products of bergman space toeplitz operators on the polydisk motivated by recent works of ahern and breve rm c u breve rm c kovic on the disk we study the generalized zero product problem for toeplitz operators acting on the bergman space of the polydisk first we extend the results to the polydisk next we study the generalized compact product problem our results are new even on the disk as a consequence on higher dimensional polydisks we show that the generalized zero and compact product properties are the same for toeplitz operators in a certain case

commuting toeplitz operators on the segal bargmann space abstract consider two toeplitz operators t g t f on the segal bargmann space over the complex plane let us assume that g is a radial function and both operators commute under certain growth condition at infinity of f and g we show that f must be radial as well we give a counterexample of this fact in case of bounded toeplitz operators but a fast growing radial symbol g in this case the vanishing commutator t g t f 0 does not imply the radial dependence of f finally we consider toeplitz operators on the segal bargmann space over c n and n 1 where the commuting property of toeplitz operators can be realized more easily

commuting toeplitz operators with quasi homogeneous symbols on the segal bargmann space abstract let t t z l z k with l k n 0 be a toeplitz operator with monomial symbol acting on the segal bargmann space over the complex plane we determine the symbols of polynomial growth at infinity such that t and t z l z k commute on the space of all holomorphic polynomials by using polar coordinates we represent as an infinite sum r e i j j r e i j then we are able to reduce the above problem to the case of quasi homogeneous symbols j e i j we obtain the radial part j r in terms of the inverse mellin transform of an expression which is a product of gamma functions and a trigonometric polynomial if we allow operator symbols of higher growth at infinity we point out that in some of the cases more than one toeplitz operator t j e i j exists commuting with t

commutants of toeplitz operators with radial symbols on the fock sobolev space abstract in the setting of the fock space over the complex plane bauer and lee have recently characterized commutants of toeplitz operators with radial symbols under the assumption that symbols have at most polynomial growth at infinity their characterization states if one of the symbols of two commuting toeplitz operators is nonconstant and radial then the other must be also radial we extend this result to the fock sobolev spaces

exponential synchronization of a class of neural networks with sampled data control abstract this paper investigates the problem of the master slave synchronization for a class of neural networks with discrete and distributed delays under sampled data control by introducing some new terms a novel piecewise time dependent lyapunov krasovskii functional lkf is constructed to fully capture the available characteristics of real sampling information and nonlinear function vector of the system based on the lkf and wirtinger based inequality less conservative synchronization criteria are obtained to guarantee the exponential stability of the error system and then the slave system is synchronized with the master system the designed sampled data controller can be obtained by solving a set of linear matrix inequalities lmis which depend on the maximum sampling period and the decay rate the criteria are less conservative than the ones obtained in the existing works a numerical example is presented to illustrate the effectiveness and merits of the proposed method

commuting toeplitz operators on the hardy space of the bidisk on the hardy space of the bidisk we give a necessary and sufficient condition for a bounded symbol of a toeplitz operator that commutes with another toeplitz operator whose symbol is a certain type of bounded symbol

commuting toeplitz operators with pluriharmonic symbols let da z denote the lebesgue volume measure on the open unit ball bn f cn normalized so that the measure of bn equals 1 the 13ergman space l2 bn is the eiilbert space consisting of holomorphic functions on bn that are also in l2 bn da for f in l90 bn the toeplitz operator tf with symbol f is desned by t h p fh where p is the orthogonal projection from l2 bnnda onto ol2tbesda n called the bergman projection let dsr be the surface area measure on the unit sphere sn for 1 p 007 h s4 is the banach space of holomorphic functions on bn with the norm defined by

almost sure stability of markov jump linear systems with deterministic switching the technical note studies a class of linear systems whose piecewise constant dynamic matrix is subject to both stochastic jumps governed by a markov chain and deterministic switches these systems will be dubbed switching dynamics markov jump linear systems sd mjls sufficient conditions for exponential almost sure stability eas stability are established under either hard or average constraints on the dwell time between switching instants the proof relies on easy to check norm contractivity conditions and the ergodic law of large numbers

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

finite time stability and stabilization for ito type stochastic markovian jump systems with generally uncertain transition rates abstract this paper investigates the problems of finite time stability and stabilization for stochastic markovian jump systems with generally uncertain transition rates smjswgutrs firstly a less conservative stability criterion is presented by a mode dependent approach then the state feedback controller and observer based controller are designed by a cone complementary linearization method and two specific algorithms are presented finally an example is used to illustrate our results

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

brief paper markov jump linear systems with switching transition rates mean square stability with dwell time the stability of a class of markov jump linear systems characterized by piecewise constant transition rates and system dynamics is investigated for these switching markov jump linear systems mean square stability is analyzed through the time evolution of the second order moment of the state the main result is a sufficient condition that guarantees mean square stability under constraints on the dwell time between switching instants an alternative condition based on kronecker calculus is worked out it is shown that both the stability criteria admit an lmi implementation

stability for delayed switched systems with markov jump parameters and generally incomplete transition rates abstract exponential mean square stability for delayed switched systems with markov jump parameters and generally incomplete transition rates is discussed the switching dynamics among the operation modes are considered to be governed by a high level with average dwell time switching adts and a low level with stochastic markov switching many practical systems such as general economic model subject to unpredictable structural changes can be described by switching markov jump systems smjss with generally incomplete transition rates by resorting to average dwell time switching approach sufficient conditions are proposed to ensure the underlying system exponentially mean square stable finally the theoretical results are applied to a general economic model to demonstrate the effectiveness applicability and superiority of the main results

brief paper stability and stabilization of markovian jump linear systems with partly unknown transition probabilities in this paper the stability and stabilization problems of a class of continuous time and discrete time markovian jump linear system mjls with partly unknown transition probabilities are investigated the system under consideration is more general which covers the systems with completely known and completely unknown transition probabilities as two special cases the latter is hereby the switched linear systems under arbitrary switching moreover in contrast with the uncertain transition probabilities studied recently the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements the sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via lmis formulation and the relation between the stability criteria currently obtained for the usual mjls and switched linear systems under arbitrary switching are exposed by the proposed class of hybrid systems two numerical examples are given to show the validity and potential of the developed results

stability analysis of markov switched stochastic differential equations with both stable and unstable subsystems abstract this paper discusses the asymptotic stability of markov switched stochastic differential equations by using the method of multiple lyapunov functions we provide sufficient conditions for stochastic asymptotic stability of markov switched stochastic differential equations with both stable and unstable subsystems via the inequality based on the multiple lyapunov functions and the stationary distribution of markovian switching process particularly our results include some existing results as special cases and improve some results in the literature two examples are given to illustrate the effectiveness of the obtained results

commuting toeplitz operators with pluriharmonic symbols on the fock space abstract in the setting of the bergman space over the disk or the ball it has been known that two toeplitz operators with bounded pluriharmonic symbols can semi commute only in the trivial cases in this paper we study the analogues on the fock space over the multi dimensional complex space as is the case in various other settings we are naturally led to the problem of characterizing a certain type of fixed points of the berezin transform for such fixed points we obtain a complete characterization by means of eigenfunctions of the laplacian we also obtain other characterizations in particular it turns out that there are many nontrivial cases on the fock space for semi commuting toeplitz operators with pluriharmonic symbols all in all our results reveal that the situation on the fock space appears to be much more complicated than that on the classical bergman space setting which partly is caused by the unboundedness of the operator symbols some of our results are restricted to the one variable case and the corresponding several variable case is left open

commuting toeplitz operators on the polydisk we obtain characterizations of essentially commuting toeplitz operators with pluriharmonic symbols on the bergman space of the polydisk we show that commuting and essential commuting properties are the same for dimensions bigger than 2 while they are not for dimensions less than or equal to 2 also the corresponding results for semi commutators are obtained

stabilization of switched linear systems with quantized output and switching delays this paper addresses the problem of designing time varying quantizers for the stabilization of switched linear systems with quantized output and switching delays the detection delays of switches are assumed to be time varying but bounded and the dwell time of the switching signal is assumed to be larger than the maximum delay given a switching controller we analyze reachable sets of the closed loop state by using a common lyapunov function and then construct a quantizer that guarantees asymptotic stability a sufficient condition for the existence of such a quantizer is characterized by the maximum switching delay and the dwell time

razumikhin type theorem for stochastic functional differential equations with levy noise and markov switching abstractthis paper is devoted to study the well known razumikhin type theorem for a class of stochastic functional differential equations with levy noise and markov switching in comparison to the standard gaussian noise levy noise and markov switching make the analysis more difficult owing to the discontinuity of its sample paths in this paper we attempt to overcome this difficulty by using the razumikhin method and lyapunov functions we obtain several razumikhin type theorems to prove the pth moment exponential stability of the suggested system based on these results we further discuss the pth moment exponential stability of stochastic delay differential equations with levy noise and markov switching in particular the results obtained in this paper improve and generalise some previous works given in the literature finally an example is provided to illustrate the effectiveness of the theoretical results

stabilization of chaotic systems under variable sampling and state quantized controller abstract this paper investigates the problem of stabilization for chaotic systems based on a t s fuzzy model under sampled data control and state quantization a novel lyapunov krasovskii functional lkf is introduced to the sampled data systems the benefit of the new approach is that the lkf develops more information about the actual sampling pattern in addition some symmetric matrices involved in the lkf are not required to be positive definite based on a recently introduced wirtinger based integral inequality that has been shown to be less conservative than jensen s inequality much less conservative stabilization conditions are obtained to ensure the maximal sampling period then the corresponding sampled data controllers can be synthesized by solving a set of linear matrix inequalities lmis finally an illustrative example is given to show the feasibility and effectiveness of the proposed method

slow state variables feedback stabilization for semi markov jump systems with singular perturbations the slow state variables feedback stabilization problem for semi markov jump discrete time systems with slow sampling singular perturbations is discussed in this work a new fairly comprehensive system model semi markov jump system with singular perturbations which is more general than markov jump model is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems based on a slow state variables feedback control scheme a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated with the help of the discrete time semi markov kernel approach some sojourn time dependent and less conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed finally an illustrative example is given to show the superiority and usefulness of the proposed method

on reciprocal transformation of a 3 component camassa holm type system abstract we construct a reciprocal transformation to connect a 3 component camassa holm type system proposed by geng and xue with the first negative flow in a generalized mkdv hierarchy we discuss the hamiltonian pair and infinitely many conserved quantities for the generalized mkdv hierarchy

stabilisation of mode dependent singular markovian jump systems with generally uncertain transition rates this paper is devoted to investigating the stability and stabilisation problems for continuous time mode dependent singular markovian jump systems smjss with generally uncertain transition rates gutrs first we establish a sufficient condition in terms of a set of coupled linear matrix inequalities lmis to ensure the systems to be regular impulse free and stochastically stable then we design a mode dependent state feedback controller to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method