest papers on linear preserver problems date back to 1897 and a great deal of effort has been devoted to the study of this type of question since then we present a brief picture of the subject aiming at giving a gentle introduction to the reader then we describe some techniques used in our recent papers on this type of problem

cross sectional dependence robust block bootstrap panel unit root tests in this paper we consider the issue of unit root testing in cross sectionally dependent panels we consider panels that may be characterized by various forms of cross sectional dependence including but not exclusive to the popular common factor framework we consider block bootstrap versions of the group mean im et al 2003 and the pooled levin et al 2002 unit root coefficient df tests for panel data originally proposed for a setting of no cross sectional dependence beyond a common time effect the tests suited for testing for unit roots in the observed data can be easily implemented as no specification or estimation of the dependence structure is required asymptotic properties of the tests are derived for t going to infinity and n finite asymptotic validity of the bootstrap tests is established in very general settings including the presence of common factors and cointegration across units properties under the alternative hypothesis are also considered in a monte carlo simulation the bootstrap tests are found to have rejection frequencies that are much closer to nominal size than the rejection frequencies for the corresponding asymptotic tests the power properties of the bootstrap tests appear to be similar to those of the asymptotic tests

self adjoint domains symplectic geometry and limit circle solutions abstract everitt and markus characterized the domains of self adjoint operator realizations of very general even and odd order symmetric ordinary differential equations in terms of lagrangian subspaces of symplectic spaces recently for the even order case with real coefficients wang sun and zettl constructed limit circle lc solutions and hao wang sun and zettl characterized the self adjoint domains in terms of lc solutions these lc solutions are higher order analogues of the celebrated titchmarsh weyl limit circle solutions in the second order case this lc characterization has been used to obtain information about the discrete continuous and essential spectra of these operators in this paper we investigate the connection between these two very different kinds of characterizations and thus add the methods of symplectic geometry to the techniques available for the investigation of the spectrum of self adjoint operators

a note on unitary similarity preserving linear mappings on b h let h be an infinite dimensional complex hilbert space we give the characterization of surjective mappings on b h that preserve unitary similarity in both directions

the spectrum of differential operators and square integrable solutions abstract we give a comprehensive account of the relationship between the square integrable solutions for real values of the spectral parameter and the spectrum of self adjoint even order ordinary differential operators with real coefficients and arbitrary deficiency index d and we solve an open problem stated by weidmann in his well known 1987 monograph according to a well known result if one endpoint is regular and for some real value of the spectral parameter the number of linearly independent square integrable solutions is less than d then is in the essential spectrum of every self adjoint realization of the equation weidmann extends this result to the two singular endpoint case provided an additional condition is satisfied here we prove this result without the additional condition

self adjoint extensions for linear hamiltonian systems with two singular endpoints abstract this paper is concerned with self adjoint extensions for a linear hamiltonian system with two singular endpoints the domain of the closure of the corresponding minimal hamiltonian operator h 0 is described by properties of its elements at the endpoints of the discussed interval decompositions of the domains of the corresponding left and right maximal hamiltonian operators are provided and expressions of the defect indices of h 0 in terms of those of the left and right minimal operators are given based on them characterizations of all the self adjoint extensions for a hamiltonian system are obtained in terms of square integrable solutions as a consequence the characterizations of all the self adjoint extensions are given for systems in several special cases

characterization of domains of self adjoint ordinary differential operators article history the gkn glazman krein naimark theorem characterizes all self adjoint realizations of linear symmetric formally self adjoint ordinary differential equations in terms of maximal domain functions these functions depend on the coefficients and this dependence is implicit and complicated in the regular case an explicit characterization in terms of two point boundary conditions can be given in the singular case when the deficiency index d is maximal the gkn characterization can be made more explicit by replacing the maximal domain functions by a solution basis for any real or complex value of the spectral parameter i n the much more difficult intermediate cases not all solutions contribute to the singular self adjoint conditions in 1986 sun found a representation of the self adjoint singular conditions in terms of certain solutions for nonreal values of in this paper we give a representation in terms of certain solutions for real this leads to a classification of solutions as limit point lp or limit circle lc in analogy with the celebrated weyl classification in the second order case the lc solutions contribute to the singular boundary conditions the lp solutions do not the advantage of using real is not only because it is in general easier to find explicit solutions but more importantly it yields information about the spectrum

similarity preserving linear maps on b h we determine kernels of similarity preserving bounded linear maps on b h and give characterizations for elementary operators of length 1 to be similarity preserving

j self adjoint extensions of a class of hamiltonian differential systems abstract this paper is concerned with j self adjoint extensions for a class of hamiltonian differential systems the domains of the corresponding minimal and maximal operators are described a classification of limit types of the systems at each of endpoints is given a property of the regularity field of the corresponding minimal operator is derived and an expression of the j defect index of the minimal operator by those of the left and right minimal operators is presented based on them a characterization of all j self adjoint extensions for the hamiltonian system is obtained in terms of square integrable solutions of a certain equation which is generated by this hamiltonian system and its formal adjoint as a consequence characterizations of all j self adjoint extensions are given for the systems in some special cases in particular all j self adjoint extensions are characterized in terms of square integrable solutions of the system itself in certain special cases

continuous spectrum and square integrable solutions of differential operators with intermediate deficiency index we explore the connection between square integrable solutions for real values of the spectral parameter and the continuous spectrum of self adjoint ordinary differential operators with arbitrary deficiency index d we show that if for all in an open interval i there are d of linearly independent square integrable solutions then for every extension of dmin the point spectrum is nowhere dense in i and there is a self adjoint extension of smin which has no continuous spectrum in i this analysis is based on our construction of limit point lp and limit circle lc solutions obtained recently in an earlier paper

boundary triples and weyl m functions for powers of the jacobi differential operator abstract the abstract theory of boundary triples is applied to the classical jacobi differential operator and its powers in order to obtain the weyl m function for several self adjoint extensions with interesting boundary conditions separated periodic and those that yield the friedrichs extension these matrix valued nevanlinna herglotz m functions are to the best knowledge of the author the first explicit examples to stem from singular higher order differential equations the creation of the boundary triples involves taking pieces determined in 26 of the principal and non principal solutions of the differential equation and putting them into the sesquilinear form to yield maps from the maximal domain to the boundary space these maps act like quasi derivatives which are usually not well defined for all functions in the maximal domain of singular expressions however well defined regularizations of quasi derivatives are produced by putting the pieces of the non principal solutions through a modified gram schmidt process

the classification of self adjoint boundary conditions separated coupled and mixed there are three basic types of self adjoint regular and singular boundary conditions separated coupled and mixed for even order problems with real coefficients one regular endpoint and arbitrary deficiency index d we give a construction for each type and determine the number of possible conditions of each type under the assumption that there are d linearly independent square integrable solutions for some real value of the spectral parameter in the separated case our construction yields non real conditions for all orders greater than two it is well known that no such conditions exist in the second order case our construction gives a direct alternative to the recent construction of everitt and markus which uses the theory of symplectic spaces we believe our construction will prove useful in the spectral analysis of these operators and in obtaining canonical forms of self adjoint boundary conditions such forms are known only in the second order i e sturm liouville case even for regular problems of order four no such forms are available

nonparametric rank tests for non stationary panels we develop a set of nonparametric rank tests for non stationary panels based on multivariate variance ratios which use untruncated kernels as such the tests do not require the choice of tuning parameters associated with bandwidth or lag length and also do not require choices with respect to numbers of common factors the tests allow for unrestricted cross sectional dependence and dynamic heterogeneity among the units of the panel provided simply that a joint functional central limit theorem holds for the panel of differenced series we provide a discussion of the relationships between our setting and the settings for which first and second generation panel unit root tests are designed in monte carlo simulations we illustrate the small sample performance of our tests when they are used as panel unit root tests under the more restrictive dgps for which panel unit root tests are typically designed and for more general dgps we also compare the small sample performance of our nonparametric tests to parametric rank tests finally we provide an empirical illustration by testing for income convergence among countries

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

on the self adjoint extensions of symmetric ordinary differential operators in direct sum spaces in this paper we give the characterizations of self adjoint domains for singular symmetric operators by describing the boundary conditions of domain of conjugate differential operator with interior singular points or in direct sum spaces last we show that there exist other self adjoint extension of t0 m which cannot be expressed as the direct sum of the self adjoint extensions over the various subintervals

unit root tests in arma models with data dependent methods for the selection of the truncation lag abstract we analyze the choice of the truncation lag in the context of the said dickey test for the presence of a unit root in a general autoregressive moving average model it is shown that a deterministic relationship between the truncation lag and the sample size is dominated by data dependent rules that take sample information into account in particular we study data dependent rules that are not constrained to satisfy the lower bound condition imposed by said dickey akaike s information criterion falls into this category the analytical properties of the truncation lag selected according to a class of information criteria are compared to those based on sequential testing for the significance of coefficients on additional lags the asymptotic properties of the unit root test under various methods for selecting the truncation lag are analyzed and simulations are used to show their distinctive behavior in finite samples our results favor methods based on sequential tests over those based on informat

boundary conditions for general ordinary differential operators and their adjoints a characterisation is obtained of all the regularly solvable operators and their adjoints generated by a general differential expression in the domains of these operators are described in terms of boundary conditions involving the solutions of mu wu and the adjoint equation the results include those of sun jiong 15 concerning self adjoint realisations of a symmetric m when the minimal operator has equal deficiency indices if the deficiency indices are unequal the maximal symmetric operators are determined by the results herein another special case concerns the j self adjoint operators where j denotes complex conjugation and for this we recover the results of zai jiu shang in 16

asymptotic similarity preserving additive maps on b x abstract let x be an infinite dimensional complex banach space and denote b x the algebra of all bounded linear operators acting on x we show that an additive surjective map on b x preserves asymptotic similarity in both directions if and only if there exist a nonzero scalar c an invertible bounded linear or conjugate linear operator a and an asymptotic similarity invariant additive functional on b x such that either t cata 1 t i for all t or t cat a 1 t i for all t in the case that x has infinite multiplicity especially if x is an infinite dimensional hilbert space above asymptotic similarity invariant additive functional is always zero

eigenvalues of limit point sturm liouville problems abstract the dependence of the eigenvalues of self adjoint sturm liouville problems on the boundary conditions when each endpoint is regular or in the limit circle case is now due to some surprisingly recent results well understood here we study this dependence for singular problems with one endpoint in the limit point case

spectral theory of higher order differential operators the absolutely continuous spectrum of a very general class of differential operators of order 2n is determined for operators whose coefficients satisfy conditions that combine smoothness and decay properties the main methods are asymptotic integration and the analysis of the associated m matrix the form of the solutions precludes the absence of a singular continuous spectrum

trend function hypothesis testing in the presence of serial correlation in this paper test statistics are proposed that can be used to test hypotheses about the parameters of the deterministic trend function of a univariate time series the tests are valid in the presence of general forms of serial correlation in the errors and can be used without having to estimate the serial correlation parameters either parametrically or nonparametrically the tests are valid for i 0 and i 1 errors trend functions that are permitted include general linear polynomial trend functions that may have breaks at either known or unknown locations asymptotic distributions are derived and consistency of the tests is established the general results are applied to a model with a simple linear trend a local asymptotic analysis is used to compute asymptotic size and power of the tests for this example size is well controlled and is relatively unaffected by the variance of the initial condition asymptotic power curves are computed for the simple linear trend model and are compared to existing tests it is shown that the new tests have nontrivial asymptotic power a simulation study shows that the asymptotic approximations are adequate for sample sizes typically used in economics the tests are used to construct confidence intervals for average gnp growth rates for eight industrialized countries using post war data

similarity preserving linear maps on matrices abstract we determine all similarity preserving linear maps on the space of n x n complex matrices and all unitary equivalence preserving linear maps on the space of n x n hermitian matrices sub majorization preserving linear maps on hermitian matrices are also determined

canonical forms of self adjoint boundary conditions for differential operators of order four abstract canonical forms of regular self adjoint boundary conditions for differential operators are well known in the second order i e sturm liouville case in this paper we find canonical forms for fourth order self adjoint boundary conditions

simple robust testing of regression hypotheses in this paper we consider the problem of hypothesis testing in models with errors that have serial correlation or heteroskedasticity of unknown form this situation is often encountered in regression models applied to economic time series data it is a classic textbook result that while ordinary least squares ols estimates of regression parameters remain consistent and asymptotically normal when errors are heteroskedastic or autocorrelated provided usual regularity conditions hold and no lagged dependent variables are in the model standard tests are no longer valid if the true form of serial correlation heteroskedasticity were known then generalized least squares gls provides efficient estimates and standard inference can be conducted on the gls transformed model but in practice the form of serial correlation heteroskedasticity is often unknown and this has led to the development of techniques that permit valid asymptotic inference without having to specify a model of the serial correlation or heteroskedasticity the most common approach is to estimate the variance covariance matrix of the ols estimates nonparametrically using spectral methods heteroskedasticity and autocorrelation consistent hac estimators and construct standard tests using the asymptotic normality of the ols estimates hac estimators have been extensively analyzed in the econometrics literature and important contributions are given by andrews 1991 andrews and monahan 1992 gallant 1987 hansen 1992 newey and west 1987 robinson 1991 1998 and white 1984 among others the benefit of hac estimator tests is asymptotically valid inference that is robust to general forms of serial correlation heteroskedasticity in the errors we propose an alternative method of constructing robust test statistics we apply a nonsingular data dependent stochastic transformation to the ols estimates the asymptotic distribution of the transformed estimates does not depend on nuisance parameters then test statistics that are asymptotically invariant to nuisance parameters asymptotic pivotal statistics are constructed the resulting test statistics have nonstandard asymptotic distributions that only depend on the number of restrictions being tested and critical values are easy to simulate using standard techniques the main advantage of our approach compared to standard approaches is that estimates of the variance covariance matrix are not explicitly required to construct the tests this is potentially important for two reasons first with the exception of the estimator proposed by robinson 1998 2 consistent nonparametric estimates of variance covariance matrices in models with serial

regular approximation of linear hamiltonian operators with two singular endpoints abstract in this paper we investigate regular approximation of linear hamiltonian operators with two singular endpoints for any given singular self adjoint hamiltonian operator its spectrum can be approximated with the eigenvalues of a sequence of regular operators the inherited restriction operators are constructed by the limit circle solutions and the limit point solutions and proved to be self adjoint via the abstract operator theory we obtain the strongly resolvent convergence of the inherited regular operators and spectral inclusion of spectrum moreover for the case with both endpoints being limit circle spectral exactness of spectrum is obtained by hilbert schmidt norm convergence in the case of friedrichs extension of singular hamiltonian systems spectral exactness also holds due to variational principle of eigenvalues

properties and decompositions of domains for powers of the jacobi differential operator abstract we set out to build a framework for self adjoint extension theory for powers of the jacobi differential operator that does not make use of classical deficiency elements instead we rely on simpler functions that capture the impact of these elements on extensions but are defined by boundary asymptotics this new perspective makes calculations much more accessible and allows for a more nuanced analysis of the associated domains the maximal domain for n th composition of the jacobi operator is characterized in terms of a smoothness condition for each derivative and the endpoint behavior of functions in the underlying hilbert space can then be classified for j n 0 by 1 x j 1 x j 1 x j and 1 x j most of these behaviors can only occur when functions are in the associated minimal domain and this leads to a formulation of the defect spaces with a convenient basis self adjoint extensions including the important left definite domain are then given in terms of the new basis functions for the defect spaces using gkn theory comments are made for the laguerre operator as well

linear regression limit theory for nonstationary panel data this paper develops a regression limit theory for nonstationary panel data with large numbers of cross section n and time series t observations the limit theory allows for both sequential limits wherein t followed by n and joint limits where t n simultaneously and the relationship between these multidimensional limits is explored the panel structures considered allow for no time series cointegration heterogeneous cointegration homogeneous cointegration and near homogeneous cointegration the paper explores the existence of long run average relations between integrated panel vectors when there is no individual time series cointegration and when there is heterogeneous cointegration these relations are parameterized in terms of the matrix regression coefficient of the long run average covariance matrix in the case of homogeneous and near homogeneous cointegrating panels a panel fully modified regression estimator is developed and studied the limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population

symmetrical differential operators and their friedrichs extension abstract symmetric operator realizations of ordinary regular differential expressions are characterized explicitly by boundary conditions for any such operator which is bounded below the boundary condition determining its friedrichs extension is identified

dependence of eigenvalues of fourth order differential equations with discontinuous boundary conditions on the problem abstract fourth order boundary value problems with discontinuous boundary conditions are studied we prove that the eigenvalues depend not only continuously but smoothly on the coefficients and on the boundary conditions and find formulas for the derivatives with respect to each of these parameters

semi boundedness of ordinary differential operators abstract the boundedness from above and from below of very general symmetric quasi differential operators s is studied here we show that i if s is regular of even order and has positive leading coefficient then it is bounded below ii if the order of s which may be regular or singular is odd then s is unbounded both above and below and iii if s is of even order regular or singular but with a leading coefficient which changes sign then s is unbounded both above and below

extreme canonical correlations and high dimensional cointegration analysis abstract we prove that the extreme squared sample canonical correlations between a random walk and its own innovations almost surely converge to the upper and lower boundaries of the support of the wachter distribution when the sample size and the dimensionality go to infinity proportionally this result is used to derive previously unknown analytic expressions for the bartlett type correction coefficients for johansen s trace and maximum eigenvalue tests in a high dimensional var 1 an analysis of cointegration among a large number of log exchange rates illustrates the usefulness of our theoretical results

similarity invariant real linear subspaces and similarity preserving additive maps let h be a separable complex infinite dimensional hilbert space all similarity invariant real linear subspaces of b h the banach algebra of all bounded linear operators on h are characterized as an application all continuous additive surjective maps on b h which preserving similarity in both directions are completely classified

dependence of eigenvalues of a class of fourth order sturm liouville problems on the boundary in this paper we consider the dependence of eigenvalues of a class of fourth order sturm liouville problems on the boundary we show that the eigenvalues depend not only continuously but smoothly on boundary points and that the derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation in addition we prove that as the length of the interval shrinks to zero all higher fourth order dirichlet eigenvalues march off to plus infinity this is also true for the first i e lowest eigenvalue

the classification of self adjoint boundary conditions of differential operators with two singular endpoints abstract for general even order linear ordinary differential equations with real coefficients and endpoints which are regular or singular and for arbitrary deficiency index d the self adjoint domains are determined by d linearly independent boundary conditions these conditions are of three types separated coupled and mixed we give a construction for all conditions of each type and determine the number of conditions of each type possible for a given self adjoint domain our construction gives a direct alternative to the recent construction of everitt and markus which uses the theory of symplectic spaces we believe our construction will prove useful in the spectral analysis of these operators and in obtaining canonical forms of self adjoint boundary conditions such forms are known only in the second order i e sturm liouville case even for regular problems of order four no such forms are available in the case when all d conditions are separated this construction yields explicit non real conditions for all orders greater than two it is well known that no such conditions exist in the second order case

singularity of the n th eigenvalue of high dimensional sturm liouville problems abstract it is natural to consider continuous dependence of the n th eigenvalue on d dimensional d 2 sturm liouville problems after the results on 1 dimensional case by kong wu and zettl 14 in this paper we find all the boundary conditions such that the n th eigenvalue is not continuous and give complete characterization of asymptotic behavior of the n th eigenvalue this renders a precise description of the jump phenomena of the n th eigenvalue near such a boundary condition furthermore we divide the space of boundary conditions into 2 d 1 layers and show that the n th eigenvalue is continuously dependent on sturm liouville equations and on boundary conditions when restricted into each layer in addition we prove that the analytic and geometric multiplicities of an eigenvalue are equal finally we obtain derivative formula and positive direction of eigenvalues with respect to boundary conditions

self adjoint extensions for discrete linear hamiltonian systems abstract this paper is concerned with self adjoint extensions for a class of discrete linear hamiltonian systems by applying the generalized von neumann theory and the gkn theory for hermitian subspaces a complete characterization of all the self adjoint subspace extensions for the systems are obtained in terms of boundary conditions via linear independent square summable solutions as a consequence characterizations of all the self adjoint subspace extensions are given in the limit point and limit circle cases in addition some sufficient conditions for the corresponding minimal subspace to be an operator or a densely defined operator are given and consequently characterizations of all the self adjoint operator extensions for the system are obtained in particular even order formally self adjoint vector difference equations are discussed as a special case

the higher order differential operators in direct sum spaces w n everitt and a zettl l introduced the concept of differential operator into the direct sum space and provided an operator theoretic framework for the study of two generalized sturm liouville differential operators together m defined on an interval i and m defined on i in particular they characterized self adjoint extensions of the minimal operator in the direct sum space in terms of boundary conditions the aim of this paper is to study the same problem for the higher order differential operators in the direct sum spaces since sturm liouville differential operators always have equal deficiency indices the minimal operators in the direct sum spaces also have equal deficiency indices and self adjoint extensions but for higher order differential operators on an interval z as is well known the values of the deficiency index are very complicated e g see 7 chap 61 hence the minimal operator in the direct sum space has equal deficiency indices only when the deficiency indices of two higher order differential operators satisfy certain conditions in this paper we use cao s and sun s methods 2 31 to give conditions which characterize the domains of self adjoint extensions of minimal operators

testing for unit roots in heterogeneous panels abstract this paper proposes unit root tests for dynamic heterogeneous panels based on the mean of individual unit root statistics in particular it proposes a standardized t bar test statistic based on the augmented dickey fuller statistics averaged across the groups under a general setting this statistic is shown to converge in probability to a standard normal variate sequentially with t the time series dimension followed by n the cross sectional dimension a diagonal convergence result with t and n while n t k k being a finite non negative constant is also conjectured in the special case where errors in individual dickey fuller df regressions are serially uncorrelated a modified version of the standardized t bar statistic is shown to be distributed as standard normal as n for a fixed t so long as t 5 in the case of df regressions with intercepts and t 6 in the case of df regressions with intercepts and linear time trends an exact fixed n and t test is also developed using the simple average of the df statistics monte carlo results show that if a large enough lag order is selected for the underlying adf regressions then the small sample performances of the t bar test is reasonably satisfactory and generally better than the test proposed by levin and lin unpublished manuscript university of california san diego 1993

testing for a unit root in a random coefficient panel data model this paper proposes new unit root tests in the context of a random autoregressive coefficient panel data model in which the null of a unit root corresponds to the joint restriction that the autoregressive coefficient has unit mean and zero variance the asymptotic distributions of the test statistics are derived and simulation results are provided to suggest that they perform very well in small samples

dissipative operators symplectic geometry and limit circle solutions for a general symmetric ordinary differential expression m and a positive weight function w the authors characterized the dissipative and strictly dissipative extensions of the minimal operator generated by m in terms of subspaces of a symplectic geometry space here we characterize these subspaces in terms of lc solutions namely we characterize the boundary conditions of the dissipative and strictly dissipative extensions by lc solutions in a hilbert space

on essential spectra of singular linear hamiltonian systems abstract the paper is concerned with essential spectra of singular linear hamiltonian systems of arbitrary order with arbitrary equal defect indices several sufficient conditions for the essential spectral points are given in terms of the number of linearly independent square integrable solutions of the corresponding hamiltonian system and a sufficient and necessary condition for the essential spectral points is obtained for hamiltonian systems of even order with one singular endpoint an advantage of these results is that one can determine the essential spectral points of hamiltonian systems by the information of solutions obtained by numerous tools available in the fundamental theory of differential equations in addition two illustrative examples are provided to show how to get some information about the essential spectrum by our results

classification of sturm liouville differential equations with complex coefficients and operator realizations in this paper a new classification of sturm liouville differential equations with complex coefficients is given compared with the corresponding result of brown et al this classification reveals the great effects of rotation angle and it is independent of the rotation angles moreover the asymptotic behaviours of functions in the maximal domain are presented and j self adjoint extensions associated with the differential equations are characterized

eigenvalues of a class of regular fourth order sturm liouville problems abstract the eigenvalues of a regular fourth order sturm liouville sl problems depend not only continuously but smoothly on the problem an expression for the derivative of the eigenvalues with respect to a given parameter an endpoint a boundary condition a coefficient or the weight function are found

matrix representations of fourth order boundary value problems with finite spectrum abstract we show that a class of regular self adjoint fourth order boundary value problems is equivalent to a certain class of matrix problems equivalent here means that they have exactly the same eigenvalues such an equivalence was previously known only in the second order case

a note on similarity preserving linear maps on matrices abstract we give a simple proof of a result of hiai concerning similarity preserving linear maps on n n complex matrices as well as its extension to fields of characteristic zero

real parameter square integrable solutions and the spectrum of differential operators abstract we continue to investigate the connection between the spectrum of self adjoint ordinary differential operators with arbitrary deficiency index d and the number of linearly independent square integrable solutions for real values of the spectral parameter we show that if for all in an open interval i there are d linearly independent square integrable solutions then there is no continuous spectrum in i this for any self adjoint realization with boundary conditions which may be separated coupled or mixed the proof is based on a new characterization of self adjoint domains and on limit point lp and limit circle lc solutions established in an earlier paper

heteroskedasticity autocorrelation robust standard errors using the bartlett kernel without truncation in this paper we analyze heteroskedasticity autocorrelation hac robust tests constructed using the bartlett kernel without truncation we show that while such an hac estimator is not consistent asymptotically valid testing is still possible we show that tests using the bartlett kernel without truncation are exactly equivalent to recent hac robust tests proposed by kiefer vogelsang and bunzel 2000 econometrica 68 pp 695 714

bootstrap unit root tests in panels with cross sectional dependency we apply bootstrap methodology to unit root tests for dependent panels with n cross sectional units and t time series observations more specifically we let each panel be driven by a general linear process which may be different across cross sectional units and approximate it by a finite order autoregressive integrated process of order increasing with t as we allow the dependency among the innovations generating the individual series we construct our unit root tests from the estimation of the system of the entire n cross sectional units the limit distributions of the tests are derived by passing t to infinity with n fixed we then apply bootstrap method to the approximated autoregressions to obtain critical values for the panel unit root tests and establish the asymptotic validity of such bootstrap panel unit root tests under general conditions the proposed bootstrap tests are indeed quite general covering a wide class of panel models they in particular allow for very general dynamic structures which may vary across individual units and more importantly for the presence of arbitrary cross sectional dependency the finite sample performance of the bootstrap tests is examined via simulations and compared to that of commonly used panel unit root tests we find that our bootstrap tests perform relatively well especially when n is small

asymptotic similarity preserving linear maps on b h it is proved that a bounded linear surjective map on b h which is asymptotic similarity preserving is nonzero scalar multiple of either an automorphism or an anti automorphism

on j selfadjoint extensions of j symmetric ordinary differential operators on donne une caracterisation des conditions aux limites qui determinent le domaine d une extension j autoadjointe d un operateur differentiel j symetrique t 0 qui a une extremite singuliere

complex j symplectic geometry characterization for j symmetric extensions of j symmetric differential operators we give complex j symplectic geometry characterizations for j symmetric extensions of j symmetric ordinary differential operators

some general techniques on linear preserver problems abstract several general techniques on linear preserver problems are described the first one is based on a transfer principle in model theoretic algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0 the second one concerns the use of some simple geometric technique to reduce linear preserver problems to standard types so that known results can be applied the third one is about solving linear preserver problems on more general operator algebras by reducing the problems to idempotent preservers numerous examples will be given to demonstrate the proposed techniques