random walks on graphs electric networks and fractals this paper is devoted to the problem of the nearest neighbour random walk on infinite graphs we investigate the rw x n started from a fixed vertex x0 x v of the graph g v e and the expected value of the first exit time t n from the n ball b n in g it will be shown that if g is sufficiently regular then d underset raise0 3em hbox smash scriptscriptstyle geqslant d omega d r underset raise0 3em hbox smash scriptscriptstyle geqslant 2 and d r d 2 d omega where d r is the rw dimension d is the fractal dimension and d is the exponent of the growth of the resistance of b n though the method of the paper was developed for the case when x0 x is a fixed vertex of the graph we hope that the result can be generalized

estimationslpdes operateurs de schrodinger sur les groupes nilpotents resume dans cet article on se propose d etudier la continuite dans les espaces l p des groupes nilpotents des operateurs 2 w 1 w 1 2 nabla w 1 et w 1 2 ou est un sous laplacien et w un potentiel qui verifie d assez bonnes conditions

sub gaussian estimates of heat kernels on infinite graphs we prove that a two sided sub gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the green kernel admits a uniform polynomial decay

comparison of hardy littlewood and dyadic maximal functions on spaces of homogeneous type abstract we obtain a comparison of the level sets for two maximal functions on a space of homogeneous type the hardy littlewood maximal function of mean values over balls and the dyadic maximal function of mean values over the dyadic sets introduced by m christ in m christ a t b theorem with remarks on analytic capacity and the cauchy integral colloq math 60 61 1990 601 628 as applications to the theory of a p weights on this setting we compare the standard and the dyadic muckenhoupt classes and we give an alternative proof of reverse holder type inequalities

a globally convergent approach for blind mimo adaptive deconvolution we discuss the blind deconvolution of multiple input multiple output mimo linear convolutional mixtures and propose a set of hierarchical criteria motivated by the maximum entropy principle the proposed criteria are based on the constant modulus cm criterion in order to guarantee that all minima achieve perfectly restoration of different sources the approach is moreover robust to errors in channel order estimation practical implementation is addressed by a stochastic adaptive algorithm with a low computational cost complete convergence proofs based on the characterization of all extrema are provided the efficiency of the proposed method is illustrated by numerical simulations

diffusion on multifractals abstract we introduce a class of random fields with variable mean square regularity order defined on multifractal domains the local singularity order of these random fields then depends on the initial variable mean square regularity order and on the variable local singularity exponent of the multifractal measure defining the local dimension of the domain considered the theory is developed in a generalized framework through the covariance factorization using the tools of reproducing kernel hilbert spaces and fractional sobolev spaces of variable order

frequency domain blind mimo system identification based on second and higher order statistics we present a novel frequency domain framework for the identification of a multiple input multiple output mimo system driven by white mutually independent unobservable inputs the system frequency response is obtained based on singular value decomposition svd of a matrix constructed based on the power spectrum and slices of polyspectra of the system output by appropriately selecting the polyspectra slices we can create a set of such matrices each of which could independently yield the solution of they could all be combined in a joint diagonalization scheme to yield a solution with improved statistical performance the freedom to select the polyspectra slices allows us to bypass the frequency dependent permutation ambiguity that is usually associated with frequency domain svd while at the same time allows us compute and cancel the phase ambiguity an asymptotic consistency analysis of the system magnitude response estimate is performed

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

two sided estimates of heat kernels of jump type dirichlet forms abstract we prove necessary and sufficient conditions for stable like estimates of the heat kernel for jump type dirichlet forms on metric measure spaces the conditions are given in terms of the volume growth function jump kernel and a generalized capacity

obtaining upper bounds of heat kernels from lower bounds we show that a near diagonal lower bound of the heat kernel of a dirichlet form on a metric measure space with a regular measure implies an on diagonal upper bound if in addition the dirichlet form is local and regular then we obtain a full off diagonal upper bound of the heat kernel provided the dirichlet heat kernel on any ball satisfies a near diagonal lower estimate this reveals a new phenomenon in the relationship between the lower and upper bounds of the heat kernel c 2007 wiley periodicals inc

on subspace methods for blind identification of single input multiple output fir systems blind identification of single input multiple output simo fir systems based on second order statistics has attracted a great deal of research effort we focus on subspace estimation procedures which exploit the structure of the range space of certain matrix valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations general subspace identifiability results are obtained based on properties of minimal polynomial bases of rational subspaces several subspace estimation procedures are then derived these estimators are all based on a weighted least square solution of an overdetermined system of linear equations an asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting

heat kernel upper bounds for jump processes and the first exit time for all t 0 x m and f l2 m the function pt x y can be considered as the transition density of the associated markov processx xt t 0 and the question of estimating of pt x y which is the main subject of this paper is closely related to the properties of x the function pt x y is also referred to as a heat kernel and this terminology goes back to the classical gauss weierstrass heat kernel associated with the heat semigroup e t 0 in r n whose markov process is brownian motion a somewhat more general but still well treated case is when m d is a riemannian metric measure space that is m is a riemannian manifold

hardy littlewood theory for semigroups soit t t t 0 un semi groupe symetrique sousmarkovien et soit n 2 alors on a les proprietes equivalentes a dim t t n b il existe c 2 0 s t t t f c 2 t n 2 f 1 f l 1 x t 0 en fait a b meme dans le cas n 2

nonlinear adaptive blind whitening for mimo channels a nonlinear adaptive whitening method is proposed for blind deconvolution of mimo systems by whitening the received signals in both time and space with a highly nonlinear function of the past output data the whitened signals are isi free and can be viewed as outputs of a memoryless paraunitary mixing system the convergence of the proposed recursive algorithm is proved numerical simulation shows that the whitening method proposed in the paper works well even if the output signal is corrupted by additive noise

bmo spaces related to schrodinger operators with potentials satisfying a reverse holder inequality we identify the dual space of the hardy type space related to the time independent schrodinger operator v with v a potential satisfying a reverse holder inequality as a bmo type space we prove the boundedness in this space of the versions of some classical operators associated to hardy littlewood semigroup and poisson maximal functions square function fractional integral operator we also get a characterization of in terms of carlesson measures

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

a finite step global convergence algorithm for the parameter estimation of multichannel ma processes an iterative algorithm for the identification of multichannel moving average ma processes using higher order statistics is proposed it is shown that the algorithm has a finite step global convergence property three multichannel ma models including one nonminimum phase ma model are estimated by this algorithm with satisfactory performances

semilinear evolution transmission problems across fractal layers abstract a semilinear parabolic transmission problem across either a fractal layer s or the corresponding prefractal layer s h is studied local existence uniqueness and regularity results for the mild solution in both cases are established as well as a sufficient condition on the initial datum for global existence is given the asymptotic behaviour of the solutions of the approximating problems is studied

well posedness of the cauchy problem for the fractional power dissipative equations abstract this paper studies the cauchy problem for the nonlinear fractional power dissipative equation u t u f u for initial data in the lebesgue space l r r n with either r r d n b 2 d or the homogeneous besov space b p r n with 2 d b n p and 1 p where 0 f u f u or q d f u with q d being a homogeneous pseudo differential operator of order d 0 2 and f u is a function of u which behaves like u b u with b 0

iterative algorithms based on multistage criteria for multichannel blind deconvolution blind deconvolution and blind equalization have been important interesting topics in diverse fields including data communication image processing and geophysical data processing recently inouye and habe introduced a multistage criterion for attaining blind deconvolution of multiple input multiple output mimo linear time invariant lti systems in this correspondence based on their criterion we present iterative algorithms for solving the blind deconvolution problem of mimo lti systems however their criterion should be subjected to several constraints of equations therefore they proposed a new constraint free multistage criterion for accomplishing the blind deconvolution of mimo lti systems based on their unconstrained criterion we show iterative algorithms for solving the blind deconvolution of multichannel lti systems

on a whitening approach to partial channel estimation and blind equalization of fir iir multiple input multiple output channels channel estimation and blind equalization of multiple input multiple output mimo communications channels is considered using primarily the second order statistics of the data such models arise when a single receiver data from multiple sources is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we consider estimation of partial channel impulse response and design of finite length minimum mean square error mmse blind equalizers the basis of the approach is the design of a zero forcing equalizer that whitens the noise free data we allow infinite impulse response iir channels moreover the multichannel transfer function need not be column reduced our approaches also work when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros the channel length or model orders need not be known the sources are recovered up to a unitary mixing matrix and are further unmixed using higher order statistics of the data a linear prediction approach is also considered under the above conditions of possibly iir channels common subchannel zeros factors and not necessarily column reduced channels four illustrative simulation examples are provided

estimates of heat kernels for non local regular dirichlet forms in this paper we present new heat kernel upper bounds for a certain class of non local regular dirichlet forms on metric measure spaces including fractal spaces we use a new purely analytic method where one of the main tools is the parabolic maximum principle we deduce off diagonal upper bound of the heat kernel from the on diagonal one under the volume regularity hypothesis restriction of the jump kernel and the survival hypothesis as an application we obtain two sided estimates of heat kernels for non local regular dirichlet forms with finite effective resistance including settings with the walk dimension greater than 2

regularity properties of schrodinger operators abstract let l be a schrodinger operator of the form l v where the nonnegative potential v satisfies a reverse holder inequality using the method of l harmonic extensions we study regularity estimates at the scale of adapted holder spaces we give a pointwise description of l holder spaces and provide some characterizations in terms of the growth of fractional derivatives of any order and carleson measures applications to fractional powers of l and multipliers of laplace transform type developed

blind spatio temporal equalization and impulse response estimation for mimo channels using a godard cost function equalization and estimation of the matrix impulse response function of multiple input multiple output mimo digital communications channels in the absence of any training sequences is considered an iterative godard 1980 cost based approach is considered for spatio temporal equalization and mimo impulse response estimation stationary points of the cost function are investigated with particular attention to the case when finite length equalizers exist sufficient conditions are derived under which all stable local minima correspond to desirable minima the inputs are extracted and cancelled one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed

a weighted procrustes criterion the procrustes criterion is a common measure for the distance between two matricesx andy and can be interpreted as the sum of squares of the euclidean distances between their respective column vectors often a weighted procrustes criterion using for example a weighted sum of the squared distances between the column vectors is called for this paper describes and analyzes the performance of an algorithm for rotating a matrixx such that the column weighted procrustes distance toy is minimized the problem of rotatingx intoy such that an aggregate measure of tucker s coefficient of congruence is maximized is also discussed

the simultaneous maximization of congruence for two or more matrices under orthogonal rotation while a rotation procedure currently exists to maximize simultaneously tucker s coefficient of congruence between corresponding factors of two factor matrices under orthogonal rotation of one factor matrix only approximate solutions are known for the generalized case where two or more matrices are rotated a generalization and modification of the existing rotation procedure to simultaneously maximize the congruence is described an example using four data matrices comparing the generalized congruence maximization procedure with alternative rotation procedures is presented the results show a marked improvement of the obtained congruence using the generalized congruence maximization procedure compared to other procedures without a significant loss of success with respect to the least squares criterion a computer program written by the author to perform the rotations is briefly discussed

bmol hn spaces and carleson measures for schrodinger operators abstract let l h n v be a schrodinger operator on the heisenberg group h n where h n is the sub laplacian and the nonnegative potential v belongs to the reverse holder class b q 2 here q is the homogeneous dimension of h n in this article we investigate the dual space of the hardy type space h l 1 h n associated with the schrodinger operator l which is a kind of bmo type space bmo l h n defined by means of a revised sharp function related to the potential v we give the fefferman stein type decomposition of bmo l functions with respect to the adjoint riesz transforms r j l for l and characterize bmo l h n in terms of the carleson measure we also establish the bmo l boundedness of some operators such as the adjoint riesz transforms r j l the littlewood paley function s q l the lusin area integral s q l the hardy littlewood maximal function and the semigroup maximal function all results hold for stratified groups as well

a two stage algorithm for mimo blind deconvolution of nonstationary colored signals a new two stage algorithm is proposed for the deconvolution of multi input multi output mimo systems with colored input signals while many blind deconvolution algorithms in the literature utilize high order statistics of the output signal for white input signals the additional information contained in colored input signals allows the design of second order statistical algorithms in fact practical signal sources such as speech signals do have distinct nonstationary colored power spectral densities we present a two stage signal separation approach in which the first step utilizes a matrix pencil between output auto correlation matrices at different delays whereas the second stage adopts a subspace method to identify and deconvolve mimo systems

weak uncertainty principle for fractals graphs and metric measure spaces we develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by okoudjou and strichartz we assume either an appropriate measure growth condition with respect to the effective resistance metric or in the absence of such a metric we assume the poincare inequality and reverse volume doubling property we also consider the weak uncertainty inequality in the context of nash type inequalities our results can be applied to a wide variety of metric measure spaces including graphs fractals and manifolds

new sobolev spaces via generalized poincare inequalities on metric measure spaces in this paper we introduce some new function spaces of sobolev type on metric measure spaces these new function spaces are defined by variants of poincare inequalities associated with generalized approximations of the identity and they generalize the classical sobolev spaces on euclidean spaces we then obtain two characterizations of these new sobolev spaces including the characterization in terms of a variant of local sharp maximal functions associated with generalized approximations of the identity for the well known hajlasz sobolev spaces on metric measure spaces we also establish some new characterizations related to generalized approximations of the identity finally we clarify the relations between the sobolev type spaces introduced in this paper and the hajlasz sobolev spaces on metric measure spaces

a monotonically convergent algorithm for orthogonal congruence rotation brokken has proposed a method for orthogonal rotation of one matrix such that its columns have a maximal sum of congruences with the columns of a target matrix this method employs an algorithm for which convergence from every starting point is not guaranteed in the present paper an iterative majorization algorithm is proposed which is guaranteed to converge from every starting point specifically it is proven that the function value converges monotonically and that the difference between subsequent iterates converges to zero in addition to the better convergence properties another advantage of the present algorithm over brokken s one is that it is easier to program the algorithms are compared on 80 simulated data sets and it turned out that the new algorithm performed well in all cases whereas brokken s algorithm failed in almost half the cases the derivation of the algorithm is given in full detail because it involves a series of inequalities that can be of use to derive similar algorithms in different contexts

calculus and heat flow in metric measure spaces and applications to spaces with ricci bounds from below this paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces x mathsf d mathfrak m our main results are a general study of the relations between the hopf lax semigroup and hamilton jacobi equation in metric spaces x d the equivalence of the heat flow in l 2 x mathfrak m generated by a suitable dirichlet energy and the wasserstein gradient flow of the relative entropy functional mathrm ent mathfrak m in the space of probability measures open image in new window the proof of density in energy of lipschitz functions in the sobolev space w 1 2 x mathsf d mathfrak m a fine and very general analysis of the differentiability properties of a large class of kantorovich potentials in connection with the optimal transport problem is the fourth achievement of the paper our results apply in particular to spaces satisfying ricci curvature bounds in the sense of lott and villani ann math 169 903 991 2009 and sturm acta math 196 65 131 2006 and acta math 196 133 177 2006 and require neither the doubling property nor the validity of the local poincare inequality

analysis on products of fractals for a class of post critically finite p c f fractals which includes the sierpinski gasket sg there is a satisfactory theory of analysis due to kigami including energy harmonic functions and laplacians in particular the laplacian coincides with the generator of a stochastic process constructed independently by probabilistic methods the probabilistic method is also available for non p c f fractals such as the sierpinski carpet in this paper we show how to extend kigami s construction to products of p c f fractals since the products are not themselves p c f this gives the first glimpse of what the analytic theory could accomplish in the non p c f setting there are some important differences that arise in this setting it is no longer true that points have positive capacity so functions of finite energy are not necessarily continuous also the boundary of the fractal is no longer finite so boundary conditions need to be dealt with in a more involved manner all in all the theory resembles pde theory while in the p c f case it is much closer to ode theory

besov class via heat semigroup on dirichlet spaces i sobolev type inequalities abstract we introduce heat semigroup based besov classes in the general framework of dirichlet spaces general properties of those classes are studied and quantitative regularization estimates for the heat semigroup in this scale of spaces are obtained as a highlight of the paper we obtain a far reaching l p analogue p 1 of the sobolev inequality that was proved for p 2 by n varopoulos under the assumption of ultracontractivity for the heat semigroup the case p 1 is of special interest since it yields isoperimetric type inequalities

lower estimates of heat kernels for non local dirichlet forms on metric measure spaces abstract we are concerned with heat kernel estimates for a non local dirichlet form on an ahlfors regular metric measure space we use an analytic approach to obtain the full lower stable like estimate of the heat kernel from the near diagonal lower estimate combining with other known results we obtain certain equivalent conditions for two sided stable like estimates of the heat kernel the results can be simplified in certain cases for example when the dirichlet form admits an effective resistance

a least squares approach to blind channel identification conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input in some practical applications however the input statistical model may not be known or there may not be sufficient data to obtain accurate enough estimates of certain statistics in this paper we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel fir systems without requiring the knowledge of the input statistical model a new blind identification algorithm based solely on the system outputs is proposed necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented

transition density estimates for brownian motion on affine nested fractals a class of affine nested fractals is introduced which have different scale factors for different similitudes but still have the symmetry assumptions of nested fractals for these fractals estimates on the transition density for the brownian motion are obtained using the associated dirichlet form an upper bound for the diagonal can be found using a nash type inequality then probabilistic techniques are used to obtain the off diagonal bound the approach differs from previous treatments as it uses only the dirichlet form and no estimates on the resolvent the bounds obtained are expressed in terms of an intrinsic metric on the fractal

characterization of sub gaussian heat kernel estimates on strongly recurrent graphs sub gaussian estimates for random walks are typical of fractal graphs we characterize them in the strongly recurrent case in terms of resistance estimates only without assuming elliptic harnack inequalities

off diagonal upper estimates for the heat kernel of the dirichlet forms on metric spaces we give equivalent characterizations for off diagonal upper bounds of the heat kernel of a regular dirichlet form on the metric measure space in two settings for the upper bounds with the polynomial tail typical for jump processes and for the upper bounds with the exponential tail for diffusions our proofs are purely analytic and do not use the associated hunt process

regularity and capacity for the fractional dissipative operator abstract this paper is devoted to exploring some analytic geometric properties of the regularity and capacity associated with the so called fractional dissipative operator t naturally establishing a diagonally sharp hausdorff dimension estimate for the blow up set of a weak solution to the fractional dissipative equation t u t x f t x subject to u 0 x 0 the methods used in this paper rely on effectively controlling the time dependent non local kernels and potentials with fractional order 0 1 dual representation of the capacity and frostman type theorem from geometric measure theory

zero forcing blind equalization based on subspace estimation for multiuser systems input signal recovery from frequency selective fading channels is a problem of great theoretical and practical importance we present several new blind algorithms that utilize second order statistics for direct multichannel equalization the algorithms are based on the subspace extraction of a preselected block column of the channel convolution matrix for a multiuser system user signal separation can be achieved based on partial information of the composite channel response these equalization algorithms do not rely on the precise separation of signal and noise subspaces and therefore tend to be less sensitive to channel order or column rank estimation errors equalization is directly achieved without channel identification furthermore the equalizability conditions of these algorithms are discussed

hos based semi blind spatial equalization for mimo rayleigh fading channels in this paper we concentrate on the direct semi blind spatial equalizer design for mimo systems with rayleigh fading channels our aim is to develop an algorithm which can outperform the classical training based method with the same training information used and avoid the problems of low convergence speed and local minima due to pure blind methods a general semi blind cost function is first constructed which incorporates both the training information from the known data and some kind of higher order statistics hos from the unknown sequence then based on the developed cost function we propose two semi blind iterative and adaptive algorithms to find the desired spatial equalizer to further improve the performance and convergence speed of the proposed adaptive method we propose a technique to find the optimal choice of step size simulation results demonstrate the performance of the proposed algorithms and comparable schemes

random walks and induced dirichlet forms on self similar sets abstract let k be a self similar set satisfying the open set condition following kaimanovich s elegant idea 25 it has been proved that on the symbolic space x of k a natural augmented tree structure e exists it is hyperbolic and the hyperbolic boundary h x with the gromov metric is holder equivalent to k in this paper we consider certain reversible random walks with return ratio 0 1 on x e we show that the martin boundary m can be identified with h x and k with this setup and a device of silverstein 41 we obtain precise estimates of the martin kernel and the naim kernel in terms of the gromov product moreover the naim kernel turns out to be a jump kernel satisfying the estimate where is the hausdorff dimension of k and depends on for suitable the kernel defines a regular non local dirichlet form on k this extends the results of kigami 27 concerning random walks on certain trees with cantor type sets as boundaries see also 5

multichannel arma processes parametric modeling of multichannel time series is accomplished by using higher than second order statistics hos of the observed nongaussian data cumulants of vector processes are defined using a kronecker product formulation and consistency of their sample estimators is addressed identifiability results in connection with the hos based parameter estimation of causal and noncausal multivariate arma processes are established estimates of the parameters of causal arma models are obtained as the solution to a set of linear equations whereas those of noncausal arma models are obtained as the solution to a cumulant matching algorithm conventional approaches based on second order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix hos based methods yield solutions that are unique to within post multiplication by an extended permutation matrix additionally the multiminimum phase assumption can be relaxed and the observations may be contaminated with colored gaussian noise frequency domain methods for nonparametric system identification are discussed briefly simulations results validating the multichannel parameter estimation algorithms are provided

semilinear fractal problems approximation and regularity results abstract we prove existence and uniqueness of the weak solution for a second order semilinear transmission problem in a bounded domain in r 3 in the case of a koch type fractal layer s or the corresponding prefractal layer approximating s we study the asymptotic behavior of the solutions of the corresponding prefractal problem and we prove regularity results for the weak solution via a generalized green formula for domains with fractal boundaries

orthogonal procrustes rotation maximizing congruence procedures for assessing the invariance of factors found in data sets using different subjects and the same variables are often using the least squares criterion which appears to be too restrictive for comparing factors

mimo blind second order equalization method and conjugate cyclostationarity the blind identification of vector valued fir transfer functions using exclusively second order statistics of the output has become conventional the so called subspace method provides a nice and efficient way of solving the problem however the extension to the multi input multi output mimo case is not that straightforward and for instance some indetermination drawbacks may occur we show in this correspondence that the introduction of some cyclostationarity at the input which still leads to feasible systems may lead to an algorithm that is far more satisfactory because for both it is less prone to indetermination problems and the required assumptions are not too sophisticated

a note on hajlasz sobolev spaces on fractals abstract we introduce hajlasz sobolev spaces involving walk dimensions on subsets of r n that will generally be fractals the relationship between this kind of new space and the besov space of jonsson and wallin is investigated the compact embedding theorems for hajlasz sobolev spaces are obtained

calderon reproducing formulas and new besov spaces associated with operators abstract let l be the generator of an analytic semigroup whose heat kernel satisfies an upper bound of poisson type acting on l 2 x where x is a possibly non doubling space of polynomial upper bound on volume growth the aim of this paper is to introduce a new class of besov spaces associated with the operator l so that when l is the laplace operator or its square root acting on the euclidean space r n the new besov spaces are equivalent to the classical besov spaces depending on the choice of l the new besov spaces are natural settings for generic estimates for certain singular integral operators such as the fractional powers l since our approach does not require the doubling volume property of the underlying space it is applicable to any subset of euclidean spaces without any smoothness requirement on the boundary we will also develop a number of calderon reproducing formulas which play an important role in the theory of function spaces and are of independent interest as an application we study besov spaces associated with schrodinger operators with non negative potentials satisfying reverse holder estimates

parabolic type equations associated with the dirichlet form on the sierpinski gasket by using analytic tools from stochastic analysis we initiate a study of some non linear parabolic equations on sierpinski gasket motivated by modellings of fluid flows along fractals which can be considered as models of simplified rough porous media unlike the regular space case such parabolic type equations involving non linear convection terms must take a different form due to the fact that convection terms must be singular to the linear part which defines the heat semigroup in order to study these parabolic type equations a new kind of sobolev inequalities for the dirichlet form on the gasket will be established these sobolev inequalities which are interesting on their own and in contrast to the case of euclidean spaces involve two l p norms with respect to two mutually singular measures by examining properties of singular convolutions of the associated heat semigroup we derive the space time regularity of solutions to these parabolic equations under a few technical conditions the burgers equations on the sierpinski gasket are also studied for which a maximum principle for solutions is derived using techniques from backward stochastic differential equations and the existence uniqueness and regularity of its solutions are obtained

heat kernels on metric measure spaces and an application to semilinear elliptic equations we consider a metric measure space m d p and a heat kernel p t x v on m satisfying certain upper and lower estimates which depend on two parameters a and we show that under additional mild assumptions these parameters are determined by the intrinsic properties of the space m d namely a is the hausdorff dimension of this space whereas called the walk dimension is determined via the properties of the family of besov spaces w 2 on m moreover the parameters a and are related by the inequalities 2 a 1 we prove also the embedding theorems for the space w 2 2 and use them to obtain the existence results for weak solutions to semilinear elliptic equations on m of the form u f x u g x where is the generator of the semigroup associated with p t the framework in this paper is applicable for a large class of fractal domains including the generalized sierpinski carpet in r n

inhomogeneous parabolic equations on unbounded metric measure spaces kenneth j falconermathematical institute university of st andrews north haugh st andrews fife ky16 9ss uk kjf st andrews ac uk jiaxin hu and yuhua sundepartment of mathematical sciences tsinghua university beijing 100084 people s republic of china hujiaxin mail tsinghua edu cn sunyh08 mails tsinghua edu cn

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

quasiconformal maps in metric spaces with controlled geometry this paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry the principal message is that such a theory is both relevant and viable the first main issue is the problem of definition which we next describe quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount this requirement makes sense in every metric space given a homeomorphism f from a metric space x to a metric space y then for x x and r 0 set

general approach to blind source separation this paper identifies and studies two major issues in the blind source separation problem separability and separation principles we show that separability is an intrinsic property of the measured signals and can be described by the concept of m row decomposability introduced in this paper we also show that separation principles can be developed by using the structure characterization theory of random variables in particular we show that these principles can be derived concisely and intuitively by applying the darmois skitovich theorem which is well known in statistical inference theory and psychology some new insights are gained for designing blind source separation filters

strichartz type estimates for fractional heat equations abstract we obtain strichartz estimates for the fractional heat equations by using both the abstract strichartz estimates of keel tao and the hardy littlewood sobolev inequality we also prove an endpoint homogeneous strichartz estimate via replacing l x r n by bmo x r n and a parabolic homogeneous strichartz estimate meanwhile we generalize the strichartz estimates by replacing the lebesgue spaces with either besov spaces or sobolev spaces moreover we establish the strichartz estimates for the fractional heat equations with a time dependent potential of an appropriate integrability as an application we prove the global existence and uniqueness of regular solutions in spatial variables for the generalized navier stokes system with l r r n data

geometric statistics in turbulence the author presents results regarding certain average properties of incompressible fluids derived from the equations of motion the author estimates the average dissipation rate the average dimension of level sets the role played by the field of direction of vorticity in the three dimensional euler and navier stokes equations is discussed and a class of two dimensional equations that are useful models of incompressible dynamics is described the author presents results concerning scaling exponents in turbulence

high order contrasts for independent component analysis this article considers high order measures of independence for the independent component analysis problem and discusses the class of jacobi algorithms for their optimization several implementations are discussed we compare the proposed approaches with gradient based techniques from the algorithmic point of view and also on a set of biomedical data