a borderline random fourier series consider a mean zero random variable x and an independent sequence x n distributed like x we show that the random fourier series n 1 n 1 x n exp 2i nt converges uniformly almost surely if and only if e x log log max e e x

symmetric spaces with maximal projection constants in this paper we introduce a special class of finite dimensional symmetric subspaces of l1 so called regular symmetric subspaces using this notion we show that for any k 2 there exist k dimensional symmetric subspaces of l1 which have maximal projection constant among all k dimensional symmetric spaces moreover l1 is a maximal overspace for these spaces see theorems 4 4 and 4 5 also a new asymptotic lower bound for projection constants of symmetric spaces is obtained see theorem 5 3 this result answers the question posed in 12 p 36 see also 15 p 38 by h koenig and co authors the above results are presented both in real and complex cases

conditional exponential moments for iterated wiener integrals we provide sharp exponential moment bounds for stratonovich iterated stochastic integrals under conditioning by certain small balls including balls in certain holder like norms of exponent greater than 1 3 the proof uses a control of the variation of the levy area under conditioning the results are applied to the computation of the onsager machlup functional of diffusion processes with constant diffusion matrix

gradient estimate for solutions to poisson equations in metric measure spaces abstract let x d be a complete pathwise connected metric measure space with a locally ahlfors q regular measure where q 1 suppose that x d supports a local 1 2 poincare inequality and a suitable curvature lower bound for the poisson equation u f on x d moser trudinger and sobolev inequalities are established for the gradient of u the local holder continuity with optimal exponent of solutions is obtained

on the lp spectrum of laplacians on graphs abstract we study the p independence of spectra of laplace operators on graphs arising from regular dirichlet forms on discrete spaces here a sufficient criterion is given solely by a uniform subexponential growth condition moreover under a mild assumption on the measure we show a one sided spectral inclusion without any further assumptions we study applications to normalized laplacians including symmetries of the spectrum and a characterization for positivity of the cheeger constant furthermore we consider laplacians on planar tessellations for which we relate the spectral p independence to assumptions on the curvature

regularity of laws and ergodicity of hypoelliptic sdes driven by rough paths we consider differential equations driven by rough paths and study the regularity of the laws and their long time behavior in particular we focus on the case when the driving noise is a rough path valued fractional brownian motion with hurst parameter h 2 1 1 our contribution in this work is twofold first when the driving vector fields satisfy hormander s c elebrated lie bracket condition we derive explicit quantitative bounds on the i nverse of the malliavin ma trix en route to this we provide a novel deterministic version of norris s lemma for differential equations driven by rough paths this result with the added assumption that the linearized equation has moments will then yield that the transition laws have a smooth density with respect to lebesgue measure our second main result states that under hormander s condi tion the solutions to rough differential equations driven by fractional brownian motion with h 2 1 1 enjoy a suitable version of the strong feller property under a standard controllability condition this implies that they admit a unique stationary solution that is physical in the sense that it does not look into the future

the limits of stochastic integrals of differential forms this paper is concerned with the integration of 1 forms against the markov stochastic process associated with a second order elliptic differential operator in divergence form it focuses on the limiting behavior of the integral as the process leaves a fixed point or goes to infinity this extends previous work in the area where advantage was usually taken of the fact that the operator was self adjoint and started with the associated invariant measure applications are given for example it is a trivial consequence that the diffusion associated to a uniformly elliptic operator on a negatively curved cartan hadamard manifold has an asymptotic direction recovering and strengthening the previous arguments of pratt sullivan and others the approach can also be used to construct a levy area for such processes to study the thinness of sets for the elliptic operator and probably has wider applications

on uniformly subelliptic operators and stochastic area let x a be a markov process with generator i j i aij j where a is a uniformly elliptic symmetric matrix thanks to the fundamental works of t lyons stochastic differential equations driven by x a can be solved in the rough path sense that is pathwise by using a suitable stochastic area process our construction of the area which generalizes previous works of lyons stoica and then lejay is based on dirichlet forms associated to subellitpic operators this enables us in particular to discuss large deviations and support descriptions in suitable rough path topologies as typical rough path corollary freidlin wentzell theory and the stroock varadhan support theorem remain valid for stochastic differential equations driven by x a

mosco convergence of dirichlet forms in infinite dimensions with changing reference measures let e be an infinite dimensional locally convex space let n be a weakly convergent sequence of probability measures on e and let en be a sequence of dirichlet forms on e such that en is defined on l2 n general sufficient conditions for mosco convergence of the gradient dirichlet forms are obtained applications to gibbs states on a lattice and to the gaussian case are given weak convergence of the associated processes is discussed

intrinsic geometry and analysis of diffusion processes and l variational problems the aim of this paper is twofold first we obtain a better understanding of the intrinsic distance of diffusion processes precisely a for all n 1 the diffusion matrix a is weak upper semicontinuous on if and only if the intrinsic differential and the local intrinsic distance structures coincide b if n 1 or if n 2 and a is weak upper semicontinuous on the intrinsic distance and differential structures always coincide c if n 2 and a fails to be weak upper semicontinuous on the non coincidence of the intrinsic distance and differential structures depend on the geometry of the non weak upper semicontinuity set of a second for an arbitrary diffusion matrix a we show that the intrinsic distance completely determines the absolute minimizer of the corresponding l variational problem and then obtain the existence and uniqueness for given boundary data we also give an example of a diffusion matrix a for which there is an absolute minimizer that is not of class c1 when a is continuous we also obtain the linear approximation property of the absolute minimizer

fredholm modules on p c f self similar fractals and their conformal geometry the aim of the present work is to show how using the differential calculus associated to dirichlet forms it is possible to construct non trivial fredholm modules on post critically finite fractals by regular harmonic structures d r the modules are d s summable the summability exponent d s coinciding with the spectral dimension of the generalized laplacian operator associated with d r the characteristic tools of the noncommutative infinitesimal calculus allow to define a d s energy functional which is shown to be a self similar conformal invariant

norms of minimal projections it is proved that the projection constants of two and three dimensional spaces are bounded by 43 and 1 5 2 respectively these bounds are attained precisely by the spaces whose unit balls are the regular hexagon and dodecahedron in fact a general inequality for the projection constant of a real or complex n dimensional space is obtained and the question of equality therein is discussed

lipschitz continuity of cheeger harmonic functions in metric measure spaces abstract we use the heat equation to establish the lipschitz continuity of cheeger harmonic functions in certain metric spaces the metric spaces under consideration are those that are endowed with a doubling measure supporting a 1 2 poincare inequality and in addition supporting a corresponding sobolev poincare type inequality for the modification of the measure obtained via the heat kernel examples are given to illustrate the necessity of our assumptions on these spaces we also provide an example to show that in the general setting the best possible regularity for the cheeger harmonic functions is lipschitz continuity

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

volume growth and spectrum for general graph laplacians we prove estimates relating exponential or sub exponential volume growth of weighted graphs to the bottom of the essential spectrum for general graph laplacians the volume growth is computed with respect to a metric adapted to the laplacian and use of these metrics produces better results than those obtained from consideration of the graph metric only conditions for absence of the essential spectrum are also discussed these estimates are shown to be optimal or near optimal in certain settings and apply even if the laplacian under consideration is an unbounded operator

a generalized conservation property for the heat semigroup on weighted manifolds in this text we study a generalized conservation property for the heat semigroup generated by a schrodinger operator with nonnegative potential on a weighted manifold we establish khasminskii s criterion for the generalized conservation property and discuss several applications

smoothness of the density for solutions to gaussian rough differential equations we consider stochastic differential equations driven by a multi dimensional gaussian process under the assumption that the vector fields satisfy hormander s bracket condition we demonstrate that the solution admits a smooth density for any strictly positive time t provided the driving noise satisfies certain non degeneracy assumptions our analysis relies on an interplay of rough path theory malliavin calculus and the theory of gaussian processes our result applies to a broad range of examples including fractional brownian motion with hurst parameter greater than 1 4 the ornstein uhlenbeck process and the brownian bridge returning after time t

subspaces of codimension two with large projection constants abstract let v be an n dimensional real banach space and let v denote its absolute projection constant for any n n n n define n n sup v dim v n v l n the aim of this paper is to determine minimal projections with respect to l 1 norm as well as with respect to l norm for subspaces given by solutions of certain extremal problems as an application we show that for any n n n n n there exists an n dimensional subspace v n l 1 n such that n n v n l 1 n also we calculate relative and absolute projection constants of some subspaces of codimension two in l 1 n and l n for n 3 being odd natural number moreover we show that for any odd natural number n 3 n n 1 max x 0 1 f n x n n 2 where f n x 2 n n 1 1 x 1 2 x 2 1 x n 1 2 1 x n 1 x 2 4 1 x x also for any n n x n 0 1 satisfying f n x n max x 0 1 f n x will be calculated

general cheeger inequalities for p laplacians on graphs abstract we prove cheeger inequalities for p laplacians on finite and infinite weighted graphs unlike in previous works we do not impose boundedness of the vertex degree nor do we restrict ourselves to the normalized laplacian and more generally we do not impose any boundedness assumption on the geometry this is achieved by a novel definition of the measure of the boundary which uses the idea of intrinsic metrics for the non normalized case our bounds on the spectral gap of p laplacians are already significantly better for finite graphs and for infinite graphs they yield non trivial bounds even in the case of unbounded vertex degree we furthermore give upper bounds by the cheeger constant and by the exponential volume growth of distance balls

the campbell baker hausdorff dynkin formula and solutions of differential equations the campbell baker hausdorff dynkin formula is a special case of a simpler and more general formula for the solution of nonautonomous systems of first order ordinary differential equations in terms of autonomous systems specifically suppose u t takes values in a c manifold and satisfies the initial value problem u t a t u t u 0 a where a t is a vector field on the manifold depending continuously on t then u t exp z t a here exp z a means the solution at s 1 to v s z v s v 0 a for z t r 1 pr e r2r 1e tr t x a s 1 a s 2 a s r ds as t 0 where tr t s rr 0 s1 s2 sr t pr is the set of permutations on 1 r e is the number of errors in ordering consecutive terms in 1 r and is the usual commutator of vector fields under appropriate analyticity assumptions the series for z t is convergent for small t this formula gives an explicit formulation of results of k t chen published in 1957 applications are given to problems in sub riemannian geometry and to improving convergence estimates for the campbell baker hausdorff dynkin formula in the context of banach algebras our formula can be thought of as a noncommutative generalization of the familiar formula u t a exp 0t a s ds in the scalar linear case in the same way that the campbell baker hausdorff dynkin formula is a noncommutative generalization of the familiar formula exey ex y

martin boundaries of elliptic skew products semismall perturbations and fundamental solutions of parabolic equations abstract we consider positive solutions of elliptic partial differential equations on non compact domains of riemannian manifolds we explicitly determine martin boundaries and martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short long time estimates for fundamental solutions of parabolic equations

levy gromov s isoperimetric inequality for an infinite dimensional diffusion generator we establish by simple semigroup arguments a levy gromov isoperimetric inequality for the invariant measure of an infinite dimensional diffusion generator of positive curvature with isoperimetric model the gaussian measure this produces in particular a new proof of the gaussian isoperimetric inequality this isoperimetric inequality strengthens the classical logarithmic sobolev inequality in this context a local version for the heat kernel measures is also proved which may then be extended into an isoperimetric inequality for the wiener measure on the paths of a riemannian manifold with bounded ricci curvature

stochastic completeness for graphs with curvature dimension conditions abstract we prove pointwise gradient bounds for heat semigroups associated to general possibly unbounded laplacians on infinite graphs satisfying the curvature dimension condition cd k using gradient bounds we show stochastic completeness for graphs satisfying the curvature dimension condition

fractal snowflake domain diffusion with boundary and interior drifts abstract we study a parabolic ventsell problem for a second order differential operator in divergence form and with interior and boundary drift terms on the snowflake domain we prove that under standard conditions a related cauchy problem possesses a unique classical solution and explain in which sense it solves a rigorous formulation of the initial ventsell problem as a second result we prove that functions that are intrinsically lipschitz on the snowflake boundary admit euclidean lipschitz extensions to the closure of the entire domain our methods combine the fractal membrane analysis the vector analysis for local dirichlet forms and pde on fractals coercive closed forms and the analysis of lipschitz functions

large time behavior of the heat kernel in this paper we study the large time behavior of the heat kernel on complete riemannian manifolds with nonnegative ricci curvature which was studied by p li with additional maximum volume growth assumption following y ding s original strategy by blowing down the metric using cheeger and colding s theory about limit spaces of gromov hausdorff convergence combining with the gaussian upper bound of heat kernel on limit spaces we succeed in reducing the limit behavior of the heat kernel on manifold to the values of heat kernels on tangent cones at infinity of manifold with renormalized measure as one application we get the consistent large time limit of heat kernel in more general context which generalizes the former result of p li furthermore by choosing different sequences to blow down the suitable metric we show the first example manifold whose heat kernel has inconsistent limit behavior which answers an open question posed by p li negatively

densities for rough differential equations under hormander s condition we consider stochastic differential equations dy v y dx driven by a multidimensional gaussian process x in the rough path sense t lyons rev mat iberoamericana 14 1998 215 310 using malliavin calculus we show that y t admits a density for t 0 t provided i the vector fields v v 1 v d satisfy hormander s condition and ii the gaussian driving signal x satisfies certain conditions examples of driving signals include fractional brownian motion with hurst parameter h 1 4 the brownian bridge returning to zero after time t and the ornstein uhlenbeck process

projection constants of symmetric spaces and variants of khintchine s inequality the projection constants of the ln p spaces for 1 p 2 satisfy ln p n c with c 2 in the real case and c 2 in the complex case further there is c 1 such that the projection constant of any n dimensional space xn with 1 symmetric basis can be estimated by xn c n the proofs of the results are based on averaging techniques over permutations and a variant of khintchine s inequality which states that n j 1 xjrj l1 2 x 2 1 2 x x r 1 the main results this paper is concerned with asymptotic results for the projection constants of 1 symmetric spaces and in particular of the l p spaces for 1 p 2 we use standard banach space notation see e g lt or tj by k we denote the scalar field either the real numbers r or the complex numbers c the relative projection constant of a closed subspace x of a banach space y is defined by x y inf p p y x y is a linear projection onto x the absolute projection constant of x is given by x sup x y y is a banach space containing xas a subspace 1 1 any separable banach space x can be imbedded isometrically into l for any such imbedding x x l i e the sup in 1 1 is attained its value may be infinite however for finite dimensional spaces xn with dim xn n the kadec snobar result states that xn n this was improved in kt1 where an upper estimate for xn was found in the form n c n 0 n 3 2 for c 1 if k r and c 1 2 if k c in general however there are spaces xn with dim xn n such that xn n 1 cf kt2 k2 this research was supported by nato collaborative research grant 960996 the third named author held canada council killam research fellowship in 1997 99

on stochastic completeness of jump processes we prove the following sufficient condition for stochastic completeness of symmetric jump processes on metric measure spaces if the volume of the metric balls grows at most exponentially with radius and if the distance function is adapted in a certain sense to the jump kernel then the process is stochastically complete we use this theorem to prove the following criterion for stochastic completeness of a continuous time random walk on a graph with a counting measure if the volume growth with respect to the graph distance is at most cubic then the random walk is stochastically complete where the cubic volume growth is sharp

isoperimetric inequality from the poisson equation via curvature in this paper we establish an isoperimetric inequality in a metric measure space via the poisson equation let x d be a complete pathwise connected metric space with locally ahlfors q regular measure where q 1 that supports a local l2 poincare inequality we show that for the poisson equation u g if the local l norm of the gradient du can be bounded by the lorentz norm lq 1 of g then we obtain an isoperimetric inequality and a sobolev inequality in x d with optimal exponents by assuming a suitable curvature lower bound we establish such optimal bounds on 2011 wiley periodicals inc

heat semigroup and singular pdes we provide in this work a semigroup approach to the study of singular pdes in the line of the paracontrolled approach developed recently by gubinelli imkeller and perkowski starting from a heat semigroup we develop a functional calculus and introduce a paraproduct based on the semigroup for which commutator estimates and schauder estimates are proved together with their paracontrolled extensions this machinery allows us to investigate singular pdes in potentially unbounded riemannian manifolds under mild geometric conditions as an illustration we study the generalized parabolic anderson model equation and prove under mild geometric conditions its well posed character in small time on a potentially unbounded 2 dimensional riemannian manifold for an equation driven by a coloured noise and for all times for the linear parabolic anderson model equation in 2 dimensional unbounded manifolds this machinery can be extended to an even more singular setting and deal with sobolev spaces rather than holder spaces

poincare inequality from remote balls to all balls abstract it is shown that the poincare inequality holds uniformly for all balls whenever it holds for z remote balls providing the set z satisfies some additional conditions including the condition that z does not separate the space the aim of this paper is to prove similar results without using this assumption

characterization of almost surely continuous 1 stable random fourier series and strongly stationary processes we complete the results of m marcus and g pisier by showing that a strongly stationary 1 stable process x t t g defined on a locally compact group has a version with sample continuous paths if and only if the entropy integral 0 log log n k d x e de is finite where k is a given neighborhood of the unit and d x is the distance induced by the process

characteristic functions of measures on geometric rough paths we define a characteristic function for probability measures on the signatures of geometric rough paths we determine sufficient conditions under which a random variable is uniquely determined by its expected signature thus partially solving the analogue of the moment problem we furthermore study analyticity properties of the characteristic function and prove a method of moments for weak convergence of random variables we apply our results to signature arising from levy gaussian and markovian rough paths

finite co dimensional banach spaces and some bounded recovery problems in this paper we study the projections and some recovery problem of a finite co dimensional banach spaces in terms of the projection of their complementations more precisely we study the following problems 1 if y is a finite co dimensional subspace of a banach space x and z is its complementation is for every projection p 0 from x onto z and every e 0 there a projection p from x onto y email protected email protected 1 email protected p email protected 2 if x is a banach space email protected x y is an n co dimensional subspace of x and f i x i i 1 n is the auerbach system of the complementation z of y in x is there an element email protected y satisfying the following two conditions i email protected i y email protected i x email protected 1 2 n where email protected i is the hahn banach extension of f i on x ii email protected

characterizations of almost surely continuous p stable random fourier series and strongly stationary processes on etend le probleme de dudley fernique aux processus p stables fortement stationnaires 1 p 2

heat kernel based decomposition of spaces of distributions in the framework of dirichlet spaces classical and nonclassical besov and triebel lizorkin spaces with complete range of indices are developed in the general setting of dirichlet space with a doubling measure and local scale invariant poincare inequality this leads to a heat kernel with small time gaussian bounds and holder continuity which play a central role in this article frames with band limited elements of sub exponential space localization are developed and frame and heat kernel characterizations of besov and triebel lizorkin spaces are established this theory in particular allows the development of besov and triebel lizorkin spaces and their frame and heat kernel characterization in the context of lie groups riemannian manifolds and other settings

evolving communities with individual preferences the goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals we model the population by a measure space f where determines the abundance of individual preferences the preferences of an individual are described by a measurable choice x of a rough path we aim to identify for each individual a choice for the forward evolution yt for an individual in the community these choices yt m ust be consistent so thatyt correctly accounts for the individual s preference and correctly models their interaction with the aggregate behaviour of the community in general solutions are continuum of interacting threads analogous to the huge number of individual atomic trajectories that together make up the motion of a fluid the evolution of the population need not be governed by any over arching partial differential equation pde although one can match the standard non linear parabolic pdes of mckean vlasov type with specific examples of communities in this case the bulk behaviour of the evolving population provides a solution to the pde we focus on the case of weakly interacting systems where we are able to exhibit the existence and uniqueness of consistent solutions an important technical result is continuity of the behaviour of the system with respect to changes in the measure assigning weight to individuals replacing the deterministic with the empirical distribution of an independent and identically distributed sample from leads to many standard models and applying the continuity result allows easy proofs for propagation of chaos the rigorous underpinning presented here leads to uncomplicated models which have wide applicability in both the physical and social sciences we make no presumption that the macroscopic dynamics are modelled by a pde this work builds on the fine probability literature considering the limit behaviour for systems where a large number of particles are interacting with independent preferences there is also work on continuum models with preferences described by a semi martingale measure we mention some of the key papers

tail estimates for markovian rough paths we work in the context of markovian rough paths associated to a class of uniformly subelliptic dirichlet forms 26 and prove a better than exponential tail estimate for the accumulated local p variation functional which has been introduced and studied in 17 we comment on the significance of these estimates to a range of currently studied problems including the recent results of ni hao 32 and chevyrev and lyons 18

geometric aspects of fleming viot and dawson watanabe processes this paper is concerned with the intrinsic metrics of the two main classes of superprocesses for the fleming viot process we identify it as the bhattacharya distance and for dawson watanabe processes we find the kakutani hellinger metric the corresponding geometries are studied in some detail in particular representation formulas for geodesics and arc length functionals are obtained the relations between the two metrics yield a geometric interpretation of the identification of the fleming viot process as a dawson watanabe superprocess conditioned to have total mass 1 as an application a functional limit theorem for super brownian motion conditioned on local extinction is proved

space of ricci flows i based on the compactness of the moduli of non collapsed calabi yau spaces with mild singularities we set up a structure theory for polarized kahler ricci flows with proper geo metric bounds our theory is a generalization of the structure theory of non collapsed kahler einstein manifolds as applications we prove the hamilton tian conjecture and the partial c 0 conjecture of tian

three dimensional subspace of l 5 with maximal projection constant let v be an n dimensional real banach space and let v denote its absolute projection constant for any n n n n define nn sup v dim v n v l n and n sup v dim v n a well known grunbaum conjecture p 465 in b grunbaum projection constants trans amer math soc 95 1960 451 465 says that 2 4 3 in this paper we show that 35 5 427 and we determine a three dimensional space v l 5 satisfying 35 v in particular this shows that proposition 3 1 from h konig n tomczak jaegermann norms of minimal projections j funct anal 119 1994 253 280 see p 259 is incorrect hence the proof of the grunbaum conjecture given in h konig n tomczak jaegermann norms of minimal projections j funct anal 119 1994 253 280 which is based on proposition 3 1 is incomplete

cheeger harmonic functions in metric measure spaces revisited let x d be a complete metric measure space with a locally doubling measure that supports a local weak l2 poincare inequality by assuming a heat semigroup type curvature condition we prove that cheeger harmonic functions are lipschitz continuous on x d gradient estimates for cheeger harmonic functions and solutions to a class of non linear poisson type equations are presented

integrability and tail estimates for gaussian rough differential equations we derive explicit tail estimates for the jacobian of the solution flow for stochastic differential equations driven by gaussian rough paths in particular we deduce that the jacobian has finite moments of all order for a wide class of gaussian process including fractional brownian motion with hurst parameter h 1 4 we remark on the relevance of such estimates to a number of significant open problems

geometry and analysis of dirichlet forms ii abstract given a regular strongly local dirichlet form e under assumption that the lower bound of the ricci curvature of bakry emery the local doubling and local poincare inequalities are satisfied we obtain that i the intrinsic differential and distance structures of e coincide ii the cheeger energy functional ch d e is a quadratic norm this shows that ii is necessary for the riemannian ricci curvature defined by ambrosio gigli savare to be bounded from below this together with some recent results of ambrosio gigli savare yields that the heat flow gives a gradient flow of boltzman shannon entropy under the above assumptions we also obtain an improvement on kuwada s duality theorem for dirichlet forms under the assumptions of doubling and poincare inequalities finally dirichlet forms are constructed to show that doubling and poincare inequalities are not enough to obtain either i or ii above that is the lower bound of the bakry emery curvature condition is essential

lipschitz algebras and derivations ii exterior differentiation abstract basic aspects of differential geometry can be extended to various non classical settings lipschitz manifolds rectifiable sets sub riemannian manifolds banach manifolds wiener space etc although the constructions differ in each of these cases one can define a module of measurable 1 forms and a first order exterior derivative we give a general construction which applies to any metric space equipped with a finite measure and produces the desired result in all of the above cases it agrees with cheeger s construction when the latter is defined it also applies to an important class of dirichlet spaces where however the known first order differential calculus in general differs from ours although the two are related

fredholm theory for elliptic operators on quasi asymptotically conical spaces we consider the mapping properties of generalized laplace type operators l r on the class of quasi asymptotically conical qac spaces which provide a riemannian generalization of the qale manifolds considered by joyce joy00 our main result gives conditions under which such operators are fredholm when between

mosco convergence and wiener measures for conductive thin boundaries abstract the mosco convergence of energy functionals and the convergence of associated wiener measures are proved for a domain with highly conductive thin boundary we obtain those results for matrix valued conductivities and a family of speed measures measures of the underlying domain in particular this family includes the lebesgue measure and the one which makes the energy functional superposition the expectation of the displacement of the associated processes close to the boundary goes to due to the explosion of the conductivity at the limit