the h infty calculus and sums of closed operators we develop a very general operator valued functional calculus for operators with an h infty calculus we then apply this to the joint functional calculus of two sectorial operators when one has an h infty calculus using this we prove theorem of dore venni type on sums of sectorial operators and apply our results to the problem of l p maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of banach spaces are essential here in the final section we exploit the special banach space structure of l 1 spaces and c k spaces to obtain some more detailed results in this setting

the h calculus and sums of closed operators we develop a very general operator valued functional calcu lus for operators with an h 1 calculus we then apply this to the joint functional calculus of two commuting sectorial operators when one has an h 1 calculus using this we prove theorem of dore venni type on sums of commuting sectorial operators and apply our results to the problem of lp maximal regularity our main assumption is the r boundedness of certain sets of operators and therefore methods from the geometry of ba nach spaces are essential here in the final section we exploit the special banach space structure of l1 spaces and c k spaces to obtain some more detailed results in this setting

distributed robust estimation over randomly switching networks using h consensus the paper considers a distributed robust estimation problem over a network with markovian randomly varying topology the objective is to deal with network variations locally by switching observer gains at affected nodes only we propose sufficient conditions which guarantee a suboptimal h level of relative disagreement of estimates in such observer networks when the status of the network is known globally these sufficient conditions enable the network gains to be computed by solving certain lmis when the nodes are to rely on a locally available information about the network topology additional rank constraints are used to condition the gains given this information the results are complemented by necessary conditions which relate properties of the interconnection graph laplacian to the mean square detectability of the plant through measurement and interconnection channels

stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic riccati equation this note addresses the jump linear quadratic problem of markov jump linear systems and the associated algebraic riccati equation necessary and sufficient conditions for stability of the optimal control and positiveness of riccati solutions are developed we show that the concept of weak detectability is not only a sufficient condition for the finiteness of cost functional to imply stability of the associated trajectory but also a necessary one this together with a characterization developed here for the kernel of the riccati solution allows us to show that the control solution stabilizes the system if and only if the system is weakly detectable and that the riccati solution is positive definite if and only if the system is weakly observable the connection between the algebraic riccati equation and the control problem is made as far as the minimal positive semidefinite solution for the algebraic riccati equation is identified with the optimal solution of the linear quadratic problem illustrative numerical examples and comparisons are included

spectral tests for observability and detectability of periodic markov jump systems with nonhomogeneous markov chain this paper addresses observability and detectability of discrete time periodic systems with nonhomogeneous markov jump parameter popov belevitch hautus pbh type criteria are proposed for the concerned structural properties it is shown that different from stochastic systems with constant coefficients or homogeneous markov chain the spectral criteria of considered plants do not rely on a single operator but on a finite sequence of linear evolution operators by use of the obtained detectability criterion an extended lyapunov theorem is established which relates asymptotic mean square stability to a periodic lyapunov equation further a difference riccati equation with periodic coefficients is studied and some sufficient conditions are presented for the existence of stabilizing solution

difference norms for vector valued bessel potential spaces with an application to pointwise multipliers abstract in this paper we prove a randomized difference norm characterization for bessel potential spaces with values in umd banach spaces the main ingredients are r boundedness results for fourier multiplier operators which are of independent interest as an application we characterize the pointwise multiplier property of the indicator function of the half space on these spaces all results are proved in the setting of weighted spaces

batalin vilkovisky algebras and two dimensional topological field theories by a batalin vilkovisky algebra we mean a graded commutative algebraa together with an operator a a 1 such that 2 0 and a a is a graded derivation ofa for alla a in this article we show that there is a natural structure of a batalin vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions we make use of a technique from algebraic topology the theory of operads

γ radonifying operators and umd valued littlewood paley stein functions in the hermite setting on bmo and hardy spaces abstract in this paper we study littlewood paley stein functions associated with the poisson semigroup for the hermite operator on functions with values in a umd banach space b if we denote by h the hilbert space l 2 0 d t t h b represents the space of radonifying operators from h into b we prove that the hermite square function defines bounded operators from bmo l r n b respectively h l 1 r n b into bmo l r n h b respectively h l 1 r n h b where bmo l and h l 1 denote bmo and hardy spaces in the hermite setting also we obtain equivalent norms in bmo l r n b and h l 1 r n b by using littlewood paley stein functions as a consequence of our results we establish new characterizations of the umd banach spaces

kodaira spencer theory of gravity and exact results for quantum string amplitudes we develop techniques to compute higher loop string amplitudes for twistedn 2 theories with 3 i e the critical case an important ingredient is the discovery of an anomaly at every genus in decoupling of brst trivial states captured to all orders by a master anomaly equation in a particular realization of then 2 theories the resulting string field theory is equivalent to a topological theory in six dimensions the kodaira spencer theory which may be viewed as the closed string analog of the chern simons theory using the mirror map this leads to computation of the number of holomorphic curves of higher genus curves in calabi yau manifolds it is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingn 2 theory relations withc 1 strings are also pointed out

mode independent cal h _ infty filters for markovian jump linear systems this note addresses the problem of hinfin filtering for continuous time linear systems with markovian jumping parameters the main contribution of the note is to provide a method for designing an asymptotically stable linear time invariant hinfin filter for systems where the jumping parameter is not accessible the cases where the transition rate matrix of the markov process is either exactly known or unknown but belongs to a given polytope are treated the robust hinfin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a lyapunov function that depends on the uncertain parameters is developed the proposed filter designs are given in terms of linear matrix inequalities

maximal regularity of second order equations with delay abstract we characterize existence and uniqueness of solutions of an inhomogeneous abstract delay equation in holder spaces the method is based on the theory of operator valued fourier multipliers

robust stability of a class of uncertain markov jump nonlinear systems this note addresses the problem of robust stability analysis for a class of markov jump nonlinear systems subject to polytopic type parameter uncertainty a condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed an estimate of a robust domain of attraction of the origin is also provided the approach is based on a stochastic lyapunov function with polynomial dependence on the system state and uncertain parameters a numerical example illustrates the proposed result

a novel iterative algorithm for solving coupled riccati equations abstract in this paper a novel iterative algorithm is developed for solving the coupled algebraic riccati equation arising from the quadratic optimal control problem for continuous time markovian jump linear systems first two existing iterative algorithms to solve the coupled riccati matrix equation are reviewed next based on analysis for these two algorithms a new iterative algorithm that combines both the information in the current iterative step and the information in the last iterative step is proposed it is shown that the proposed algorithm with proper initial conditions can monotonically converge to the unique positive definite solution of the coupled riccati matrix equation if the associated markovian jump system is stochastically stabilizable also numerical examples show that the presented algorithm is faster than some previous algorithms when the weighted parameter is appropriately selected

on operator valued sequences of multipliers and r boundedness in recent papers cf j l arregui o blasco p q summing sequences j math anal appl 274 2002 812 827 j l arregui o blasco p q summing sequences of operators quaest math 26 2003 441 452 s aywa j h fourie on summing multipliers and applications j math anal appl 253 2001 166 186 j h fourie i rontgen banach space sequences and projective tensor products j math anal appl 277 2 2003 629 644 the concept of p q summing multiplier was considered in both general and special context it has been shown that some geometric properties of banach spaces and some classical theorems can be described using spaces of p q summing multipliers the present paper is a continuation of this study whereby multiplier spaces for some classical banach spaces are considered the scope of this research is also broadened by studying other classes of summing multipliers let e x and f y be two banach spaces whose elements are sequences of vectors in x and y respectively and which contain the spaces c00 x and c00 y of all x valued and y valued sequences which are eventually zero respectively generally spoken a sequence of bounded linear operators un l x y is called a multiplier sequence from e x to f y if the linear operator from c00 x into c00 y which maps xi c00 x onto unxn c00 y is bounded with respect to the norms on e x and f y respectively several cases where e x and f y are different classical spaces of sequences including for instance the spaces rad x of almost unconditionally summable sequences in x are considered several examples properties and relations among spaces of summing multipliers are discussed important concepts like r bounded semi r bounded and weak r bounded from recent papers are also considered in this context

discrete state estimators for systems on a lattice we address the problem of estimating discrete variables in a class of deterministic transition systems in which the continuous variables are available for measurement we propose a novel approach to the estimation of discrete variables using lattice theory that overcomes some of the severe complexity issues encountered in previous work the methodology proposed for the estimation of discrete variables is general as it is applicable to any observable system extensions generalize the approach to nondeterministic transition systems the proposed estimator is finally constructed for a multi robot system involving two teams competing against each other

computational tools for the safety control of a class of piecewise continuous systems with imperfect information on a partial order this paper addresses the two agent safety control problem for piecewise continuous systems with disturbances and imperfect state information in particular we focus on a class of systems that evolve on a partial order and whose dynamics preserve the ordering while the safety control problem with imperfect state information is prohibitive for general classes of nonlinear and hybrid systems the class of systems considered in this paper admits an explicit solution we compute this solution with linear complexity discrete time algorithms that are guaranteed to terminate the proposed algorithms are illustrated on a two vehicle collision avoidance problem and implemented on a hardware roundabout test bed

on fourier multiplier transformations of banach valued functions we obtain analogues of the mihlin multiplier theorem and littlewood paley inequalities for functions with values in a suitable banach space b the requirement on b is that it have the unconditionality property for martingale difference sequences

lagrange asymptotic stability of weak detectable markov jump linear systems with bounded long run average cost in this note we study the stability of markov jump linear systems with additive noise we show in a rather direct manner that the system is mean square lagrange asymptotic stable if and only if the long run average cost is bounded and the system is weak detectable generalizing previous results employing observability notions in control applications this means that for detectable systems closed loop controls incurring in bounded long run average cost are ensured to be stabilizing a numerical example is included

cal h representation and applications to generalized lyapunov equations and linear stochastic systems this paper introduces an h representation method to express an n2 1 vector x as x h x tilde based on the introduced h representation approach several topics are extensively discussed including the generalized lyapunov equations gles arising from stochastic control stochastic observability generalized d stability and d stabilization weak stability and stabilization a necessary and sufficient condition for the existence and uniqueness of the symmetric and skew symmetric solutions of gles is presented respectively moreover the solution structure of gles is also clarified through the h representation method several necessary and sufficient conditions are also obtained for stochastic observability generalized d stability and d stabilization weak stability and stabilization

non autonomous maximal regularity for forms given by elliptic operators of bounded variation abstract we show maximal l p regularity for non autonomous cauchy problems provided the trace spaces are stable in some parameterized sense and the time dependence is of bounded variation in particular on l 2 for lipschitz domains and under mixed boundary conditions we obtain maximal l p regularity for all p 1 2 for elliptic operators with coefficients a i j c satisfying a i j x bv uniformly in x

on semi r boundedness and its applications abstract r boundedness is a randomized boundedness condition for sets of operators which in recent years has found many applications in the maximal regularity theory of evolution equations stochastic evolution equations spectral theory and vector valued harmonic analysis however in some situations additional geometric properties such as pisier s property are required to guaranty the r boundedness of a relevant set of operators in this paper we show that a weaker property called semi r boundedness can be used to avoid these geometric assumptions in the context of schauder decompositions and the h calculus furthermore we give weaker conditions for stochastic integrability of certain convolutions

observability and detectability of discrete time stochastic systems with markovian jump abstract this paper studies detectability and observability of markov jump discrete time linear stochastic systems with multiplicative noise mjdls for short the relations between some concepts of detectability and observability are established these relations together with equivalent expressions of observability gramian allow us to obtain some other sufficient and necessary conditions of detectability and observability as applications discrete time stochastic lyapunov equations and stochastic discrete algebraic riccati equations sdare are discussed

operator valued fourier multiplier theorems on lp x and geometry of banach spaces abstract this paper gives the optimal order l of smoothness in the mihlin and hormander conditions for operator valued fourier multiplier theorems this optimal order l is determined by the geometry of the underlying banach spaces e g fourier type this requires a new approach to such multiplier theorems which in turn leads to rather weak assumptions formulated in terms of besov norms

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

operator valued fourier haar multipliers abstract criteria are given to ensure the boundedness of fourier haar multiplier operators from l p 0 1 x to l q 0 1 y where the fourier haar multiplier sequences come not from r as in the classical setting but rather from the space of bounded linear operators from a banach space x into a banach space y

on operad structures of moduli spaces and string theory we construct a real compactification of the moduli space of punctured rational algebraic curves and show how its geometry yields operads governing homotopy lie algebras gravity algebras and batalin vilkovisky algebras these algebras appeared recently in the context of string theory and we give a simple deduction of these algebraic structures from the formal axioms of conformal field theory and string theory

singular convolution integrals with operator valued kernel we study operators f mapsto kf of the form kf t int bf r n k t s f s rm d s where f is a vector valued function and k an operator valued singular kernel sufficient conditions for boundedness on lp spaces of umd valued functions are given in terms of a hormander type condition involving r boundedness the results cover large classes of kernels and also provide new proofs of recent operator valued fourier multiplier theorems moreover they give new information about families of singular integral operators

on unified concepts of detectability and observability for continuous time stochastic systems this paper is concerned with detectability and observability of continuous time stochastic linear systems by adopting the idea used in defining these two concepts for time varying systems and markovian jump linear systems that have been studied in the literature corresponding definitions for continuous time stochastic linear systems are proposed these two definitions are not only able to unify some recent definitions on these two concept reported in the literature but also allow us to propose an efficient rank criterion to test observability of continuous time stochastic linear systems it seems that this rank criterion is quite analogous to the rank criterion for deterministic linear systems with the help of these two concepts and the new criteria the stochastic lyapunov equation is revisited and some recent published work on this equation are generalized numerical examples are given to illustrate the effectiveness of the proposed approach

observability analysis of conewise linear systems via directional derivative and positive invariance techniques belonging to the broad framework of hybrid systems conewise linear systems clss form a class of lipschitz piecewise linear systems subject to state triggered mode switchings motivated by state estimation of nonsmooth switched systems this paper exploits directional derivative and positive invariance techniques to characterize finite time and long time local observability of a general cls for the former observability notion directional derivative results are developed from the simple switching property and they yield improved observability conditions for the latter notion we focus on the case where a nominal trajectory has finitely many switchings in order to characterize long time behaviors of the cls necessary and sufficient conditions are obtained for the interior of a positively invariant cone by employing these conditions we establish connections between finite time and long time local observability underlying positive invariance properties are unveiled

on the observability and detectability of continuous time markov jump linear systems the paper introduces a new detectability concept for continuous time markov jump linear systems with finite markov space that generalizes previous concepts found in the literature the detectability in the weak sense is characterized as mean square detectability of a certain related stochastic system making both detectability senses directly comparable the concept can also ensure that the solution of the coupled algebraic riccati equation associated to the quadratic control problem is unique and stabilizing making other concepts redundant the paper also obtains a set of matrices that plays the role of the observability matrix for deterministic linear systems and it allows geometric and qualitative properties tests for weak observability and detectability of a system are provided the first consisting of a simple rank test similar to the usual observability test for deterministic linear systems

the operator valued marcinkiewicz multiplier theorem and maximal regularity given a closed linear operator on a umd space we characterize maximal regularity of the non homogeneous problem

a t1 theorem for integral transformations with operator valued kernel we consider generalized calderon zygmund operators whose kernel k x y takes values in l x continuous linear operators on the banach space x and satis es variants of the classical standard estimates involving rboundedness which has recently become a crucial notion in connection with operator valued singular integrals boundedness criteria in the spirit of the t1 theorem of david and journe are proved for such operators on the bochner spaces lp rn x where 1 p and x is a umd space for some results x is also required to have pisier s property in the special case t1 t 1 0 we obtain an essentially complete analogue of the scalar valued theorem we also provide su cient conditions for the general case but they are stronger in general than the necessary t1 t 1 bmo type conditions although they reduce to them in the classical situation a counterexample is given to show that the natural necessary conditions are not su cient in general

on the relation between open and closed topological strings we discuss the relation between open and closed string correlators using topological string theories as a toy model we propose that one can reconstruct closed string correlators from the open ones by considering the hochschild cohomology of the category of d branes we compute the hochschild cohomology of the category of d branes in topological landau ginzburg models and partially verify the conjecture in this case

topological conformal field theories and calabi yau categories abstract this is the first of two papers which construct a purely algebraic counterpart to the theory of gromov witten invariants at all genera these gromov witten type invariants depend on a calabi yau a category which plays the role of the target in ordinary gromov witten theory when we use an appropriate a version of the derived category of coherent sheaves on a calabi yau variety this constructs the b model at all genera when the fukaya category of a compact symplectic manifold x is used it is shown under certain assumptions that the usual gromov witten invariants are recovered the assumptions are that open closed gromov witten theory can be constructed for x and that the natural map from the hochschild homology of the fukaya category of x to the ordinary homology of x is an isomorphism

on the detectability and observability of continuous stochastic markov jump linear systems abstract this paper is concerned with the detectability and observability of continuous linear stochastic systems subject to markov jump by introducing some operators we investigate the relationship between some different concepts of detectability and observability and obtain their sufficient and necessary conditions continuous time stochastic lyapunov equations and stochastic continuous algebraic riccati equations are also discussed to serve as analysis tools

dunkl spectral multipliers with values in umd lattices we show a h ormander spectral multiplier theorem for a a 0 otimes mathrm id y acting on the bochner space l p mathbb r d h 2 kappa y where a 0 is the dunkl laplacian h 2 kappa a weight function invariant under the action of a reflection group and y is a umd banach lattice we follow hereby a transference method developed by bonami clerc and dai xu passing through a marcinkiewicz multiplier theorem on the sphere we hereby generalize works for a 0 delta acting on l p mathbb r d dx by girardi weis hyt onen and others before we apply our main result to maximal regularity for cauchy problems involving a