fredholm integral equation with potential kernel and its structure resolvent the purpose of this paper is to establish and solve the fredholm integral equation of the second kind with potential kernel from the semi symmetric hertz problem for two different elastic materials in three dimensions the kernel of the problem is represented in the non homogeneous wave equation also the structure resolvent of the problem is obtained

operator theoretic differences between hardy and dirichlet type spaces abstract for 0 p the dirichlet type space d p 1 p consists of the analytic functions f in the unit disc d such that d f z p 1 z p 1 d a z motivated by operator theoretic differences between the hardy space h p and d p 1 p the integral operator t g f z 0 z f g d z d acting from one of these spaces to another is studied in particular it is shown on one hand that t g d p 1 p h p is bounded if and only if g bmoa when 0 p 2 and on the other hand that this equivalence is very far from being true if p 2 those symbols g such that t g d p 1 p h q is bounded or compact when p q are also characterized moreover the best known sufficient l type condition for a positive borel measure on d to be a p carleson measure for d p 1 p p 2 is significantly relaxed and the established result is shown to be sharp in a very strong sense

carleson measures and multipliers for dirichlet spaces abstract we characterize carleson measures on the dirichlet spaces our result leads to necessary and sufficient conditions for multipliers of the dirichlet spaces

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

toeplitz matrix method and nonlinear integral equation of hammerstein type the existence and uniqueness solution of the nonlinear integral equation of hammerstein type with discontinuous kernel are discussed the normality and continuity of the integral operator are proved toeplitz matrix method is used as a numerical method to obtain a nonlinear system of algebraic equations also many important theorems related to the existence and uniqueness of the produced algebraic system are derived finally numerical examples when the kernel takes a logarithmic and carleman forms are discussed and the estimate error in each case is calculated

riemann stieltjes operators and multipliers on q p spaces in the unit ball of c n this paper is devoted to characterizing the riemann stieltjes operators and pointwise multipliers acting on mobius invariant spaces q p which unify bmoa and bloch space in the scale of p the boundedness and compactness of these operators on q p spaces are determined by means of an embedding theorem i e q p spaces boundedly embedded in the non isotropic tent type spaces t q infinity c 2010 elsevier inc all rights reserved

a generalized shift splitting preconditioner for singular saddle point problems recently some authors cao et al 2014 chen and ma 2015 salkuyeh et al 2014 discussed the generalized shift splitting preconditioner for nonsingular saddle point problems in this paper we further study the generalized shift splitting preconditioner for solving singular saddle point problems with symmetric positive definite 1 1 block theoretical analysis shows that the generalized shift splitting iteration method is unconditionally semi convergent numerical experiments are given to illustrate the efficiency of the proposed preconditioner with appropriate parameters

on the augmented system approach to sparse least squares problems we study the augmented system approach for the solution of sparse linear least squares problems it is well known that this method has better numerical properties than the method based on the normal equations we use recent work by arioli et al 1988 to introduce error bounds and estimates for the components of the solution of the augmented system in particular we find that using iterative refinement we obtain a very robust algorithm and our estimates of the error are accurate and cheap to compute the final error and all our error estimates are much better than the classical or skeel s error analysis 1979 indicates moreover we prove that our error estimates are independent of the row scaling of the augmented system and we analyze the influence of the bjorck scaling 1967 on these estimates we illustrate this with runs both on large scale practical problems and contrived examples comparing the numerical behaviour of the augmented systems approach with a code using the normal equations these experiments show that while the augmented system approach with iterative refinement can sometimes be less efficient than the normal equations approach it is comparable or better when the least squares matrix has a full row and is in any case much more stable and robust

a solution of a nonlinear integral equation in this work we will prove the existence of integrable solution of nonlinear integral equation of type hammerstein volterra of the second kind by using the technique of measure of weak noncompactness and schauder fixed point theorem also the solution of the integral equation is obtained and studied

symmetric sor method for augmented systems in this paper we develop symmetric successive overrelaxation ssor method to find solution of augmented systems these systems have appeared in many different applications of scientific computing e g the finite element approximation to solve the navier stokes equation and the constrained optimization the convergence of ssor method are studied finally we apply the new method to solve augmented systems the iteration number of this method to receive the solution is very better than sor like method

on convergence and semi convergence of ssor like methods for augmented linear systems abstract in this paper we analyze the convergence and semi convergence of a class of ssor like methods with four real functions for augmented systems the class takes most existed ssor like methods as its special cases for nonsingular systems we obtain the minimum of convergence factors of all the ssor like methods in the class and study when it can be reached by the convergence factors of methods in the class by considering the equivalence of methods we show that most of the existed ssor like methods have the same minimum of convergence factors

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

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

shift invert arnoldi approximation to the toeplitz matrix exponential the shift invert arnoldi method is employed to generate an orthonormal basis from the krylov subspace corresponding to a real toeplitz matrix and an initial vector the vectors and recurrence coefficients produced by this method are exploited to approximate the toeplitz matrix exponential toeplitz matrix inversion formula and rapid toeplitz matrix vector multiplications are utilized to lower the computational costs for convergence analysis a sufficient condition is established to guarantee that the error bound is independent of the norm of the matrix numerical results are given to demonstrate the efficiency of the method

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

an additive formula for samuel multiplicities on hilbert spaces of analytic functions abstract we establish a short exact sequence to relate the germ model of invariant subspaces of a hilbert space of vector valued analytic functions and the sheaf model of the corresponding coinvariant subspaces as a consequence we obtain an additive formula for samuel multiplicities as an application we give a different proof for a formula relating the fibre dimension and the samuel multiplicity which is first proved in fang 2005 11 the feature of the new proof is that the analytic arguments in fang 2005 11 are now subsumed by algebraic machinery

on semi convergence of parameterized uzawa methods for singular saddle point problems abstract bai et al recently proposed an efficient parameterized uzawa method for solving the nonsingular saddle point problems z z bai b n parlett z q wang on generalized successive overrelaxation methods for augmented linear systems numer math 102 2005 1 38 in this paper we further prove the semi convergence of this method when it is applied to solve the singular saddle point problems under suitable restrictions on the involved iteration parameters the optimal iteration parameters and the corresponding optimal semi convergence factor for the parameterized uzawa method are determined in addition numerical experiments are used to show the feasibility and effectiveness of the parameterized uzawa method for solving singular saddle point problems

on generalized symmetric sor method for augmented systems in this paper we establish the generalized symmetric sor method gssor for solving the large sparse augmented systems of linear equations which is the extension of the ssor iteration method the convergence of the gssor method for augmented systems is studied numerical resume shows that this method is effective

optimal accelerated sor like asor method for singular symmetric saddle point problems abstract in a recent paper a new iterative method for the solution of the nonsingular symmetric saddle point problem was proposed njeru and guo 2016 the asor method belongs to the family of the sor like methods and uses two parameters and convergence intervals for the parameters involved were found in the present work we analyze and study an extension of the above problem to the singular case and determine optimal values for the two parameters as well as for the semi convergence factor of the asor method numerical results are presented to show the efficiency of the optimal singular asor method

open embeddings and pseudoflat epimorphisms abstract we characterize open embeddings of stein spaces and of c manifolds in terms of certain flatness type conditions on the respective homomorphisms of function algebras

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

preconditioning for the steady state navier stokes equations with low viscosity we introduce a preconditioner for the linearized navier stokes equations that is effective when either the discretization mesh size or the viscosity approaches zero for constant coefficient problems with periodic boundary conditions we show that the preconditioning yields a system with a single eigenvalue equal to 1 so that performance is independent of both viscosity and mesh size for other boundary conditions we demonstrate empirically that convergence depends only mildly on these parameters and we give a partial analysis of this phenomenon we also show that some expensive subsidiary computations required by the new method can be replaced by inexpensive approximate versions of these tasks based on iteration with virtually no degradation of performance

forelli rudin estimates carleson measures and f p q s functions abstract a classical theorem of l carleson states that the injection map from the hardy space h p into l p d is bounded if and only if the positive measure on the unit disc is a bounded carleson measure in this paper forelli rudin estimates for arbitrary positive measures on the unit disc are proved and then these estimates are applied to characterize bounded s carleson measures in terms of bloch and f p q s functions

on parameterized inexact uzawa methods for generalized saddle point problems abstract for the large sparse saddle point problems bai et al recently studied a class of parameterized inexact uzawa piu methods z z bai b n parlett z q wang on generalized successive overrelaxation methods for augmented linear systems numer math 102 2005 1 38 for a special case that the 1 1 block is solved exactly they determined the convergence domain and computed the optimal iteration parameters and the corresponding optimal convergence factor for the induced method in this paper we develop these methods to the large sparse generalized saddle point problems for the obtained parameterized inexact uzawa method we prove its convergence under suitable restrictions on the iteration parameters in particular we determine its quasi optimal iteration parameters and the corresponding quasi optimal convergence factor for the saddle point problems furthermore this piu method is generalized to obtain a framework of accelerated variants of the parameterized inexact uzawa methods for solving both symmetric and nonsymmetric generalized saddle point problems by using the techniques of vector extrapolation matrix relaxation and inexact iteration

continuous time collocation methods for volterra fredholm integral equations integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study continuous time collocation time discretization and their global and discrete convergence properties

numerical methods for generalized least squares problems usually generalized least squares problems are solved by transforming them into regular least squares problems which can then be solved by well known numerical methods however this approach is not very effective in some cases and besides is very expensive for large scale problems in 1979 paige suggested another approach which consists of solving an equivalent equality constrained least squares problem by the orthogonal decomposition the bnp algorithm or the james implicit nullspace iterative methods in this paper we present some new developments of the numerical methods for example 2 cycle sor method and preconditioned conjugate gradient method for generalized least squares problems some numerical comparisons are included as well

multipliers and integration operators on dirichlet spaces for 0 1 we let d p denote the space of those functions f which are analytic in the unit disc d in c and satisfy d 1 z 2 f z p dx dy 1 furthermore we present a number of results on the self multipliers of d p 0 1 we prove that 0 is the only compact multiplier from d p p 1 to itself 0 1 this result plays a basic role in our work concerning integration operators

on a method for solving an integral equation in the displacement contact problem in this paper the solution in a series form of the integral equation of the mixed type in the space l w xc 0 t is obtained where w x y z

the dirac operator of a commuting d tuple abstract given a commuting d tuple t t1 td of otherwise arbitrary operators on a hilbert space there is an associated dirac operator dt significant attributes of the d tuple are best expressed in terms of dt including the taylor spectrum and the notion of fredholmness in fact all properties of t derive from its dirac operator we introduce a general notion of dirac operator in dimension d 1 2 that is appropriate for multivariable operator theory we show that every abstract dirac operator is associated with a commuting d tuple and that two dirac operators are isomorphic iff their associated operator d tuples are unitarily equivalent by relating the curvature invariant introduced in a previous paper to the index of a dirac operator we establish a stability result for the curvature invariant for pure d contractions of finite rank it is shown that for the subcategory of all such t that are a fredholm and and b graded the curvature invariant k t is stable under compact perturbations we do not know if this stability persists when t is fredholm but ungraded although there is concrete evidence that it does

on generalized successive overrelaxation methods for augmented linear systems for the augmented system of linear equations golub wu and yuan recently studied an sor like method bit 41 2001 71 85 by further accelerating it with another parameter in this paper we present a generalized sor gsor method for the augmented linear system we prove its convergence under suitable restrictions on the iteration parameters and determine its optimal iteration parameters and the corresponding optimal convergence factor theoretical analyses show that the gsor method has faster asymptotic convergence rate than the sor like method also numerical results show that the gsor method is more effective than the sor like method when they are applied to solve the augmented linear system this gsor method is further generalized to obtain a framework of the relaxed splitting iterative methods for solving both symmetric and nonsymmetric augmented linear systems by using the techniques of vector extrapolation matrix relaxation and inexact iteration besides we also demonstrate a complete version about the convergence theory of the sor like method

fiber dimension for invariant subspaces abstract in this paper we study the fiber dimension of invariant subspaces for a large class of operators we define a class of invariant subspaces called cf subspaces which are related to the codimension one property we obtain several characterizations of cf subspaces including one in terms of samuel multiplicity other new findings include 1 a lattice additive formula and its applications section 4 2 a new concept of absorbance which describes a rough containment relation for invariant subspaces section 5 3 the existence of a unique smallest cf subspace containing an arbitrary invariant subspace and preserving the fiber dimension section 6

semi convergence analysis of gmssor methods for singular saddle point problems recently some authors darvishi and hessari 2011 zhang et al 2012 discussed the generalized modified symmetric successive over relaxation gmssor method for saddle point problems in this paper we further study the gmssor method for solving singular saddle point problems we prove the semi convergence of the gmssor method without the assumption that the 1 1 block sub matrix a should be symmetric and analyze the spectral property of the corresponding preconditioned matrix numerical experiments are given to illustrate the efficiency of gmssor with appropriate parameters

a modified ssor iterative method for augmented systems golub wu and yuan g h golub x wu j y yuan sor like methods for augmented systems bit 41 2001 71 85 have presented the sor like algorithm to solve augmented systems in this paper we present the modified symmetric successive overrelaxation mssor method for solving augmented systems which is based on darvishi and hessari s work above we derive its convergence under suitable restrictions on the iteration parameter determine its optimal iteration parameter and the corresponding optimal convergence factor under certain conditions finally we apply the mssor method to solve augmented systems

unitary invariants for hilbert modules of finite rank we associate a sheaf model to a class of hilbert modules satisfying a natural finiteness condition it is obtained as the dual to a linear system of hermitian vector spaces in the sense of grothendieck a refined notion of curvature is derived from this construction leading to a new unitary invariant for the hilbert module a division problem with bounds originating in douady s privilege is related to this framework a series of concrete computations illustrate the abstract concepts of the paper

numerical solution of integral equations 1 a survey of boundary integral equation methods for the numerical solution of laplace s equation in three dimensions 2 superconvergence 3 perturbed projection methods for various classes of operator and integral equations 4 numerical solution of parallel processors of two point boundary value problems of astrodynamics 5 introduction to the numerical solution of cauchy singular integral equations 6 convergence theorems for singular integral equations 7 planing surfaces 8 abel integral equations

convergence of a generalized mssor method for augmented systems recently wu et al s l wu t z huang x l zhao a modified ssor iterative method for augmented systems j comput appl math 228 1 2009 424 433 introduced a modified ssor mssor method for augmented systems in this paper we establish a generalized mssor gmssor method for solving the large sparse augmented systems of linear equations which is the extension of the mssor method furthermore the convergence of the gmssor method for augmented systems is analyzed and numerical experiments are carried out which show that the gmssor method with appropriate parameters has a faster convergence rate than the mssor method with optimal parameters

extended cesaro operators from bergman spaces to besov spaces in the unit ball in this paper we characterize the holomorphic symbols g h b for which the induced extended cesaro operator t g is bounded or compact from bergman spaces to besov spaces in the unit ball in addition we obtain the properties of the p q carleson measure

fredholm integral equation of the second kind with potential kernel a method is used to solve the fredholm integral equation of the second kind which is investigated from the semi symmetric hertz problem for two different elastic materials in three dimensions also the kernel is represented in the nonhomogeneous wave equation form

a note on the generalization of parameterized inexact uzawa method for singular saddle point problems abstract recently zhang and wang studied the generalized parameterized inexact uzawa methods gpiu for solving singular saddle point problems zhang and wang 2013 22 in this note we continue to discuss the semi convergence of gpiu for solving singular saddle point problems and weaken some semi convergent conditions

estimates for hilbertian koszul homology abstract the objective of this paper is to give new kind of estimates for hilbertian koszul homology inspired by commutative algebra in multivariable fredholm theory

on a method for solving a two dimensional nonlinear integral equation of the second kind in this article the existence of at least one solution of a nonlinear integral equation of the second kind is proved the degenerate method is used to obtain a nonlinear algebraic system where the existence of at least one solution of this system is discussed finally computational results with error estimates are obtained using maple software

the koebe semigroup and a class of averaging operators on hp d we study on the hardy space h p the operators t f given by formule where f z is analytic on the unit disc d and has re f z 0 each such operator is closely related to a strongly continuous semigroup of weighted composition operators by studying first an extremal such semigroup the koebe semigroup we are able to obtain the upper bound t f p 2p re 1 f 0 im 1 f 0 for the norm we also show that t f is compact on h p if and only if the measure in the herglotz representation of 1 f is continuous

semi convergence analysis of uzawa methods for singular saddle point problems recently zheng bai and yang studied the parameterized uzawa method for solving singular saddle point problems b zheng z z bai x yang on semi convergence of parameterized uzawa methods for singular saddle point problems linear algebra appl 431 2009 808 817 in this paper we discuss the inexact uzawa method which covers the uzawa method the preconditioned uzawa method and the parameterized uzawa method to solve the singular saddle point problems we prove the semi convergence result under restrictions by verifying two necessary and sufficient conditions that is all elementary divisors associated with the eigenvalue 1 of its iterative matrix are linear and the pseudo spectral radius of the iterative matrix is less than 1 sufficient conditions for the semi convergence of several uzawa type methods are also provided in addition numerical examples are given to demonstrate the semi convergence of uzawa type methods

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

block sor methods for rank deficient least squares problems many papers have discussed preconditioned block iterative methods for solving full rank least squares problems however very few papers studied iterative methods for solving rank deficient least squares problems miller and neumann 1987 proposed the 4 block sor method for solving the rank deficient problem here a 2 block sor method and a 3 block sor method are proposed to solve such problem the convergence of the block sor methods is studied the optimal parameters are determined comparison between the 2 block sor method and the 3 block sor method is given also

the fredholm index of a pair of commuting operators ii this paper concerns fredholm theory in several variables and its applications to hilbert spaces of analytic functions one feature is the introduction of ideas from commutative algebra to operator theory specifically we introduce a method to calculate the fredholm index of a pair of commuting operators to achieve this we define and study the hilbert space analogs of samuel multiplicities in commutative algebra then the theory is applied to the symmetric fock space in particular our results imply a satisfactory answer to arveson s program on developing a fredholm theory for pure d contractions when d 2 including both the fredholmness problem and the calculation of indices we also show that arveson s curvature invariant is in fact always equal to the samuel multiplicity for an arbitrary pure d contraction with finite defect rank it follows that the curvature is a similarity invariant

on the numerical solution of nonlinear volterra fredholm integral equations by collocation methods particular cases of nonlinear mixed volterra fredholm integral equations of the second kind arise in the mathematical modeling of the spatio temporal development of an epidemic this paper is concerned with the numerical solution of general integral equations of this type by continuous time and discrete time spline collocation methods its focus is on the derivation and analysis of methods of high order of convergence

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

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

preconditioned conjugate gradient method for generalized least squares problems abstract a variant of the preconditioned conjugate gradient method to solve generalized least squares problems is presented if the problem is min ax b t w 1 ax b with a r m n and w r m m symmetric and positive definite the method needs only a preconditioner a 1 r n n but not the inverse of matrix w or of any of its submatrices freund s comparison result for regular least squares problems is extended to generalized least squares problems an error bound is also given

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

embedding theorems and integration operators on bergman spaces with rapidly decreasing weights we completely describe those positive borel measures in the unit disc d such that the bergman space ap w lq 0 0 and some double exponential type weights as an application of that result we characterize the boundedness and the compactness of tg ap w aq w 0 p q w w where tg is the integration operator tgf z 0zf g d the particular choice of the weight w r answers an open question posed by a aleman and a siskakis we also describe those analytic functions in d for which tg belongs to the schatten p class of a2 w 0 p

on equivalence of optimal relaxed block iterative methods for the singular nonsymmetric saddle point problem abstract there exist many classes of relaxed block iterative methods for the solution of the nonsingular and singular saddle point problems recently the singular nonsymmetric saddle point problem has been optimally solved by means of a stationary linear second order iterative method using the manteuffel algorithm hadjidimos 2016 19 the main purpose of this work is to extend analyze and study a number of classes of stationary iterative methods based on generalizations of sor like methods determine their optimal parameters via the optimal parameters in the aforementioned work and show the equivalence of the optimal methods studied finally a computational comparison of the performances of the above optimal methods and their nonstationary counterparts shows the superiority of the latter methods

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

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

a modified symmetric successive overrelaxation method for augmented systems in this paper we establish a modified symmetric successive overrelaxation mssor method to solve augmented systems of linear equations which uses two relaxation parameters this method is an extension of the symmetric sor ssor iterative method the convergence of the mssor method for augmented systems is studied numerical examples show that the new method is an efficient method

carleson measures multipliers and integration operators for spaces of dirichlet type for 0 1 we let d p denote the space of those functions f which are analytic in the unit disc d z c z 1 and satisfy d 1 z 2 f z p dx dy in this paper we characterize the positive borel measures in d such that d p l q d 0 p q we also characterize the pointwise multipliers from d p to d q 0 p q i fp 2 p in particular we prove that if

a generalization of the inexact parameterized uzawa methods for saddle point problems abstract for large sparse saddle point problems bai and wang recently studied a class of parameterized inexact uzawa methods see z z bai z q wang on paramaterized inexact uzawa methods for generalized saddle point problems linear algebra appl 428 2008 2900 2932 in this paper we generalize these methods and propose a class of generalized inexact parameterized iterative schemes for solving the saddle point problems we derive conditions for guaranteeing the convergence of these iterative methods with different choices of the parameter matrices the generalized iterative methods lead to a series of existing and new iterative methods including the classical uzawa method the inexact uzawa method the gsor method and the giaor method

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

strict singularity of volterra type operators on hardy spaces abstract in this paper we first characterize the boundedness and compactness of volterra type operator s g f z 0 z f g d z d defined on hardy spaces h p 0 p the spectrum of s g is also obtained then we prove that s g fixes an isomorphic copy of l p and an isomorphic copy of l 2 if the operator s g is not compact on h p 1 p in particular this implies that the strict singularity of the operator s g coincides with the compactness of the operator s g on h p at last we post an open question for further study