commutators and related operators on harmonic bergman space of rn 1 abstract we study commutators and related operators on harmonic bergman space the l 2 r n 1 closure of the null space of laplacian by decomposing l 2 r n 1 into the sum of null spaces of powers of laplacian and using the theory of paracommutators studied in jp we characterize harmonic symbols for which the associated commutators are bounded or compact operators associated to the div curl theorem in clms in the theory of compensated compactness are also characterized

the m matrix inverse problem for singular and symmetric jacobi matrices abstract we aim here at characterizing when the moore penrose inverse of a singular and symmetric jacobi m matrix is also an m matrix this characterization involves a highly non linear system of inequalities in the off diagonal entries of the matrix we obtain all the solutions of this system for n 3 but when n 4 the system becomes much more complicated our main result establishes that for any n there exist singular symmetric and tridiagonal m matrices of order n whose moore penrose inverse is also an m matrix

on the membership of hankel operators in a class of lorentz ideals abstract recall that the lorentz ideal c p is the collection of operators a satisfying the condition a p j 1 j p 1 p s j a consider hankel operators h f h 2 s l 2 s d h 2 s where h 2 s is the hardy space on the unit sphere s in c n in this paper we characterize the membership h f c p 2 n p

interval censored data a note on the nonparametric maximum likelihood estimator of the distribution function summary gentleman geyer 1994 discuss the analysis of interval censored data and present results based on standard convex optimisation theory here this problem is viewed from the perspective of a mixing problem of indicator functions using an analogy with the problem of mixture distributions a variety of results are easily derived including a characterisation theorem for the maximum likelihood estimator and various reliably convergent algorithms software for the analysis of mixture distributions can be used to find the nonparametric estimate of the distribution function of the interval censored survival time examples are provided to demonstrate the theory

the bergman space the bloch space and commutators of multiplication operators soit d le disque unite ouvert dans le plan complexe c soit h d l ensemble des fonctions analytiques bornees sur d on caracterise les fonctions feh d telles que t f t f tft f est un operateur compact ou t f est l operateur multiplication t f l a 2 l a 2 defini par t f g fg

solving boundary value problems on networks using equilibrium measures abstract the purpose of this paper is to construct solutions of self adjoint boundary value problems on finite networks to this end we obtain explicit expressions of the green functions for all different boundary value problems the method consists of reducing each boundary value problem either to a dirichlet problem or to a poisson equation on a new network closely related with the former boundary value problem in this process we also get an explicit expression of the poisson kernel for the dirichlet problem in all cases we express the green function in terms of equilibrium measures solely which can be obtained as the unique solution of linear programming problems in particular we get analytic expressions of the green function for the following problems the poisson equation on a distance regular graph the dirichlet problem on an infinite distance regular graph and the neumann problem on a ball of an homogeneous tree

bounded functions of vanishing mean oscillation on compact metric spaces abstract a well known theorem of wolff duke math j 49 1982 321 asserts that for every f l on the unit circle t there is a non trivial q qa vmo h such that fq qc in this paper we consider the situation where t is replaced by a compact metric space x d equipped with a measure satisfying the condition b x 2 r c b x r we generalize wolff s theorem to the extent that every function in l x can be multiplied into vmo x d in a non trivial way by a function in vmo x d l x wolff s proof relies on the fact that t has a dyadic decomposition but since this is not available for x d in general our approach is completely different furthermore we show that the analyticity requirement for the function q in wolff s theorem must be dropped if t is replaced by s 2 n 1 with n 2 move precisely if n 2 then there is a g l s 2 n 1 where is the standard spherical measure on s 2 n 1 such that if q h s 2 n 1 and if q is not the constant function 0 then gq does not have vanishing mean oscillation on s 2 n 1 the particular g that we construct also serves to show that a famous factorization theorem of axler ann of math 106 1977 567 for l functions on the unit circle t cannot be generalized to s 2 n 1 when n 2 we conclude the paper with an index theorem for toeplitz operators on s 2 n 1

essential normality of polynomial generated submodules hardy space and beyond abstract recently douglas and wang proved that for each polynomial q the submodule q of the bergman module generated by q is essentially normal 11 using improved techniques we show that the hardy space analogue of this result holds and more

inversion of a tridiagonal jacobi matrix abstract a formula for the inverse of a general tridiagonal matrix is given in terms of the principal minors

boundedness and compactness of hankel operators on the sphere abstract we consider hankel operators on the hardy space of the unit sphere in c n we show that a large amount of information about the function f p f can be recovered from the hankel operator h f for example if h f is compact then the function f p f is necessarily in vmo

alternative em methods for nonparametric finite mixture models summary this research focuses on a general class of maximum likelihood problems in which it is desired to maximise a nonparametric mixture likelihood with finitely many known component densities over the set of unknown weight parameters convergence of the conventional em algorithm for this problem is extremely slow when the component densities are poorly separated and when the maximum likelihood estimator requires some of the weights to be zero as the algorithm can never reach such a boundary point alternative methods based on the principles of em are developed using a two stage approach first a new data augmentation scheme provides improved convergence rates in certain parameter directions secondly two cyclic versions of this data augmentation are created by changing the missing data formulation between the em steps these extend the acceleration directions to the whole parameter space giving another order of magnitude increase in convergence rate examples indicate that the new cyclic versions of the data augmentation schemes can converge up to 500 times faster than the conventional em algorithm for fitting nonparametric finite mixture models

operators on weighted bergman spaces 0 p leq 1 and applications we describe the boundedness of a linear operator from bp f d c analytic d 1 z 1 z f z da z 1 p for 0 p 1 under some conditions on the weight function into a general banach space x by means of the growth conditions at the boundary of certain fractional derivatives of a single x valued analytic function this in particular allows us to characterize the dual of bp for 0 p 1 and to give a formulation of generalized carleson measures in terms of the inclusion b1 l d we then apply the result to the study of multipliers hankel operators and composition operators acting on bp spaces 1991 math subject class primary 47b38 47b35 secondary 42a45

on the essential commutant of the toeplitz algebra on the bergman space let tt be the c c algebra generated by the toeplitz operators tf f l b dv tf f l b dv on the bergman space of the unit ball we show that the essential commutant of tt equals tg g vobdd k tg g vobdd k where vobddvobdd is the collection of bounded functions of vanishing oscillation on b and kk denotes the collection of compact operators on la2 b dv

mobius invariant hilbert spaces of holomorphic functions in the unit ball of ⁿ we prove that there exists a unique hilbert space of holomorphic functions in the open unit ball of c n whose semi inner product is invariant under mobius transformations

characterizations of certain classes of hankel operators on the bergman spaces of the unit disk let f be an integrable function on the unit disk the hankel operator hf is densely defined on the bergman space ap by hfg fg p fg where g is a bounded analytic function and p is the bergman projection orthogonal projection from l2 to a2 extended to l1 via its integral formula in this paper the functions f for which hf extends to a bounded operator from ap to lp are characterized 1 p also characterized are the functions f for which hf extends to a compact or schatten class operator on a2 the proofs can be extended to handle any smoothly bounded domain in c in place of the unit disk

resistance distances in extended or contracted networks abstract in this paper we introduce new effective resistances on a given network associated with a positive value and two weights on the vertex set and investigate under which conditions they determine a distance we prove that this property is closely related with superharmonicity moreover we analyze the behavior of these distances under the usual network transformations specially the so called star mesh transformation we also compute the effective resistance for an extended network that is the network obtained from the former one by joining a new vertex and then study the effect of the contraction of this new network that is we apply a star mesh transformation with center in the joined vertex

products of hankel and toeplitz operators on the bergman space we consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products tftg are bounded on the bergman space we prove results analogous to those obtained by the second author 17 for such toeplitz products on the hardy space we furthermore obtain similar results for hankel products hfh g where f and g are square integrable on the unit disk and for the mixed haplitz products hftg and tgh f where f and g are square integrable on the unit disk and g is analytic

kirchhoff indexes of a network in this work we define the effective resistance between any pair of vertices with respect to a value 0 and a weight on the vertex set this allows us to consider a generalization of the kirchhoff index of a finite network it turns out that is the lowest eigenvalue of a suitable semi definite positive schrodinger operator and is the associated eigenfunction we obtain the relation between the effective resistance and hence between the kirchhoff index with respect to and and the eigenvalues of the associated schrodinger operator however our main aim in this work is to get explicit expressions of the above parameters in terms of equilibrium measures of the network from these expressions we derive a full generalization of foster s formulae that incorporate a positive probability of remaining in each vertex in every step of a random walk finally we compute the effective resistances and the generalized kirchhoff index with respect to a and for some families of networks with symmetries specifically for weighted wagon wheels and circular ladders

bmo in the bergman metric on bounded symmetric domains for bounded symmetric domains in cn a notion of bounded mean oscillation in terms of the bergman metric is introduced it is shown that for in l2 dv is in bmo if and only if the densely defined operator m p m p pm on l2 dv is bounded here m is multiplication by and p is the bergman projection with range the bergman subspace h2 dv la2 dv of holomorphic functions in l2 dv an analogous characterization of compactness for m p is provided by functions of vanishing mean oscillation at the boundary of

inversion of jacobi s tridiagonal matrix abstract this paper gives a simple algorithm for finding the explicit inverse of a general jacobi tridiagonal matrix a few illustrations are also provided to demonstrate the applicability of our algorithm

computer assisted analysis of mixtures c a man statistical algorithms summary this paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one parameter family of densities and provides a unifying computeroriented concept for the statistical analysis of unobserved heterogeneity i e observations stemming from different subpopulations in a univariate sample the case with unknown number of population subgroups as well as the case with known number of population subgroups with emphasis on the first is considered in the computer package c a man computer assisted mixture analysis it includes an algorithmic menu with choices of the em algorithm the vertex exchange algorithm a combination of both as well as the vertex direction method to ensure reliable convergence a steplength menu is provided for the three latter methods each achieving monotonicity for the direction of choice c a man has the option to work with restricted support size that is the case when the number of components is known a priori in the latter case the em algorithm is used applications of mixture modelling in medical problems are discussed

nearly weakly orthonormal sequences singular value estimates and calderon zygmund operators abstract the direct way to estimate the singular values of a compact operator is to decompose it as a sum of orthogonal rank one pieces however such decompositions can generally not be found in practice we give a variation of the decomposition using nearly weakly orthonormal nwo sequences the nwo decomposition is easier to do in examples but is still strong enough to give good singular value estimates we illustrate this by giving sharp trace ideal estimates for the double layer potential and for the first and higher commutators of multiplication operators and calderon zygmund operators in particular nwo sequences seem well suited for dealing with operators which depend nonlinearly on their symbol we also show that the class of operators which admit nwo expansions is well behaved under composition under conjugation by weights and under conjugation by changes of variable

duality for logarithmic interpolation spaces when 0 q 1 and applications abstract we work with spaces a 0 a 1 q a which are logarithmic perturbations of the real interpolation spaces we determine the dual of a 0 a 1 q a when 0 q 1 as we show if 0 or 1 then the dual space depends on the relationship between q and a furthermore we apply the abstract results to compute the dual space of besov spaces of logarithmic smoothness and the dual space of spaces of compact operators in a hilbert space which are close to the macaev ideals

the geometry of mixture likelihoods a general theory in this paper certain fundamental properties of the maximum likelihood estimator of a mixing distribution are shown to be geometric properties of the likelihood set the existence support size likelihood equations and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull it is shown using geometric techniques that the estimator exists under quite general conditions with a support size no larger than the number of distinct observations analysis of the convex dual of the likelihood set leads to a dual maximization problem a convergent algorithm is described the defining equations for the estimator are compared with the usual parametric likelihood equations for finite mixtures sufficient conditions for uniqueness are given part ii will deal with a special theory for exponential family mixtures

hankel operators and toeplitz operators on the bergman space abstract we consider in this paper the question of when the semi commutator t fg t f t g on the bergman space with bounded harmonic symbols is compact several conditions equivalent to compactness of t fg t f t g are given as a consequence we prove a conjecture of axler that for bounded analytic functions f and g on the unit disk t fg t g t f is compact iff either f or g is constant on each gleason part p m except d

updating the inverse of a matrix the sherman morrison woodbury formulas relate the inverse of a matrix after a small rank perturbation to the inverse of the original matrix the history of these fomulas is presented and various applications to statistics networks structural analysis asymptotic analysis optimization and partial differential equations are discussed the sherman morrison woodbury formulas express the inverse of a matrix after a small rank perturbation in terms of the inverse of the original matrix this paper surveys the history of these formulas and we examine some applications where these formulas are helpful

hankel operators and the stieltjes moment problem let s be a non vanishing stieltjes moment sequence and let be a representing measure of it we denote by n the image measure in cn of n under the map t t where n is the rotation invariant probability measure on the unit sphere we show that the closure of holomorphic polynomials in l2 n is a reproducing kernel hilbert space of analytic functions and describe various spectral properties of the corresponding hankel operators with anti holomorphic symbols in particular if n 1 we prove that there are nontrivial hilbert schmidt hankel operators with anti holomorphic symbols if and only if s is exponentially bounded in this case the space of symbols of such operators is shown to be the classical dirichlet space we mention that the classical weighted bergman spaces the hardy space and fock type spaces fall in this setting

analysis of a randomized trial to prevent vertical transmission of hiv 1 abstract we analyze data from a randomized trial of breastfeeding versus formula feeding in hiv 1 infected mothers and their infants estimates of infant hiv 1 free survival and the timing of vertical transmission of hiv 1 are complicated by the fact that the infants hiv 1 status at death may be unknown the time of hiv 1 infection may be interval censored and the tests used to detect hiv 1 infection in the infants may be less than 100 sensitive or specific to address these problems we develop nonparametric and semiparametric approaches to estimating the joint distribution of hiv 1 infection time and death time the nonparametric estimator is based on a self consistency algorithm and in the current application provides a unique estimate of the hiv 1 free survival at 24 months old however the estimate of the cumulative probability of hiv 1 infection over time is nonunique to resolve the nonuniqueness of the nonparametric estimator a semiparametric approach is proposed in which the joint distributi

maximum likelihood for interval censored data consistency and computation summary standard convex optimization techniques are applied to the analysis of interval censored data these methods provide easily verifiable conditions for the self consistent estimator proposed by turnbull 1976 to be a maximum likelihood estimator and for checking whether the maximum likelihood estimate is unique a sufficient condition is given for the almost sure convergence of the maximum likelihood estimator to the true underlying distribution function

likelihood inference for mixtures geometrical and other constructions of monotone step length algorithms summary this paper considers algorithms for the maximum likelihood estimator of the mixing distribution of a family of parametric densities specific interest is devoted to the monotonicity of the step length of the solution in 2 we introduce the idea of estimating the area above the second derivative curve and in theorem 1 we relate area overestimation to the monotonicity of the associated algorithm in 3 we apply theorem 1 to the monotonicity analysis of well known algorithms as well as to the construction of a new class of monotone step length choices which is particularly simple in the mixture setting numerical comparisons and refinements in keeping the monotonic step length from becoming too conservative are given theorem 3 characterizes conditions under which the newton raphson step is monotonic and if these conditions fail to hold states that the regula falsi step is monotonic

hankel operators on the bergman space of bounded symmetric domains let q be a bounded symmetric domain in cin with normalized volume measure dv let p be the orthogonal projection from l 2 q d v onto the bergman space la q of holomorphic functions in l 2 q d v let a p be the orthogonal projection from l 2 q dv onto the closed subspace of antiholomorphic functions in l 2 2 d v the little hankel operator hf with symbol f is the operator from l2 q into l2 q d v defined by hfg p fg we characterize the boundedness compactness and membership in the schatten classes of the hankel operators hf in terms of a certain integral transform of the symbol f these characterizations are further studied in the special cases of the open unit ball and the poly disc in cn

schatten class membership of hankel operators on the unit sphere abstract let h 2 s be the hardy space on the unit sphere s in c n n 2 consider the hankel operator h f 1 p m f h 2 s where the symbol function f is allowed to be arbitrary in l 2 s d we show that for p 2 n h f is in the schatten class c p if and only if f p f belongs to the besov space b p to be more precise the if part of this statement is easy the main result of the paper is the only if part we also show that the membership h f c 2 n implies f p f 0 i e h f 0

diffuse scattering on graphs abstract we formulate and analyze difference equations on graphs analogous to time independent diffusion equations arising in the study of diffuse scattering in continuous media moreover we show how to construct solutions in the presence of weak scatterers from the solution to the homogeneous background problem using born series providing necessary conditions for convergence and demonstrating the process through numerous examples in addition we outline a method for finding green s functions for cayley graphs for both abelian and non abelian groups finally we conclude with a discussion of the effects of sparsity on our method and results outlining the simplifications that can be made provided that the scatterers are weak and well separated

on deriving the inverse of a sum of matrices available expressions are reviewed and new ones derived for the inverse of the sum of two matrices one of them being nonsingular particular attention is given to text bf a text bf ubv 1 where textbf a is nonsingular and textbf u b and textbf v may be rectangular generalized inverses of textbf a textbf ubv are also considered several statistical applications are discussed

bergman commutators and norm ideals let p be the orthogonal projection from l2 b dv onto the bergman space la2 b dv of the unit ball in cn in this paper we characterize the membership of commutators of the form mf p in the norm ideal c where the symmetric gauge function is allowed to be arbitrary

a new characterization of dirichlet type spaces on the unit ball of cn abstract in this paper a bmo type characterization of dirichlet type spaces d p on the unit ball of cn is given

generalizations of the forelli rudin estimates we give elementary proofs of the forelli rudin estimates and generalizations of these estimates as an application we obtain lp boundedness results for classes of integral operators that include bergman projections and hankel operators

the inverses of some circulant matrices we present here necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three parameters and moreover we explicitly compute the inverse our study also encompasses a wide class of circulant symmetric matrices the techniques we use are related with the solution of boundary value problems associated to second order linear difference equations consequently we reduce the computational cost of the problem in particular we recover the inverses of some well known circulant matrices whose coefficients are arithmetic or geometric sequences horadam numbers among others we also characterize when a general symmetric circulant and tridiagonal matrix is invertible and in this case we compute explicitly its inverse

generalized inverses of symmetric m matrices abstract in this work we carry out an exhaustive analysis of the generalized inverses of singular irreducible symmetric m matrices the key idea in our approach is to identify any symmetric m matrix with a positive semi definite schrodinger operator on a connected network whose conductances are given by the off diagonal elements of the m matrix moreover the potential of the operator is determined by the positive eigenvector of the m matrix we prove that any generalized inverse can be obtained throughout a green kernel plus some projection operators related to the positive eigenfunction moreover we use the discrete potential theory associated with any positive semi definite schrodinger operator to get an explicit expression for any generalized inverse in terms of equilibrium measures finally we particularize the obtained result to the cases of tridiagonal matrices and circulant matrices

paracommutators boundedness and schatten von neumann properties definition d une classe d operateurs denommes paracommutateurs operant sur les fonctions de l 2 r d par analogie avec la para multiplication de bony et les commutateurs des operateurs de calderon zygmund etablissement de la borne et des proprietes de schatten von neumann

the dixmier trace of hankel operators on the bergman space abstract we give a formula for the dixmier trace of big hankel operators on the bergman space of the disk or of finitely connected domains for harmonic symbols we find the regularity required of the symbol for the formula to hold

commutators and localization on the drury arveson space let f be a multiplier for the drury arveson space hn2 of the unit ball and let 1 n denote the coordinate functions we show that for each 1 i n the commutator mf m i belongs to the schatten class cp p 2n this leads to a localization result for multipliers

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

explicit inverses of some tridiagonal matrices abstract we give explicit inverses of tridiagonal 2 toeplitz and 3 toeplitz matrices which generalize some well known results concerning the inverse of a tridiagonal toeplitz matrix

norm estimates for iterated commutators on the bergman spaces of the unit ball introduction we study the iterated commutators of the bergman projection and the multiplication by measurable functions called the symbols unlike the commutators the iterated commutators are no longer depending linearly on their symbols therefore most of the techniques used successfully in studying the first order commutators fail to work effectively for the nth order iterated commutators these operators are also very different from their analogs on l2 rm which has been studied by l peng t qian in pq using the s jason and j peeter s technique established in jp and r rochberg s semmes in rs where deeper tools of harmonic analysis in r are employed in this paper by using the bergman geometry properties of holomorphic functions and related analyses we characterize the conjugate holomorphic symbols for which the corresponding iterated commutators are bounded compact or in the schatten p class some lp estimates are also included in our discussion let 1m be the open unit ball of cm and dv z be the volume measure on blm

compactness of hankel operators and analytic discs in the boundary of pseudoconvex domains abstract using several complex variables techniques we investigate the interplay between the geometry of the boundary and compactness of hankel operators let be a function smooth up to the boundary on a smooth bounded pseudoconvex domain c n we show that if is convex or the levi form of the boundary of is of rank at least n 2 then compactness of the hankel operator h implies that is holomorphic along analytic discs in the boundary furthermore when is convex in c 2 we show that the condition on is necessary and sufficient for compactness of h

m matrix generalized inverses of m matrices abstract let p be an n n nonnegative irreducible and stochastic matrix and consider the associated singular and irreducible m matrix q i p we show that without further restrictive spectral or combinatorial assumptions on p it is reasonable to expect that the group inverse q of q will be an m matrix only when p lies in a small wedge about a rank 1 nonnegative matrix a wedge whose existence is itself dependent on p we go on to consider the question of when q has a nonzero generalized inverse not necessarily the group inverse which is an m matrix we give examples of all sorts of classes of p for which such is the case but point out that the general problem remains unsolved

discrete elliptic operators and their green operators abstract semi definite positive schrodinger operators on finite connected networks are particular examples of a general class of self adjoint operators called elliptic operators any elliptic operator defines an automorphism on the subspace orthogonal to the eigenfunctions associated with the lowest eigenvalue whose inverse is called orthogonal green operator our aim is to study the effect of a perturbation of an elliptic operator on its orthogonal green operator the perturbation here considered is performed by adding a self adjoint and positive semi definite operator we show that schrodinger operators on networks that are obtained by adding weighted edges to a given network can be seen as perturbations of the schrodinger operators on the original network therefore we can compute the green function the effective resistances and the kirchhoff index of a perturbed network in terms of the corresponding ones on the original network we apply the obtained results to the study of perturbations of a weighted star which includes as particular cases the wheel and fan networks

perturbations of discrete elliptic operators abstract given v a finite set a self adjoint operator k on c v is called elliptic if it is positive semi definite and its lowest eigenvalue is simple therefore there exists a unique up to sign unitary function c v satisfying k and then k is named elliptic clearly a elliptic operator is singular iff 0 examples of elliptic operators are the so called schrodinger operators on finite connected networks as well as the signless laplacian of connected bipartite networks a elliptic operator k defines an automorphism on whose inverse is called orthogonal green operator of k we aim here at studying the effect of a perturbation of k on its orthogonal green operator the perturbation here considered is performed by adding a self adjoint and positive semi definite operator to k as particular cases we consider the effect of changing the conductances on semi definite schodinger operators on finite connected networks and on the signless laplacian of connected bipartite networks the expression obtained for the perturbed network is explicitly given in terms of the orthogonal green function of the original network

trace ideal criteria for toeplitz operators for a complex measure on the open unit disk u define an operator t on a hilbert space h of analytic functions with reproducing kernel k z w by u for a certain scale of hilbert spaces h 1 which includes the hardy space h2 and weighted bergman spaces a2 conditions are obtained which imply t belongs to a schatten ideal sp if is a positive measure then these conditions are necessary and sufficient application to composition operators and restriction operators are indicated

recent developments in computer assisted analysis of mixtures this paper reviews recent developments in the area of computer assisted analysis of mixture distributions c a man given a biometric situation of interest in which under homogeneity assumptions a certain parametric density occurs such as the poisson the binomial the geometric the normal and so forth then it is argued that this situation can easily be enlarged to allow a variation of the scalar parameter in the population this situation is called unobserved heterogeneity this naturally leads to a specific form of nonparametric mixture distribution that can then be assumed to be the standard model in the biometric application of interest since it also incorporates the homogeneous situations as a special case besides developments in theory and algorithms the work focuses on developments in biometric applications such as meta analysis fertility studies estimation of prevalence under clustering and estimation of the distribution function of survival time under interval censoring the approach is nonparametric for the mixing distribution including leaving the number of components subpopulations of the mixing distribution unknown

bmo on strongly pseudoconvex domains hankel operators duality and overline partial estimates we study the condition that characterizes the symbols of bounded hankel operators on the bergman space of a strongly pseudoconvex domain and show that it is equivalent to bmo plus analytic here we mean the bergman metric bmo of berger coburn and zhu in the course of the proof we obtain new 0 estimates that may be of independent interest some applications include a decomposition of bmo similar to the classical li l and two characterizations of the dual of vmo which is also a predual of bmo in addition we obtain some partial results on the boundedness of hankel operators in l1 norm

characterizations for besov spaces and applications part i the main theorem of this paper gives a characterization for holomorphic besov space bp d over a large class of bounded domains d in cn which states that there is a bounded linear operator vd bp d lp d d so that pvd i on bp d where p is the bergman projection and d z k z z dv is the biholomorphic invariant measure with k z z being bergman kernel function for d moreover some application for characterizing schatter von neumann p class small hankel operation is given as a direct consequence of this theorem

robust nonparametric estimation of monotone regression functions with interval censored observations nonparametric estimation of monotone regression functions is a classical problem of practical importance robust estimation of monotone regression functions in situations involving interval censored data is a challenging yet unresolved problem herein we propose a nonparametric estimation method based on the principle of isotonic regression using empirical process theory we show that the proposed estimator is asymptotically consistent under a specific metric we further conduct a simulation study to evaluate the performance of the estimator in finite sample situations as an illustration we use the proposed method to estimate the mean body weight functions in a group of adolescents after they reach pubertal growth spurt

nonnegative alternating circulants leading to m matrix group inverses abstract let c be the set of all an n n nonnegative irreducible alternating circulant matrices we characterize a subset c of c such that if b c and the perron root of b is r then the group inverse ri b of the singular and irreducible m matrixri b is also an m matrix this is equivalent to the fact that for each such b the perron root at b is a concave function in each of the off diagonal entries the characterization for the case when n is odd presents more difficulties than for the case when n is even so the two cases are treated separately

toeplitz operators and hankel operators on the hardy space of the unit sphere abstract a sufficient condition is found for the product of two toeplitz operators on the hardy space of the unit sphere to be a compact perturbation of a toeplitz operator the condition leads to a criterion for a hankel operator to be compact

localization carleson measure and bmo toeplitz operators on the bergman space abstract in this paper we prove that a toeplitz operator with complex borel measure symbol whose total variation is carleson is weakly localized on the bergman space we define strongly localized and sufficiently localized operators on the bergman space and show that they are also weakly localized finally we show that bounded toeplitz operators with b m o 1 symbols are strongly and therefore also weakly localized and that the bergman space toeplitz algebra has yet another characterization as the c algebra generated by this class of operators

duality and hankel operators on the bergman spaces of bounded symmetric domains soit un domaine symetrique borne dans c n avec dv la mesure de volume normalisee l espace de bergman l a p est le sous espace clos de l p dv constitue des fonctions holomorphes on decrit le dual et le predual de l a 1 pour tous les domaines symetriques bornes

green operators of networks with a new vertex abstract any elliptic operator defines an automorphism on the orthogonal subspace to the eigenfunctions associated with the lowest eigenvalue whose inverse is the orthogonal green operator in this study we show that elliptic schrodinger operators on networks that have been obtained by adding a new vertex to a given network can be seen as perturbations of the schrodinger operators on the initial network therefore the green function of the new network can be computed in terms of the green function of the original network

forward and reverse carleson inequalities for functions in bergman spaces and their derivatives is satisfied in the process a simple proof of certain inequalities on derivatives of functions in hp is obtained section 3 as well as some information on interpolation sequences for lp section 5 inequalities like 1 1 have already been used to provide information on bergman toeplitz operators l1 and are useful for obtaining representations of functions in lp section 4 theorem 4 6 the inequality which reverses the roles of a and m in 1 1 is relatively easy even if an appropriate weighting factor is included with m theorem a below it was obtained by oleinik and pavlov op and independently when p q 1 by stegenga s and with c 0 hastings ha the results of oleinik and pavlov which are more general than theorem a were extended somewhat by oleinik in 0 cima and wogen cw using stegenga s methods proved the analogue of theorem a in several variables the methods of l3 more or less supercede all these results

models for interval censoring and simulation based inference for lifetime distributions summary interval censored lifetime data arise when individuals in a study are inspected inter mittently so that a lifetime is observed to lie between two successive times in settings where only these two times are available methods exist for nonparametric or parametric estimation of lifetime distributions however there has been virtually no discussion of how inspection processes may be estimated or identified such estimates are needed if one is to generate interval censored data by simulation this paper identifies which aspects of an independent inspection process are estimable from interval censored data and shows how to obtain nonparametric estimates the results allow interval censored data from any specified distribution to be generated and give new simulation procedures for estimation or testing a new omnibus goodness of fit test is introduced

a local inequality for hankel operators on the sphere and its application abstract let h 2 s be the hardy space on the unit sphere s in c n we establish a local inequality for hankel operators h f 1 p m f h 2 s as an application of this local inequality we characterize the membership of h f in the lorentz like ideal c p 2 n p

on schatten class perturbations of toeplitz operators let d denote the unit ball or the unit polydisc in cncn with n 2n 2 for 1 p 2n1 p 2n in the case of the ball and 1 p 1 p for the polydisc we show that a bounded operator s on the hardy space h2 d h2 d commutes with all analytic toeplitz operators modulo the schatten class spsp if and only if s x ks x k with an analytic toeplitz operator x and an operator k spk sp this partially answers a question of guo and wang 14 for 1 p 1 p and a strictly pseudoconvex or bounded symmetric and circled domain d cnd cn we show that a given operator s on h2 d h2 d is a schatten p class perturbation of a toeplitz operator if and only if t st s sp for every inner function on d

green matrices associated with generalized linear polyominoes a polyomino is an edge connected union of cells in the planar square lattice here we consider generalized linear polyominoes that is the polyominoes supported by an n a 2 lattice in this paper we obtain the green function and the kirchhoff index of a generalized linear polyomino as a perturbation of a 2n path by adding weighted edges between opposite vertices this approach deeply links generalized linear polyomino green functions with the inverse m matrix problem and especially with the so called green matrices

characterization of symmetric m matrices as resistive inverses abstract we aim here at characterizing those nonnegative matrices whose inverse is an irreducible stieltjes matrix specifically we prove that any irreducible stieltjes matrix is a resistive inverse to do this we consider the network defined by the off diagonal entries of the matrix and we identify the matrix with a positive definite schrodinger operator whose ground state is determined by the lowest eigenvalue of the matrix and the corresponding positive eigenvector we also analyze the case in which the operator is positive semidefinite which corresponds to the study of singular irreducible symmetric m matrices

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial

approximation in weighted bergman spaces and hankel operators on strongly pseudoconvex domains suppose d is a bounded strongly pseudoconvex domain in mathbb c n with smooth boundary and let rho be its defining function for 1 p infty and alpha 1 we show that the weighted bergman projection p alpha is bounded on l p d rho alpha dv with non isotropic estimates for overline partial and stein s theorem on non tangential maximal operators we prove that bounded holomorphic functions are dense in the weighted bergman space a p d rho alpha dv and hence hankel operators can be well defined on these spaces for all 1 p q infty we characterize bounded resp compact hankel operators from p th weighted bergman space to q th weighted lebesgue space with possibly different weights as a consequence we generalize the main results in pau et al indiana univ math j 65 1639 1673 2016 and resolve a question posed in lv and zhu integr equ oper theory 2019