sampling and interpolation in large bergman and fock spaces we obtain sampling and interpolation theorems in weighted spaces of analytic functions for radial weights of arbitrary more rapid than polynomial growth we give an application to invariant subspaces of arbitrary index in large weighted bergman spaces

krein space quantization in curved and flat spacetimes we re examine in detail a canonical quantization method a la gupta bleuler in which the fock space is built over a so called krein space this method has already been successfully applied to the massless minimally coupled scalar field in de sitter spacetime for which it preserves covariance here it is formulated in a more general context an interesting feature of the theory is that although the field is obtained by canonical quantization it is independent of bogoliubov transformations moreover no infinite term appears in the computation of t mean values and the vacuum energy of the free field vanishes 0t000 0 we also investigate the behaviour of the krein quantization in minkowski space for a theory with interaction we show that one can recover the usual theory with the exception that the vacuum energy of the free theory is zero

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

a predictive control scheme for systems with variable time delay this article deals with the robust control design problem for linear time invariant systems affected by variable feedback delay constraints on the system state are considered in the system description the starting point is the construction of a predictive control law which guarantees the existence of a nonempty robust positive invariant rpi set with respect to the closed loop dynamics subsequently an iterative algorithm is proposed in order to obtain an approximation of the maximal rpi set the problem can be treated in the framework of piecewise affine systems due to the explicit formulations of the control law obtained via multiparametric programming

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

on the stress energy tensor of quantum fields in curved spacetimes comparison of different regularization schemes and symmetry of the hadamard seeley dewitt coefficients we review a few rigorous and partly unpublished results on the regularisation of the stress energy in quantum field theory on curved spacetimes 1 the symmetry of the hadamard seeley dewitt coefficients in smooth riemannian a lorentzian spacetimes 2 the equivalence of the local function and the hadamard point splitting procedure in smooth static spacetimes 3 the equivalence of the dewitt schwinger and the hadamard point splitting pro cedure in smooth riemannian and lorentzian spacetimes

bergman spaces with exponential weights abstract in this paper we introduce a kind of bergman space a p on the unit disk d with exponential weights which cover those defined by borichev et al 2007 6 we obtain upper and lower bound estimates on the bergman kernel as an application we discuss the bergman projection and duality

parameter dependent lyapunov functions for discrete time systems with time varying parametric uncertainties abstract in this paper we consider discrete time systems with polytopic time varying uncertainty we look for a class of parameter dependent lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter we show that extending the new discrete time stability condition proposed by de oliveira et al systems control lett 36 1999 135 to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a lyapunov function this allows to check asymptotic stability of the system under study the obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem

local causal structures hadamard states and the principle of local covariance in quantum field theory in the framework of the algebraic formulation we discuss and analyse some new features of the local structure of a real scalar quantum field theory in a strongly causal spacetime in particular we use the properties of the exponential map to set up a local version of a bulk to boundary correspondence the bulk is a suitable subset of a geodesic neighbourhood of an arbitrary but fixed point p of the underlying background while the boundary is a part of the future light cone having p as its own tip in this regime we provide a novel notion for the extended algebra of wick polynomials on the aforesaid cone and on the one hand we prove that it contains the information of the bulk counterpart via an injective homomorphism while on the other hand we associate to it a distinguished state whose pull back in the bulk is of hadamard form the main advantage of this point of view arises if one uses the universal properties of the exponential map and of the light cone in order to show that for any two given backgrounds m and m and for any two subsets of geodesic neighbourhoods of two arbitrary points it is possible to engineer the above procedure such that the boundary extended algebras are related via a restriction homomorphism this allows for the pull back of boundary states in both spacetimes and thus to set up a machinery which permits the comparison of expectation values of local field observables in m and m

a dynamic output feedback controller for ncs based on delay estimates the stabilization of a network controlled system including a global time varying delay is investigated in this note this delay is considered to be unknown but it is assumed that a bounded error estimate is available the exponential uncertainty induced by the time varying delay is decomposed into the sum of a polytopic term and an uncertain bounded term sufficient conditions to design a dynamic output feedback controller depending on an estimate of the time varying delay are proposed as linear matrix inequalities an illustration shows how our methodology enlarges the design techniques of the literature

construction of ym 4 with an infrared cutoff we provide the basis for a rigorous construction of the schwinger functions of the pure su 2 yang mills field theory in four dimensions in the trivial topological sector with a fixed infrared cutoff but no ultraviolet cutoff in a regularized axial gauge the construction exploits the positivity of the axial gauge at large field for small fields a different gauge more suited to perturbative computations is used this gauge and the corresponding propagator depends on large background fields of lower momenta the crucial point is to control in a non perturbative way the combined effect of the functional integrals over small field regions associated to a large background field and of the counterterms which restore the gauge invariance broken by the cutoff we prove that this combined effect is stabilizing if we use cutoffs of a certain type in momentum space we check the validity of the construction by showing that slavnov identities which express infinitesimal gauge invariance do hold non perturbatively

delay dependent sampled data control based on delay estimates in this paper the sampled data stabilization of linear time invariant systems with feedback delay is considered we assume that the delay is time varying and that its value is approximatively known we investigate how to use the available information about the evolution of delays for adapting the control law in real time numerical methods for the design of a delay dependent controller are presented this allows for providing a control for some cases in which the stabilization cannot be ensured using a controller with a fixed structure

a new approach for analysis and synthesis of time varying systems in this paper new techniques are developed for the analysis of linear time varying ltv systems these lead to a formally simple treatment of robust control problems for ltv systems allowing methods more usually restricted to time invariant systems to be employed in the time varying case as an illustration of this methodology the so called h sub spl infin synthesis problem is solved for ltv systems

asymptotic behavior of eigenvalues of toeplitz operators on the weighted analytic spaces abstract in this paper we consider toeplitz operators on a class of analytic function spaces including standard bergman spaces on the unit disc and bargman fock spaces we give a complete characterization of those compact operators whose eigenvalues have a prescribed slow decay to zero

a note on sampled data stabilization of lti systems with aperiodic sampling in this technical note we are concerned with linear matrix inequality lmi approaches for solving sampled data state feedback control design problems of linear time invariant systems this short contribution discusses a simple alternative to a family of lmi approaches based on the polytopic linear difference inclusion representation of the original problem with the aid of the so called matrix dilation technique the proposed condition is capable of being directly derived from the discrete time lyapunov inequality without the polytopic modeling finally numerical experiments are given to illustrate the results

cal h _ infty delay scheduled control of linear systems with time varying delays this paper deals with h infin delay scheduled control of linear systems with time varying delays first a new model transformation is given which allows to provide a unified approach to stability analysis and state feedback control synthesis for time delay systems represented in linear fractional transformation lft form a new type of controller is then synthesized where the state feedback is scheduled by the value of the delay delay scheduled controllers the results are provided in terms of linear matrix inequalities lmis which are known to be efficiently solvable

conformal generally covariant quantum field theory the scalar field and its wick products in this paper we generalize the construction of generally covariant quantum theories given in bfv03 to encompass the conformal covariant case after introducing the abstract framework we discuss the massless conformally coupled klein gordon field theory showing that its quantization corresponds to a functor between two certain categories at the abstract level the ordinary fields could be thought of as natural transformations in the sense of category theory we show that the wick monomials without derivatives wick powers can be interpreted as fields in this generalized sense provided a non trivial choice of the renormalization constants is given a careful analysis shows that the transformation law of wick powers is characterized by a weight and it turns out that the sum of fields with different weights breaks the conformal covariance at this point there is a difference between the previously given picture due to the presence of a bigger group of covariance it is furthermore shown that the construction does not depend upon the scale appearing in the hadamard parametrix used to regularize the fields finally we briefly discuss some further examples of more involved fields

some spectral properties of the canonical solution operator to on weighted fock spaces abstract we characterize the schatten class membership of the canonical solution operator to acting on l 2 e 2 where is a subharmonic function with a doubling measure the obtained characterization is in terms of as part of our approach we study hankel operators with anti analytic symbols acting on the corresponding fock space of entire functions in l 2 e 2

dimensional regularization in position space and a forest formula for epstein glaser renormalization we reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time ordered products as solutions to the induction scheme of epstein glaser this closed expression which we call the epstein glaser forest formula is analogous to zimmermann s forest formula for bph renormalization for scalar fields the resulting renormalization method is always applicable we compute several examples we also analyze the hopf algebraic aspects of the combinatorics our starting point is the main theorem of renormalization of stora and popineau and the arising renormalization group as originally defined by stuckelberg and petermann

an lmi approach to stability analysis of coupled parabolic systems we analyze the exponential stability of a class of distributed parameter systems the system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients we approximate the coefficients by splitting space domains but take into account approximation errors during stability analysis using a quadratic lyapunov function we obtain sufficient conditions for exponential stability in terms of linear matrix inequalities

bounds for the remainders of uncertain matrix exponential and sampled data control of polytopic linear systems this paper determines an explicit upper bound to the norm of any given degree of the taylor s expansion remainder for the matrix exponential function it depends on the spectral norm and the corresponding measure of a square matrix the generalization to cope with uncertain polytopic matrices follows from the definition of a norm and a measure for this mathematical entity and the determination of the corresponding upper bound for the expansion remainder naturally the results are applied to robust stability analysis and state feedback control synthesis of sampled data polytopic systems it is shown that a sampled data uncertain system obtained from a continuous time polytopic one can be expressed through a nonconservative sufficient condition by a feedback interconnection of a discrete time polytopic system and a norm bounded linear operator academical examples illustrate the theoretical results

micro local approach to the hadamard condition in quantum field theory on curved space time for the two point distribution of a quasi free klein gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space time we prove the equivalence of 1 the global hadamard condition 2 the property that the feynman propagator is a distinguished parametrix in the sense of duistermaat and hormander and 3 a new property referred to as the wave front set spectral condition wfssc because it is reminiscent of the spectral condition in axiomatic quantum field theory on minkowski space results in micro local analysis such as the propagation of singularities theorem and the uniqueness up toc of distinguished parametrices are employed in the proof we include a review of kay and wald s rigorous definition of the global hadamard condition and the theory of distinguished parametrices specializing to the case of the klein gordon operator on a globally hyperbolic space time as an alternative to a recent computation of the wave front set of a globally hadamard two point distribution on a globally hyperbolic curved space time given elsewhere by kohler to correct an incomplete computation in 32 we present a version of this computation that does not use a deformation argument such as that used in fulling narcowich and wald and is independent of the cauchy evolution argument of fulling sweeny and wald both of which are relied upon in kohler s proof this leads to a simple micro local proof of the preservation of hadamard form under cauchy evolution first shown by fulling sweeny and wald relying only on the propagation of singularities theorem in another paper 33 the equivalence theorem is used to prove a conjecture by kay that a locally hadamard quasi free klein gordon state on any globally hyperbolic curved space time must be globally hadamard

the epstein glaser approach to perturbative quantum field theory graphs and hopf algebras the paper aims at investigating perturbative quantum field theory in the approach of epstein and glaser eg and in particular its formulation in the language of graphs and hopf algebras has various has are encountered each one associated with a special combination of physical concepts such as normalization localization pseudounitarity causal regularization and renormalization the algebraic structures representing the perturbative expansion of the s matrix are imposed on operator valued distributions equipped with appropriate graph indices translation invariance ensures the algebras to be analytically well defined and graded total symmetry allows to formulate bialgebras the algebraic results are given embedded in the corresponding physical framework covering the two eg versions by fredenhagen and scharf that differ with respect to the concrete recursive implementation of causality besides the ultraviolet divergences occurring in feynman s representation are mathematically reasoned as a final result the change of the renormalization scheme in the context of eg is modeled via a ha and interpreted as the eg analog of kreimer s ha the paper aims at investigating perturbative quantum field theory in the approach of epstein and glaser eg and in particular its formulation in the language of graphs and hopf algebras has various has are encountered each one associated with a special combination of physical concepts such as normalization localization pseudounitarity causal regularization and renormalization the algebraic structures representing the perturbative expansion of the s matrix are imposed on operator valued distributions equipped with appropriate graph indices translation invariance ensures the algebras to be analytically well defined and graded total symmetry allows to formulate bialgebras the algebraic results are given embedded in the corresponding physical framework covering the two eg versions by fredenhagen and scharf that differ with respect to the concrete recursive implementation of causality besides the ultraviolet divergences occurring in feynman s representation are mathematically reasoned as a

prediction based control for lti systems with uncertain time varying delays and partial state knowledge abstractthe stability of a prediction based controller for linear time invariant lti systems is studied in the presence of time varying input and output delays the uncertain delay case is treated as well as the partial state knowledge case the reduction method is used in order to prove the convergence of the closed loop system including the state observer the predictor and the plant explicit conditions that guarantee the closed loop stability are given thanks to a lyapunov razumikhin analysis simulations illustrate the theoretical results

stabilization of nonlinear delay systems using approximate predictors and high gain observers we provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only the solution is global employs the predictor approach over the period that combines the input and output delays addresses nonlinear systems with sampled measurements and with control applied using a zero order hold and requires that the sampling holding periods be sufficiently short though not necessarily constant our approach considers a class of globally lipschitz strict feedback systems with disturbances and employs an appropriately constructed successive approximation of the predictor map a high gain sampled data observer and a linear stabilizing feedback for the delay free system the obtained results guarantee robustness to perturbations of the sampling schedule and different sampling and holding periods are considered the approach is specialized to linear systems where the predictor is available explicitly

controller synthesis for networked control systems this paper presents a discrete time model for networked control systems ncss that incorporates all network phenomena time varying sampling intervals packet dropouts and time varying delays that may be both smaller and larger than the sampling interval based on this model constructive lmi conditions for controller synthesis are derived such that stabilizing state feedback controllers can be designed besides the proposed controller synthesis conditions a comparison is made between the use of parameter dependent lyapunov functions and lyapunov krasovskii functions for stability analysis several examples illustrate the effectiveness of the developed theory

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

passivity based non fragile control for markovian jump systems with aperiodic sampling in this paper the problem of non fragile passive control for markovian jump systems with aperiodic sampling is investigated the considered controller is assumed to have either additive or multiplicative norm bounded uncertainties a time dependent lyapunov functional capturing the available information of the sampling pattern is constructed to derive a sufficient condition for non fragile stochastic passivity of the resultant closed loop system based on the condition a mode independent state feedback sampled data controller is designed such that for all admissible uncertainties the closed loop system is robustly stochastically passive two illustrative examples are included to demonstrate the effectiveness and merits of the proposed techniques

on the issue of imposing boundary conditions on quantum fields an interesting example of the deep interrelation between physics and mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields this procedure has recently been re examined with care comments on that and previous analysis are provided here together with considerations on the results of the purely mathematical zeta function method in an attempt at clarifying the issue hadamard regularization is invoked in order to fill the gap between the infinities appearing in the qft renormalized results and the finite values obtained in the literature with other procedures

microlocal analysis and interacting quantum field theories renormalization on physical backgrounds we present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic curved space times we develop a purely local version of the stuckelberg bogoliubov epstein glaser method of renormalization by using techniques from microlocal analysis relying on recent results of radzikowski kohler and the authors about a formulation of a local spectrum condition in terms of wave front sets of correlation functions of quantum fields on curved space times we construct time ordered operator valued products of wick polynomials of free fields they serve as building blocks for a local perturbative definition of interacting fields renormalization in this framework amounts to extensions of expectation values of time ordered products to all points of space time the extensions are classified according to a microlocal generalization of steinmann scaling degree corresponding to the degree of divergence in other renormalization schemes as a result we prove that the usual perturbative classification of interacting quantum field theories holds also on curved space times finite renormalizations are deferred to a subsequent paper as byproducts we describe a perturbative construction of local algebras of observables present a new definition of wick polynomials as operator valued distributions on a natural domain and we find a general method for the extension of distributions which were defined on the complement of some surface

lq optimal sampled data control under stochastic delays gridding approach for stabilizability and detectability we solve a linear quadratic optimal control problem for sampled data systems with stochastic delays the delays are stochastically determined by the last few delays the proposed optimal controller

fredholm toeplitz operators with vmo symbols and the duality of generalized fock spaces with small exponents we characterize fredholmness of toeplitz operators acting on generalized fock spaces of the n dimensional complex space for symbols in the space of vanishing mean oscillation vmo our results extend the recent characterizations for toeplitz operators on standard weighted fock spaces to the setting of generalized weight functions and also allow for unbounded symbols in vmo for the first time another novelty is the treatment of small exponents 0 p 1 which to our knowledge has not been seen previously in the study of the fredholm properties of toeplitz operators on any function spaces we accomplish this by describing the dual of the generalized fock spaces with small exponents

weighted composition operators between large fock spaces in several complex variables abstract let be an entire self map of c n and let u be an entire function on c n a weighted composition operator induced by with weight u is given by u c f z u z f z for z in c n and f is an entire function on c n in this paper we study weighted composition operators acting between two large weighted fock spaces f p and f q we characterize the bounded compact and schatten class membership operators u c acting from f p to f q when 0 p and 0 q our results use certain integral transforms that generalize the usual berezin transform

existence of local covariant time ordered products of quantum fields in curved spacetime we establish the existence of local covariant time ordered products of local wick polynomials for a free scalar field in curved spacetime our time ordered products satisfy all of the hypotheses of our previous uniqueness theorem so our construction essentially completes the analysis of the existence uniqueness and renormalizability of the perturbative expansion for nonlinear quantum field theories in curved spacetime as a byproduct of our analysis we derive a scaling expansion of the time ordered products about the total diagonal that expresses them as a sum of products of polynomials in the curvature times lorentz invariant distributions plus a remainder term of arbitrarily low scaling degree

wavefront sets in algebraic quantum field theory the investigation of wavefront sets of n point distributions in quantum field theory has recently acquired some attention stimulated by results obtained with the help of concepts from microlocal analysis in quantum field theory in curved spacetime in the present paper the notion of wavefront set of a distribution is generalized so as to be applicable to states and linear functionals on nets of operator algebras carrying a covariant action of the translation group in arbitrary dimension in the case where one is given a quantum field theory in the operator algebraic framework this generalized notion of wavefront set called asymptotic correlation spectrum is further investigated and several of its properties for physical states are derived we also investigate the connection between the asymptotic correlation spectrum of a physical state and the wavefront sets of the corresponding wightman distributions if there is a wightman field affiliated to the local operator algebras finally we present a new result generalizing known facts which shows that certain spacetime points must be contained in the singular supports of the 2n point distributions of a non trivial wightman field

the microlocal spectrum condition and wick polynomials of free fields on curved spacetimes quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis we discuss a condition on the wave front set for the correspondingn point distributions called microlocal spectrum condition sc on minkowski space this condition is satisfied as a consequence of the usual spectrum condition based on radzikowski s determination of the wave front set of the two point function of a free scalar field satisfying the hadamard condition in the kay and wald sense we construct in the second part of this paper all wick polynomials including the energy momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition