gaussian heat kernel upper bounds via the phragmen lindelof theorem we prove that in presence of l gaussian estimates so called davies gaffney estimates on diagonal upper bounds imply precise off diagonal gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces

estimates on the fundamental solution to heat flows with uniformly elliptic coefficients we obtain estimates from above and below on the fundamental solution to the cauchy initial value problem for parabolic equations having uniformly elliptic coefficients we impose minimal regularity requirements on the coefficients the estimates are expressed in terms of an energy functional associated with the coefficients

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

non linear iterative learning by an adaptive lyapunov technique we consider the iterative learning control problem from an adaptive control viewpoint it is shown that some standard lyapunov adaptive designs can be modified in a straightforward manner to give a solution to either the feedback or feedforward ilc problem some of the common assumptions of non linear iterative learning control are relaxed e g we relax the common linear growth asssumption on the non linearities and handle systems of arbitrary relative degree it is shown that generally a linear rate of convergence of the mse can be achieved and a simple robustness analysis is given for linear plants we show that a linear rate of mse convergence can be achieved for non minimum phase plants

examples of non kahler hamiltonian torus actions an important question with a rich history is the extent to which the symplectic category is larger than the kahler category many interesting examples of non kahler symplectic manifolds have been constructed t m g however sufficiently large symmetries can force a symplectic manifolds to be kahler d kn in this paper we solve several outstanding problems by constructing the first symplectic manifold with large non trivial symmetries which does not admit an invariant kahler structure the proof that it is not kahler is based on the atiyah guillemin sternberg convexity theorem at gs using the ideas of this paper c woodward shows that even the symplectic analogue of spherical varieties need not be kahler w

transportation cost inequalities on path and loop groups let g be a connected lie group with the lie algebra g the action of cameron martin space h g on the path space pe g introduced by l gross illinois j math 36 1992 447 is free using this fact we define the h distance on pe g which enables us to establish a transportation cost inequality on pe g this method will be generalized to the path space over the loop group le g so that we obtain a transportation cost inequality for heat measures on le g

iterative learning control design for linear discrete time systems with multiple high order internal models this work is focused on the iterative learning control ilc design for linear discrete time systems with iteration varying factors including reference initial state and exogenous disturbances first multiple high order internal models hoims are given for various iteration varying factors the reference is generated by an hoim and the initial state and the exogenous disturbances ultimately satisfy hoims but do not strictly follow hoims in finite iteration interval then a new ilc scheme a special high order ilc ho ilc is constructed according to an augmented hoim that is the aggregation of all hoims for simplicity the case with only iteration varying reference is first considered where the asymptotic stability and monotone convergence based ilc design methods are both presented by using the 2 d analysis approach next more iteration varying factors are further considered in this situation the hoim based ilc is transformed into a controller design problem of a 2 d roesser model with non zero boundary states and disturbances where the 2 d h performance is studied in consequence an ilc design criterion is presented to achieve perfect tracking and 2 d h performance for comparison the monotone convergence based ilc design method is extended to the situation with more iteration varying factors utilizing information provided by the multiple hoims it is verified that ho ilc outperforms low order ilc lo ilc in presence of iteration varying factors meanwhile the 2 d h based ilc is shown to be superior to the monotone convergence based ilc finally a microscale robotic deposition system with iteration varying factors is given to illustrate the advantage of the proposed 2 d h based ilc

learning strictly positive real linear systems with uncertain parameters and unknown input disturbances a learning control scheme is derived for the learning of strictly positive real spr linear systems by using the spr lemma it is shown that the exponential rate of convergence of the learning system can be set arbitrarily fast by choosing the learning control gain without the use of any normed inequality condition

the equivariant cohomology theory of twisted generalized complex manifolds it has been shown recently by kapustin and tomasiello that the mathematical notion of hamiltonian actions on twisted generalized kahler manifolds is in perfect agreement with the physical notion of general 2 2 gauged sigma models with three form fluxes in this article we study the twisted equivariant cohomology theory of hamiltonian actions on h twisted generalized complex manifolds if the manifold satisfies the overline partial partial lemma we establish the equivariant formality theorem if in addition the manifold satisfies the generalized kahler condition we prove the kirwan injectivity in this setting we then consider the hamiltonian action of a torus on an h twisted generalized calabi yau manifold and extend to this case the duistermaat heckman theorem for the push forward measure

analysis of degenerate elliptic operators of grusin type we analyse degenerate second order elliptic operators h in divergence form on l 2 r n r m we assume the coefficients are real symmetric and a 1 h h a 2 h for some a 1 a 2 0 where h delta nabla x 1 cdot c delta 1 delta 1 x 1 nabla x 1 c delta 2 delta 2 x 1 nabla x 2 2 here x 1 r n x 2 r m and c delta i delta i are positive measurable functions such that c delta i delta i x behaves like x delta i as x 0 and x delta i as x to infty with delta 1 delta 1 in 0 1 rangle and delta 2 delta 2 geq 0 our principal results state that the submarkovian semigroup s t e th is conservative and its kernel k t satisfies bounds 0 leq k t x y leq a b x t 1 2 b y t 1 2 1 2 where b x r denotes the volume of the ball b x r centred at x with radius r measured with respect to the riemannian distance associated with h the proofs depend on detailed subelliptic estimations on h a precise characterization of the riemannian distance and the corresponding volumes and wave equation techniques which exploit the finite speed of propagation we discuss further implications of these bounds and give explicit examples that show the kernel is not necessarily strictly positive nor continuous

data driven control for relative degree systems via iterative learning iterative learning control ilc is a kind of effective data driven method that is developed based on online and or offline input output data the main purpose of this paper is to supply a unified 2 d analysis approach for both continuous time and discrete time ilc systems with relative degree it is shown that the 2 d roesser system framework can be established for general ilc systems regardless of relative degree under which convergence conditions can be provided to guarantee both asymptotic stability and monotonic convergence of the ilc processes in particular conditions for the monotonic convergence of ilc can be given in terms of linear matrix inequalities and formulas for the updating law can be derived simultaneously simulation results are presented to illustrate the effectiveness of ilc determined through the 2 d design approach in dealing with the higher order relative degree problem of ilc systems as well as the robustness of such ilc against uncertainties

on initial conditions in iterative learning control initial conditions or initial resetting conditions play a fundamental role in all kinds of iterative learning control methods in this note we study five different initial conditions disclose the inherent relationship between each initial condition and corresponding learning convergence or boundedness property the iterative learning control method under consideration is based on lyapunov theory which is suitable for plants with time varying parametric uncertainties and local lipschitz nonlinearities

small time gaussian behavior of symmetric diffusion semi groups this work is involved with the short time asymptotics of diffusion semigroups in a general setting a generalization of fang s version of varadhan s formula is proven for general dirichlet spaces that are local and conservative the intrinsic metric appearing in the formula is characterized by pointwise distance for canonical dirichlet spaces on loop groups

design of strictly positive real systems using constant output feedback the authors present a linear matrix inequality lmi approach to the strictly positive real spr synthesis problem find an output feedback k such that the closed loop system t s is spr the authors establish that if no such constant output feedback k exists then no dynamic output feedback with a proper transfer matrix exists to make the closed loop system spr the existence of k to guarantee the spr property of the closed loop system is used to develop an adaptive control scheme that can stabilize any system of arbitrary unknown order and unknown parameters

logarithmic sobolev inequalities on loop groups let g be a compact lie group denote by m the brownian bridge measure on the loop group y g c 0 1 g g 0 g 1 e the finite energy subgroup of y determines in a natural way a gradient operation for functions on y the following logarithmic sobolev inequality is proven f2 log f dm gradf y 2 v y f y 2 dm f 2log f wherein f denotes the l2 m norm and v is a potential which is quadratic in the associated lie algebra valued brownian motion the inequality is derived by a method of inheritance from the known inequality for the g valued brownian motion

a cameron martin type quasi invariance theorem for pinned brownian motion on a compact riemannian manifold the results in driver 13 for quasi invariance of wiener measure on the path space of a compact riemannian manifold m are extended to the case of pinned wiener measure to be more explicit let h 0 1 tom be a c1 function where m is a compact riemannian manifold o e m is a base point and tom is the tangent space to m at o e m let w m be the space of continuous paths from 0 1 into m v be wiener measure on w m concentrated on paths starting at o e m and hs w denote the stochastic parallel translation operator along a path to e w m up to time s note hs w is only well defined up to v equivalence for c e w m let xh w denote the vector field along a given by xsh c hs cw h s for each s e 0 1 one should interpret xh as a vector field on w m the vector field xh induces a flow sh t w m w m which leaves wiener measure v quasi invariant see driver 13 it is shown in this paper that the same result is valid if h l 0 and the wiener measure v is replaced by a pinned wiener measure ive the measure ve is proportional to the measure v conditioned on the set of paths which start at 0 e m and end at a fixed end point e e m also as in 13 one gets an integration by parts formula for the vector fields xh defined above

on the p type learning control sufficient conditions for the robustness and convergence of p type learning control algorithms for a class of time varying nonlinear systems are presented the authors prove the uniform boundedness of the system state and the input control with respect to the existence of errors of initialization measurement noises and fluctuations of system dynamics furthermore the system output converges uniformly to the desired one in absence of all disturbances finally specialization of the results to linear systems are presented

geometry and analysis of dirichlet forms let e be a regular strongly local dirichlet form on l2 x m and d the associated intrinsic distance assume that the topology induced by d coincides with the original topology on x and that x is compact satisfies a doubling property and supports a weak 1 2 poincare inequality we first discuss the non coincidence of the intrinsic length structure and the gradient structure under the further assumption that the ricci curvature of x is bounded from below in the sense of lott sturm villani the following are shown to be equivalent i the heat flow of e gives the unique gradient flow of u ii e satisfies the newtonian property iii the intrinsic length structure coincides with the gradient structure moreover for the standard resistance dirichlet form on the sierpinski gasket equipped with the kusuoka measure we identify the intrinsic length structure with the measurable riemannian and the gradient structures we also apply the above results to the coarse ricci curvatures and asymptotics of the gradient of the heat kernel

sobolev spaces of banach valued functions associated with a markov process we discuss sobolev spaces of banach valued functions they are extensions of sobolev spaces of scalar functions we use a gamma transform of a semigroup associated with a markov process a typical example is the ornstein uhlenbeck process on the wiener space

logarithmic sobolev inequalities and exponential integrability we prove the exponential integrability of lipschitz functions in abstract wiener spaces by using logarithmic sobolev inequalities we introduce two notions of lipschitz continuity and apply the method of davis and simon j funct anal 59 1984 335 395 to prove our main theorem moreover we give several conditions under which the function is exponentially integrable

entropic measure and wasserstein diffusion we construct a new random probability measure on the circle and on the unit interval which in both cases has a gibbs structure with the relative entropy functional as hamiltonian it satisfies a quasi invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interval respectively the associated integration by parts formula is used to construct two classes of diffusion processes on probability measures on the sphere or the unit interval by dirichlet form methods the first one is closely related to malliavin s brownian motion on the homeomorphism group the second one is a probability valued stochastic perturbation of the heat flow whose intrinsic metric is the quadratic wasserstein distance it may be regarded as the canonical diffusion process on the wasserstein space

an output based adaptive iterative learning controller for high relative degree uncertain linear systems in this paper we derive an output tracking error model based on signals filtered from plant input and output and then present a new output based adaptive iterative learning controller for repeatable linear systems with unknown parameters high relative degree initial resetting error input disturbance and output noise the proposed controller solves the important robustness issues without assuming the bounds of uncertainties to be sufficiently small and can be applied to high relative degree plants without using output differentiation control parameters are updated between successive iterations so as to compensate for unknown system parameters and uncertainties it is shown that the internal signals inside closed loop learning system remain bounded and the output tracking error will asymptotically converge to a profile tunable by some design parameters furthermore the learning speed is easily improved if the learning gain is increased

brief paper analysis of two particular iterative learning control schemes in frequency and time domains this paper deals with iterative learning control design for multiple input multiple output mimo linear time invariant lti systems two particular ilc schemes are considered and analyzed in both frequency and time domains some remarks on the convergence implementation robustness with respect to disturbances and reinitialization errors as well as positive realness issues related to both schemes are provided

short time asymptotics in dirichlet spaces this work is involved with the short time asymptotics of the heat semigroup in a general setting a generalization of fang s version of varadhan s formula is proved a spectral gap or the possibility of obtaining one by an appropriate change of measure is required 2001 john wiley sons inc

robust iterative learning control design is straightforward for uncertain lti systems satisfying the robust performance condition this note demonstrates that the design of a robust iterative learning control is straightforward for uncertain linear time invariant systems satisfying the robust performance condition it is shown that once a controller is designed to satisfy the well known robust performance condition a convergent updating rule involving the performance weighting function can be directly obtained it is also shown that for a particular choice of this weighting function one can achieve a perfect tracking in the case where this choice is not allowable a sufficient condition ensuring that the least upper bound of the spl lscr sub 2 norm of the final tracking error is less than the least upper bound of the spl lscr sub 2 norm of the initial tracking error is provided this sufficient condition also guarantees that the infinity norm of the final tracking error is less than the infinity norm of the initial tracking error

integration on loop groups i quasi invariant measures on a riemannian manifold m the brownian motion defines a wiener measure on the loops over m in the case of r quasi invariance means the cameron martin theorem s which fully describes the quasi invariance by translation of the wiener measure in order to state a generalization of this theorem we suppose that m is an homogeneous space under the action of a compact lie group the noncommutativity of this situation introduces a completely new phenomenon the hypoellipticity associated to the lie bracket of the basic vector fields curiously enough hypoellipticity which helps to get regularity in finite dimensions works against quasi invariance in infinite dimensions 18 we denote by g a compact connected lie group by h a connected subgroup of g and by m the homogeneous space g h we denote by y and 2 the corresponding lie algebras we choose a euclidean metric on 9 which is ad g invariant this metric induces a riemannian metric on g and on m we denote p g the paths space on g that is the space of continuous maps y from 0 l into g such that y o e we denote by l g the space of loops on g that is

on singularity of energy measures on self similar sets we provide general criteria for energy measures of regular dirichlet forms on self similar sets to be singular to bernoulli type measures in particular every energy measure is proved to be singular to the hausdorff measure for canonical dirichlet forms on 2 dimensional sierpinski carpets

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

a robust high order p type iterative learning controller using current iteration tracking error a high order p type updating law in which the current iteration tracking error cite is employed is proposed for iterative learning control ilc of a class of uncertain nonlinear repetitive systems uniform boundedness of the tracking error is established in the presence of uncertainty disturbance and initialization error the bound and the ilc convergence rate can be adjusted by tuning the learning gain of the cite

on the equivalence of measures on loop space let k be a simply connected compact lie group equipped with an ad k invariant inner product on the lie algebra of k given this data there is a well known left invariant h 1 riemannian structure on l k the infinite dimensional group of continuous based loops in k as well as a heat kernel t k 0 associated with the laplace beltrami operator on l k here t 0 k 0 l k and t k 0 is a certain probability measure on l k in this paper we show that 1 e is equivalent to pinned wiener measure on k on s0 x t t 0 s 0 the algebra generated by truncated loops up to time s 0

examples of non kahler hamiltonian circle manifolds with the strong lefschetz property abstract in this paper we construct six dimensional compact non kahler hamiltonian circle manifolds which satisfy the strong lefschetz property themselves but nevertheless have a non lefschetz symplectic quotient this provides the first known counterexamples to the question whether the strong lefschetz property descends to the symplectic quotient we also give examples of hamiltonian strong lefschetz circle manifolds which have a non lefschetz fixed point submanifold in addition we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong lefschetz manifold we then use it to show the existence of lefschetz four manifolds with non lefschetz finite covering spaces

explicit constants for gaussian upper bounds on heat kernels on utilise des inegalites logarithmiques de sobolev pour obtenir des bornes superieures gaussiennes sur les noyaux de la chaleur associes a des operateurs d ordre 2 elliptiques et hypoelliptiques

optimal transport maps for monge kantorovich problem on loop groups let g be a compact lie group and consider the loop group leg l c 0 1 g l 0 l 1 e let be the heat kernel measure at the time 1 for any density function f on leg such that ent f we shall prove that there exists a unique optimal transportation map t leg leg which pushes forward to f

on the length of chains in a metric space abstract we obtain an upper bound on the minimal number of points in an e chain joining two points in a metric space this generalizes a bound due to hambly and kumagai 1999 for the case of resistance metric on certain self similar fractals as an application we deduce a condition on e chains introduced by grigor yan and telcs 2012 this allows us to obtain sharp bounds on the heat kernel for spaces satisfying the parabolic harnack inequality without assuming further conditions on the metric a snowflake transform on the euclidean space shows that our bound is sharp

multi periodic repetitive control system a lyapunov stability analysis for mimo systems a multi input multi output mimo repetitive control problem of tracking and disturbance rejection is considered when both reference and disturbance signals are finite linear combinations of periodic but not necessarily sinusoidal signals lyapunov stability analyses under a positive real condition and a natural relaxation and exponential stability under a strict positive real condition are provided together with bounds on the induced l 2 and rms gains of the closed loop system it is shown that similar lyapunov stability results apply when the plant is a positive real state delay system extension of the analyses to a class of non linear systems is discussed and indicates a good degree of robustness in the design

absolute continuity of heat kernel measure with pinned wiener measure on loop groups let t 0 k be a connected compact lie group equipped with an ad k invariant inner product on the lie algebra of k associated to this data are two measures 0 t and t 0 on l k the space of continuous loops based at e e k the measure 0 t is pinned wiener measure with variance t while the measure 0 t is a heat kernel measure on l k the measure 0 t is constructed using a k valued brownian motion while the measure 0 t is constructed using a l k valued brownian motion in this paper we show that 0 t is absolutely continuous with respect to 0 t and the radon nikodym derivative d 0 t d 0 t is bounded

integration by parts and quasi invariance for heat kernel measures on loop groups abstract integration by parts formulas are established both for wiener measure on the path space of a loop group and for the heat kernel measures on the loop group the wiener measure is defined to be the law of a certain loop group valued brownian motion and the heat kernel measures are time t t 0 distributions of this brownian motion a corollary of either of these integrations by parts formulas is the closability of the pre dirichlet form considered by b k driver and t lohrenz 1996 j functional anal 140 381 448 we also show that the heat kernel measures are quasi invariant under right under right and left translations by finite energy loops

an iterative learning control theory for a class of nonlinear dynamic systems abstract an iterative learning control scheme is presented for a class of nonlinear dynamic systems which includes holonomic systems as its subset the control scheme is composed of two types of control methodology a linear feedback mechanism and a feedforward learning strategy at each iteration the linear feedback provides stability of the system and keeps its state errors within uniform bounds the iterative learning rule on the other hand tracks the entire span of a reference input over a sequence of iterations the proposed learning control scheme takes into account the dominant system dynamics in its update algorithm in the form of scaled feedback errors in contrast to many other learning control techniques the proposed learning algorithm neither uses derivative terms of feedback errors nor assumes external input perturbations as a prerequisite the convergence proof of the proposed learning scheme is given under minor conditions on the system parameters

brief sampled data iterative learning control for nonlinear systems with arbitrary relative degree in this paper a sampled daata iterative learning control method is proposed for nonlinear systems without restriction on system relative degree the learning algorithm does not require numerical differentiations of any order from the tracking error a sufficient condition is derived to guarantee the convergence of the system output at each sampling instant to the desired trajectory numerical simulation is conducted to demonstrate the theoretical result

on the small time asymptotics of diffusion processes on hilbert spaces in this paper we establish a small time large deviation principle and obtain the following small time asymptotics lim t 0 2t log p x 0 b x t c d 2 b c for diffusion processes on hilbert spaces where d b c is the intrinsic metric between two subsets b and c associated with the diffusions the case of perturbed ornstein uhlenbeck processes is treated separately at the end of the paper

sobolev spaces over loop groups abstract in this paper we study the properties of orstein uhlenbeck operators over loop groups which are naturally defined by the group structure we establish the hypoellipticity of the laplacians acting on the space of tensors by using this we show the essential self adjointness of the laplacians acting on the real valued function spaces

optimal transport cheeger energies and contractivity of dynamic transport distances in extended spaces abstract we introduce the setting of extended metric topological measure spaces as a general wiener like framework for optimal transport problems and nonsmooth metric analysis in infinite dimension after a brief review of optimal transport tools for general radon measures we discuss the notions of the cheeger energy of the radon measures concentrated on absolutely continuous curves and of the induced dynamic transport distances we study their main properties and their links with the theory of dirichlet forms and the bakry emery curvature condition in particular concerning the contractivity properties and the evi formulation of the induced heat semigroup

on the small time behavior of ornstein uhlenbeck processes with unbounded linear drifts in this paper we study the small time behavior of ornstein ulenbeck processes with unbounded linear drifts on hilbert spaces the large deviations estimates are obtained the general theory of dirichlet forms lyons zheng s decompositions and the convolution representation of the processes play an important role

the subelliptic heat kernel on su 2 representations asymptotics and gradient bounds the lie group su 2 endowed with its canonical subriemannian structure appears as a three dimensional model of a positively curved subelliptic space the goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities

uniqueness of ground states for schrodinger operators over loop groups abstract over the space l of based loops in a compact connected lie group g there is a natural gradient operator induced by the left action on l of the hilbert lie group k 0 which consists of finite energy elements of l denote by pinned brownian motion measure on l the schrodinger operator v acting in l 2 l is shown to have a unique ground state over each homotopy class in l the proof of uniqueness is reduced to the proof of ergodicity of the left action of k 0 on l for a simply connected group g of compact type ergodicity in turn is proved by first characterizing the ito expansion coefficients of k 0 invariant functions and then regularizing such functions via a smooth approximation of multiple stratonovich integrals as a byproduct of this method one obtains an isometric isomorphism of l 2 g heat kernel measure at time one with a natural completion of the universal enveloping algebra of g thus extending to the noncommutative case the well known isometry between l 2 r d gauss measure and the space of symmetric tensors over r d

stochastic 3d tamed navier stokes equations existence uniqueness and small time large deviation principles abstract in this paper we first give a direct approach to the existence and uniqueness of strong solutions to stochastic 3d tamed navier stokes equations in case of dirichlet boundary conditions for the stokes laplacian then we prove a small time large deviation principle for the solutions

learning control for nonlinear systems in output feedback form abstract the class of single input single output minimum phase nonlinear time invariant systems with unknown output dependent nonlinearities unknown parameters and known relative degree is considered the output regulation problem is addressed and solved in the presence of unknown periodic reference and or disturbance signals of known common period a simple learning control algorithm is designed which guarantees asymptotic output tracking for any initial condition belonging to any given connected compact set it can be interpreted as a generalization of the classical pid 1 control which solves the regulator problem when reference and disturbance signals are constant as far as linear systems are concerned global results are achieved