estimates for schrodinger evolution equations on demontre que pour des donnees de cauchy dans l 1 r n la solution d une equation d evolution de schrodinger a coefficients constants d ordre 2m est uniformement bornee pour t 0 de borne 1 t c ou c est un entier c n 2m 1

generation of the integrated semigroups by superelliptic differential operators abstract let a be a superelliptic differential operator of order 2m introduced by e b davies e b davies uniformly elliptic operators with measurable coefficients j funct anal 132 1995 141 169 in the case of 2 m n he obtained the upper gaussian bound of the integral kernel representing e z a z c and the estimates of the l p operator norm of the semigroup for all p 1 the purpose of the present paper is to show that i a k for some constant k 0 generates an integrated semigroup on l p weighted l p space and l p l q to prove this we need norm estimates of e z a z c on each of these spaces also we get another norm estimate of e z a z c on l p when 2 m n without using the integral kernel this norm estimate is better than that in e b davies uniformly elliptic operators with measurable coefficients j funct anal 132 1995 141 169 and gives a better times of the integration of the integrated semigroup

space analyticity for the navier stokes and related equations with initial data inlp abstract we introduce a method of estimating the space analyticity radius of solutions for the navier stokes and related equations in terms of l p and l norms of the initial data the method enables us to express the space analyticity radius for 3d navier stokes equations in terms of the reynolds number of the flow also for the kuramoto sivashinsky equation we give a partial answer to a conjecture that the radius of space analyticity on the attractor is independent of the spatial period

further results on infinity norms as lyapunov functions for linear systems this note continues on the results proposed in two previous papers for computing vector 1 or infin norm based lyapunov functions for linear discrete time systems by presenting a finitely terminating algorithm for the construction of lyapunov functions of that class the algorithm utilizes the solution of a finite sequence of feasibility linear programs lps with very few constraints or equivalently very simple algebraic tests in contrast to solving the original problem where a bilinear matrix equation with rank and norm constraint needs to be solved

the minkowski lyapunov equation for linear dynamics theoretical foundations we consider the lyapunov equation for the linear dynamics which arises naturally when one seeks for a lyapunov function with a uniform exact decrease in this setting a solution to the lyapunov equation has been characterized only for quadratic lyapunov functions we demonstrate that the lyapunov equation is a well posed equation for strictly stable dynamics and a much more general class of lyapunov functions specified via minkowski functions of proper c sets which include euclidean and weighted euclidean vector norms polytopic and weighted polytopic 1 vector norms as well as vector semi norms induced by the minkowski functions of proper c sets furthermore we establish that the lyapunov equation admits a basic solution i e the unique solution within the class of minkowski functions associated with proper c sets finally we provide a characterization of the lower and upper approximations of the basic solution that converge pointwise and compactly to it while in addition the upper approximations satisfy the classical lyapunov inequality

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

integrated semigroups and the cauchy problem for systems in lp spaces abstract in this note we prove that under suitable hypotheses every homogeneous differential operator on lp r n n corresponding to a system which is well posed in l2 r n n generates an times integrated semigroup on lp r n n 1 n 1 2 1 p for some special systems of mathematical physics such as the wave equation or maxwell s equations this constant can be improved to be n 1 1 2 1 p

on input to state stability of min max nonlinear model predictive control in this paper we consider discrete time nonlinear systems that are affected possibly simultaneously by parametric uncertainties and other disturbance inputs the min max model predictive control mpc methodology is employed to obtain a controller that robustly steers the state of the system towards a desired equilibrium the aim is to provide a priori sufficient conditions for robust stability of the resulting closed loop system using the input to state stability iss framework first we show that only input to state practical stability can be ensured in general for closed loop min max mpc systems and we provide explicit bounds on the evolution of the closed loop system state then we derive new conditions for guaranteeing iss of min max mpc closed loop systems using a dual mode approach an example illustrates the presented theory

schrodinger type evolution equations in lp ω abstract let ap be a strongly elliptic operator of order 2m m n in lp 1 p a bounded domain of rn with dirichlet or neumann boundary conditions of concern is the cauchy problem for schrodinger type evolution equations in lp formula by showing that iap is the generator of a c0 group on a certain interpolation space we obtain results of wellposedness for which are stronger than those derived from the regularized or integrated groups on lp as a by product it is shown that iap is the generator of a ap r regularized group 0 on lp for all formula

elliptic differential operators on lie groups abstract each strongly elliptic operator in the enveloping lie algebra associated with a continuous representation of a lie group generates a holomorphic semigroup s whose action is determined by a universal integral kernel k we derive pointwise bounds and lp bounds on k and its derivatives for example if the operator is mth order and the group has dimension d then we prove that k t g at d m e b g m t l m 1 e t for all g g and t 0 where a b and are positive constants the derivative bounds have similar decrease properties as a function over g the correct singularity as a function of t and also reflect the joint analyticity of k one new feature in the analysis is a generalized nash inequality for the differential structure of the group representation and one application is to sobolev embeddings for lie groups

stabilizing model predictive control of hybrid systems in this note we investigate the stability of hybrid systems in closed loop with model predictive controllers mpc a priori sufficient conditions for lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion while allowing for discontinuous system dynamics and discontinuous mpc value functions for constrained piecewise affine pwa systems as prediction models we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions for quadratic mpc costs these conditions translate into a linear matrix inequality while for mpc costs based on 1 infin norms they are obtained as norm inequalities new ways for calculating low complexity piecewise polyhedral positively invariant sets for pwa systems are also presented an example illustrates the developed theory

approximation of local convoluted semigroups abstract we extend the trotter kato theorem on c 0 semigroups to local convoluted semigroups on dual spaces and apply these results to the general banach space setting compared to known results we obtain weaker convergence assumptions on the resolvent

model predictive control based on linear programming the explicit solution we study model predictive control mpc schemes for discrete time linear time invariant systems with constraints on inputs and states that can be formulated using a linear program lp in particular we focus our attention on performance criteria based on a mixed 1 norm namely 1 norm with respect to time and norm with respect to space first we provide a method to compute the terminal weight so that closed loop stability is achieved we then show that the optimal control profile is a piecewise affine and continuous function of the initial state and briefly describe the algorithm to compute it the piecewise affine form allows to eliminate online lp as the computation associated with mpc becomes a simple function evaluation besides practical advantages the availability of the explicit structure of the mpc controller provides an insight into the type of control action in different regions of the state space and highlights possible conditions of degeneracies of the lp such as multiple optima

minkowski terminal cost functions for mpc this technical communique delivers a systematic procedure for obtaining a suitable terminal cost function for model predictive control based on minkowski cost functions it is shown that for any given stabilizing linear state feedback control law and associated contractive proper c set there always exists a non trivial scaling of the contractive proper c set such that the associated minkowski function satisfies the standard mpc terminal cost stability inequality

criteria of asymptotic stability of differential and difference inclusions encountered in control theory abstract for a class of differential inclusions to which many of the practically important control systems can be reduced necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of lyapunov functions similar results are obtained for the corresponding class of difference inclusions