toeplitz and hankel operators on bergman spaces in this paper we consider toeplitz and hankel operators on the bergman spaces of the unit ball and the polydisk in c n whose symbols are bounded measurable functions we giv e necessary and sufficient conditions on the symbols for these operators to be compact we study the fredholm theory of topelitz operators for which the corresponding hankel operator is compact for these toeplitz operators the essential spectrum is computed and shown to be connected we also consider symbols that extend to continuous functions on the maximal ideal space of h for these symbols we describe when the toeplitz or hankel operators are compact

the distribution function inequality and products of toeplitz operators and hankel operators abstract in this paper we study hankel operators and toeplitz operators through a distribution function inequality on the lusin area integral function and the littlewood paley theory a sufficient condition and a necessary condition are obtained for the boundedness of the product of two hankel operators they lead to a way to approach sarason s conjecture on products of toeplitz operators and shed light on the compactness of the product of hankel operators an elementary necessary and sufficient condition for the product of two toeplitz operators to be a compact perturbation of a toeplitz operator is obtained moreover a necessary condition is given for the product of hankel operators to be in the commutator ideal of the algebra generated by the toeplitz operators with symbols in a sarason algebra

sharp two weight inequalities for singular integrals with applications to the hilbert transform and the sarason conjecture abstract we prove two weight norm inequalities for calderon zygmund singular integrals that are sharp for the hilbert transform and for the riesz transforms in addition we give results for the dyadic square function and for commutators of singular integrals as an application we give new results for the sarason conjecture on the product of unbounded toeplitz operators on hardy spaces

innovation based on gaussian elimination to compute generalized inverse at s 2 abstract in this paper we execute elementary row and column operations on the partitioned matrix g a g g g 0 into i s 0 0 0 0 0 a t s 2 to compute generalized inverse a t s 2 of a given complex matrix a where g is a matrix such that r g t and n g s the total number of multiplications and divisions operations is t m n s 2 m n 2 4 m s 1 2 n s m s n s m n s and the upper bound of t m n s is less than 6 m n 2 3 2 n 3 1 2 n 2 when n m a numerical example is shown to illustrate that this method is correct

invertibility and spectral properties of dual toeplitz operators abstract in this paper we consider dual toeplitz operators with continuous symbols and bounded harmonic symbols on the orthogonal complement of the bergman space over the open unit disk we construct a dual toeplitz operator with continuous symbol such that its spectrum is disconnected on the other hand we show that the spectra of dual toeplitz operators with certain class of bounded harmonic symbols are connected which leads to some partial answers to the open question posed by stroethoff and zheng 18 in 2002 we obtain a complete characterization for the hyponormality of dual toeplitz operators with bounded harmonic symbols moreover we establish some sufficient conditions that are convenient to check for dual toeplitz operators with continuous symbols and bounded harmonic symbols to be invertible respectively

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

on the space requirement of interval routing interval routing is a space efficient method for point to point networks it is based on labeling the edges of a network with intervals of vertex numbers called interval labels an m label scheme allows up to m labels to be attached on an edge for arbitrary graphs of size m n the number of vertices the problem is to determine the minimum rp necessary for achieving optimality in the length of the longest routing path the longest routing path resulted from a labeling is an important indicator of the performance of any algorithm that runs on the network we prove that there exists a graph with d spl omega n sup 1 3 such that if m spl les n 18d o spl radic n d the longest path is no shorter than d spl theta d spl radic m as a result for any m label 1rs if the longest path is to be shorter than d spl theta d spl radic m at least m spl theta n d labels per edge would be necessary

invertible toeplitz products we will discuss invertibility of toeplitz products tftg for analytic f and g on the bergman space and the hardy space we will furthermore describe when these toeplitz products are fredholm

algebraic and spectral properties of dual toeplitz operators dual toeplitz operators on the orthogonal complement of the bergman space are defined to be multiplication operators followed by projection onto the orthogonal complement in this paper we study algebraic and spectral properties of dual toeplitz operators

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

bounded toeplitz products on the bergman space of the polydisk abstract we consider the question for which square integrable analytic functions f and g on the polydisk the densely defined products t f t g are bounded on the bergman space we prove results analogous to those we obtained in the setting of the unit disk k stroethoff d zheng j funct anal 169 1999 289 313

a survey on interval routing we survey in this paper the classical results and also the most recent results in the field of interval routing a well known strategy to code in a compact way distributed routing algorithms these results are classified in several themes characterization compactness and shortest path dilation and stretch factor specific class of graphs interconnection networks bounded degree planar chordal rings random graphs etc and the other recent extensions proposed in the literature dead lock free congestion non deterministic and distributed problems related to interval routing for each of these themes we review the state of the art and propose several open problems

an implicit difference method for the numerical solution of coupled systems of partial differential equations an explicit and computable solution for coupled partial difference systems appearing when one considers difference approximations of coupled systems of partial differential equations is given our approach is based on the consideration of a discrete matrix separation of variables method by using discrete fourier series we avoid the problem of solving algebraic linear systems

bounded toeplitz products on the weighted bergman spaces of the unit ball abstract let p 1 and let q denote the number such that 1 p 1 q 1 we give a necessary condition for the product of toeplitz operators t f t g to be bounded on the weighted bergman space of the unit ball a p 1 where f a p and g a q as well as a sufficient condition for t f t g to be bounded on a p we use techniques different from those in k stroethoff d zheng bounded toeplitz products on bergman spaces of the unit ball j math anal appl 325 2007 114 129 in which the case p 2 was proved

numerical multisteps matrix methods for y f t y abstract in this paper numerical multistep matrix methods for solving coupled systems of second order differential equations are proposed these methods permit the simultaneous computation of all the entries of a coupled differential system using algebraic symbolic languages error bounds for the discretization error in terms of the data are given the proposed methods avoid the increase of the computational cost derived from the standard transformation of the differential problem into an extended first order system

a matrix d alembert formula for coupled wave initial value problems if c is an invertible matrix in cr r the coupled wave equation initial value problem utt c2uxx 0 u x 0 f x and ut x 0 g x for x is studied a matrix d alembert formula for the closed form solution of the coupled wave equation is given the approach is based on the fourier transform the holomorphic matrix functional calculus and some elements of complex variable functions for the scalar case the proposed d alembert formula coincides with the classical one

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

analytic and numerical solution of coupled implicit semi infinite diffusion problems abstract this paper deals with singular coupled implicit semi infinite mixed diffusion problems by application of the sine fourier transform existence conditions and an analytic closed form solution is first obtained given an admissible error and a rectangular bounded closed domain analytic numerical approximations whose error with respect to the exact solution is less than the admissible error in the bounded domain are constructed an algorithm and an illustrative example are included

computation of weighted moore penrose inverse through gauss jordan elimination on bordered matrices abstract in this paper two new algorithms for computing the weighted moore penrose inverse a m n of a general matrix a for weights m and n which are based on elementary row and column operations on two appropriate block partitioned matrices are introduced and investigated the computational complexity of the introduced two algorithms is analyzed in detail these two algorithms proposed in this paper are always faster than those in sheng and chen 2013 and ji 2014 respectively by comparing their computational complexities in the end an example is presented to demonstrate the two new algorithms

invariant subspaces quasi invariant subspaces and hankel operators abstract in this paper using the theory of hilbert modules we study invariant subspaces of the bergman spaces on bounded symmetric domains and quasi invariant subspaces of the segal bargmann spaces we completely characterize small hankel operators with finite rank on these spaces

a reproducing kernel thesis for operators on bergman type function spaces abstract in this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on bergman type spaces in particular the results in this paper apply to the weighted bergman space on the unit ball the unit polydisc and more generally to weighted fock spaces

the finite sum of finite products of toeplitz operators on the polydisk abstract a limit theorem is established for a finite sum of finite products of toeplitz operators on the hardy space of the polydisk as a consequence we show that the product of six toeplitz operators with pluriharmonic symbols is compact iff the product equals zero iff one of these toeplitz operators equals zero

using gauss jordan elimination to compute the index generalized nullspaces and drazin inverse abstract we develop and analyze a new algorithm that computes bases for the null spaces of all powers of a given matrix as well as its index the algorithm uses row operations and shuffling steps in which rows of pairs of matrices are interchanged in particular the new algorithm may be viewed as an extension of the classic gauss jordan elimination method for inverting a nonsingular matrix it is also shown that the drazin inverse has a simple representation in terms of the output of the algorithm and the original matrix

essentially commuting hankel and toeplitz operators abstract we characterize when a hankel operator and a toeplitz operator have a compact commutator

bounds on distances between eigenvalues explicit computable lower and upper bounds on the distances between a given real eigenvalue of a real square matrix and the remaining not necessarily real eigenvalues of the matrix are developed

the finite rank perturbations of the product of hankel and toeplitz operators in this paper we completely characterize when the product of a hankel operator and a toeplitz operator on the hardy space is a finite rank perturbation of a hankel operator and when the commutator of a hankel operator and a toeplitz operators has finite rank

an algebraic analytic approach to nonnegative bases abstract rothblum and independently richman and schneider have used a combination of graph theoretic and algebraic approaches based on the frobenius normal form of a matrix to show that if a is an n n nonnegative matrix then the generalized eigenspace of a corresponding to its perron root a has a nonnegative basis moreover they showed that among the jordan chains corresponding to a a has a chain of maximal length consisting entirely of nonnegative generalized eigenvectors in this paper we develop an algebraic analytic approach to the proofs of these results which is based on the asymptotic behavior of the resolvent operator the approach allows us to suggest an algorithm for computing a nonnegative basis

new bounds for multi label interval routing interval routing ir is a space efficient routing method for computer networks for longest routing path analysis researchers have focused on lower bounds for many years for any n node graph g of diameter d there exists an upper bound of 2d for ir using one or more labels and an upper bound of 3 2d for ir using o nlogn or more labels we present two upper bounds in the first part of the paper we show that for every integer i 0 every n node graph of diameter d has a k dominating set of size o i 1 n for k 1 1 3i d this result implies a new upper bound of 2 1 3i d for ir using o i 1 n or more labels where i is any positive integer constant we apply the result by kutten and peleg 7 to achieve an upper bound of 1 d for ir using o n d or more labels where is any constant in 0 1 the second part of the paper offers some lower bounds for planar graphs for any m label interval routing scheme m irs where m o 3 n we derive a lower bound of 2m 1 2m d 1 on the longest path for m o n and a lower bound of 2 1 m 1 2 1 m d where 0 1 for m o n the latter result implies a lower bound of n on the number of labels needed to achieve optimality

on optimal condition numbers for markov chains let t and tilde t t e be arbitrary nonnegative irreducible stochastic matrices corresponding to two ergodic markov chains on n states a function is called a condition number for markov chains with respect to the norm pair if pi tilde pi alpha leq kappa t e beta here and tilde pi are the stationary distribution vectors of the two chains respectively various condition numbers particularly with respect to the 1 and norm pairs have been suggested in the literature they were ranked according to their size by cho and meyer in a paper from 2001 in this paper we first of all show that what we call the generalized ergodicity coefficient tau p a rm sup y t e 0 frac y ta p y 1 where e is the n vector of all 1 s and a is the group generalized inverse of a i t is the smallest condition number of markov chains with respect to the p norm pair we use this result to identify the smallest condition number of markov chains among the and 1 norm pairs these are respectively 3 and 6 in the cho meyer list of 8 condition numbers kirkland has studied 3 t he has shown that kappa 3 t geq frac n 1 2n and he has characterized transition matrices for which equality holds we prove here again that 2 3 t 6 which appears in the cho meyer paper and we characterize the transition matrices t for which kappa 6 t frac n 1 n there is actually only one such matrix t j n i n 1 where j n is the n n matrix of all 1 s

a decomposition theorem for bmo and applications abstract every function having bounded mean oscillation bmo on the line is written as a sum of coefficients times normalized rational functions with the coefficients satisfying a carleson measure packing condition this decomposition theorem and related techniques are used to obtain operator norm estimates for first and second order commutators and direct and converse singular value estimates for hankel operators and products of hankel operators

on the computation of the rank of block bidiagonal toeplitz matrices in the present paper we study the computation of the rank of a block bidiagonal toeplitz bbt sequence of matrices we propose matrix based numerical and symbolical updating and direct methods computing the rank of bbt matrices and comparing them with classical procedures the methods deploy the special form of the bbt sequence significantly reducing the required flops and leading to fast and efficient algorithms the numerical implementation of the algorithms computes the numerical rank in contrast with the symbolical implementation which guarantees the computation of the exact rank of the matrix the combination of numerical and symbolical operations suggests a new approach in software mathematical computations denoted as hybrid computations

a two weight inequality for the hilbert transform assuming an energy hypothesis let and be locally finite positive borel measures on r subject to the pair of weights satisfying a side condition we characterize boundedness of the hilbert transform h from l2 to l2 in terms of the a2 condition i i i x xi 2d x i i i x xi 2d x 12 c i and the two testing conditions for all intervals i in r ih 1i x 2d x c id x ih 1i x 2d x c id x the proof uses the beautiful corona argument of nazarov treil and volberg there is a range of side conditions termed energy conditions at one endpoint the energy conditions are also a consequence of the testing conditions above and at the other endpoint they are the pivotal conditions of nazarov treil and volberg we detail an example which shows that the pivotal conditions are not necessary for boundedness of the hilbert transform

the complexity of shortest path and dilation bounded interval routing abstract interval routing is a popular compact routing method for point to point networks which found industrial applications in novel transputer routing technology may and thompson transputers and routers components for concurrent machines inmos 1991 recently much effort is devoted to relate the efficiency measured by the dilation or the stretch factor to space requirements measured by the compactness or the total number of memory bits in a variety of compact routing methods eilam moran and zaks 10th international workshop on distributed algorithms wdag lecture notes in computer science vol 1151 springer berlin 1996 pp 191 205 fraigniaud and gavoille 8th annual acm symp on parallel algorithms and architectures spaa acm press new york 1996 gavoille and perennes proc sircco 96 carleton press 1996 pp 88 103 kranakis krizanc 13th annual symp on theoretical aspects of computer science stacs lecture notes in computer science vol 1046 springer berlin 1996 pp 529 540 meyer auf der heide and scheideler proc 37th symp on foundations of computer science focs november 1996 peleg and upfal j acm 36 1989 510 530 tse and lau proc sirocco 95 carleton press 1995 pp 123 134 we add new results in this direction for interval routing for the shortest path interval routing we apply a technique from flammini van leeuwen and marchetti spaccamela mfcs 95 lecture notes in computer science vol 969 springer berlin 1995 pp 37 49 to some interconnection networks shuffie exchange se cube connected cycles ccc butterfly bf and star s and get improved lower bounds on compactness in the form n 1 2 e any e 0 for se n log n for ccc and bf and n log log n log n 5 for s where n is the number of nodes in the corresponding network previous lower bounds for these networks were only constant fraigniaud and gavoille conpar 94 lecture notes in computer science vol 854 springer berlin 1994 pp 785 796 for the dilation bounded interval routing we give a routing algorithm with the dilation 1 5d and the compactness o n log n on n node networks with the diameter d it is the first nontrivial upper bound on the dilation bounded interval routing on general networks moreover we construct a network on which each interval routing with the dilation 1 5d 3 needs the compactness at least n it is an asymptotical improvement over the previous lower bounds in tse and lau proc sirocco 95 carleton press 1995 pp 123 134 and it is also better than independently obtained lower bounds in tse and lau proc computing the australasian theory symp cats 97 sydney australia february 1997

the distribution function inequality for a finite sum of finite products of toeplitz operators abstract a generalized area function associated with a finite sum of finite products of toeplitz operators is introduced a distribution function inequality is established for the generalized area function by using the distribution function inequality we characterize when a finite sum of finite products of toeplitz operators on the hardy space is a compact perturbation of a toeplitz operator

the representation and computation of generalized inverse at s 2 this paper presents a novel representation for the generalized inverse a t s 2 based on this we give an algorithm to compute this generalized inverse as an application we use gauss jordan elimination to compute the weighted moore penrose inverse a m n and the drazin inverse a d

bounded toeplitz products on bergman spaces of the unit ball abstract we consider the question for which square integrable analytic functions f and g on the unit ball the densely defined products t f t g are bounded on the weighted bergman spaces we prove results analogous to those we obtained in the setting of the unit disk and the polydisk

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

higher order implicit multistep methods for matrix differential equations abstract this paper proposes implicit multistep matrix methods for the numerical solution of stiff initial value matrix problems the study of matrix difference equations involving the matrix coefficients of the multistep method permits one to obtain convergence results as well as bounds for the global discretization error in terms of the data an illustrative example is included

a closed form solution of singular regular higher order difference initial and boundary value problems in this paper existence conditions and a closed form expression for solutions of coupled singular systems of higher order difference equations are given the approach avoids the computational drawbacks derived from the standard approach based on the consideration of an equivalent first order system

products of hankel operators on the fock space abstract for entire functions f and g we study the problem of when the hankel product h f h g is bounded or compact on the fock space f 2 this is a companion to sarason s toeplitz product problem which was completely solved for the fock space by cho park zhu in 2014 surprisingly our results here are different from the natural conjectures motivated by the toeplitz product problem

products of several toeplitz operators in this paper we give a necessary and sufficient condition for ta1ta2 tan ta1a2 an where the tai s are toeplitz operators on the hardy space of the unit disk we then show that ta1ta2ta3ta4ta5ta6 0 if and only if one of ai is identically zero a criteria for the compactness of ta1ta2 tan ta1a2 an is also given