a paley wiener theorem for real reductive groups le groupe sl 3 r prequantification des orbites de dimension minimale parmi celles non triviales dans la representation co adjointe de sl 3 r noyaux de blattner kostant steinberg irreductibilite et unicite du prolongement de certaines representations de p 3 a sl 3 r etude du prolongement des representations e a sl 3 r la representation type s s 2 minimal parametres de langlands et operateur d entrelacement avec la serie principale pour les representations e et

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 new method for the numerical solution of simultaneous nonlinear equations a new technique is developed for the numerical solution of simultaneous nonlinear equations snes this is achieved by the iterative solution of a parametric linear system coupled with a nonlinear single variable equation the new technique converges very quickly and is ideal for cases where the system of equations can be easily differentiated it is motivated by the multivariable newton raphson mnr method and is approximately of second order convergence furthermore we introduce the zeros jacobian for the jacobian evaluated at some arbitrary zeros of the vector function components this is utilized in computing a feasible starting point for snes the computation of a starting point would be very useful for systems where one has no prior knowledge of the possible solutions

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

sur le theoreme de paley wiener d arthur the fourier transform of a c function f with compact support on a real reductive lie group g is given by a collection of operators o p e ip e f for a suitable family of representations of g which depends on a family indexed by p in a finite set of parabolic subgroups of g of pairs of parameters e varying in a set of discrete series e lying in a complex finite dimensional vector space the ip e are generalized principal series induced from p it is easy to verify the holomorphy of the fourier transform in the complex parameters also it satisfies some growth properties moreover an intertwining operator between two representations ip e ip e of the family implies an intertwining property for o p e and o p e there is also a way to introduce hsuccessive partial derivatives h of the family of representations ip e along the parameter e and intertwining operators between subquotients of these successive derivatives imply the intertwining property for the successive derivatives of the fourier transform o we show that these properties characterize the collections of operators p e o p e which are fourier transforms of a c function with compact support for g linear the proof which uses harish chandra fs plancherel formula rests on a similar result for left and right k finite functions which is due to j arthur we give also a proof of arthur fs result purely in term of representations involving the work of a knapp and e stein on intertwining integrals and langlands and vogan fs classifications of irreducible representations of g

derivations as square roots of dirichlet forms abstract the aim of this work is to analyze the structure of a tracially symmetric dirichlet form on a c algebra in terms of a killing weight and a closable derivation taking values in a hilbert space with a bimodule structure it is shown that the generator of the associate markovian semigroup always appears in a natural way as the divergence of a closable derivation applications are shown to the decomposition of dirichlet forms and to the construction of differential calculus on metric spaces

the principal series for a reductive symmetric space ii eisenstein integrals in this paper we develop a theory of eisenstein integrals related to the principal series for a reductive symmetric space g h here g is a real reductive group of harish chandra s class an involution of g and h an open subgroup of the group g of xed points for the group g itself is a symmetric space for the left right action of g g we refer to this setting as the group case up to a normalization our eisenstein integrals generalize those of harish chandra 18 associated with a minimal parabolic subgroup in the group case

dirichlet forms and markovian semigroups on standard forms of von neumann algebras we characterize w continuous markovian semigroups on a von neumann algebra m which are 0 symmetric w r t a faithful normal state 0in m in terms of quadratic forms on the hilbert space h of a standard form m h p j we characterize also symmetric strongly continuous contraction semigroups on a real hilbert space h which leave invariant a closed convex set in h in terms of a contraction property of the associated quadratic forms we apply the results to give criteria of essential selfadjointness for quadratic form sums and to give a characterization of w continuous markovian semigroups on m which commute with the modular automorphism group 0t

invariance principle for the random conductance model with unbounded conductances we study a continuous time random walk x in an environment of i i d random conductances e 1 we obtain heat kernel bounds and prove a quenched invariance principle for x this holds even when e e

sinc galerkin method for solving nonlinear boundary value problems the sinc galerkin method is used to approximate solutions of nonlinear problems involving nonlinear second fourth and sixth order differential equations with homogeneous and nonhomogeneous boundary conditions the scheme is tested on four nonlinear problems the results demonstrate the reliability and efficiency of the algorithm developed

a local paley wiener theorem for compact symmetric spaces abstract the fourier coefficients of a smooth k invariant function on a compact symmetric space m u k are given by integration of the function against the spherical functions for functions with support in a neighborhood of the origin we describe the size of the support by means of the exponential type of a holomorphic extension of the fourier coefficients

analysis on graphs and noncommutative geometry abstract we study the form of the continuous time heat kernel for a second order discrete laplacian on a weighted graph the analysis is shown to be closely related to the theory of symmetric markov semigroups on noncommutative l p spaces and to the noncommutative geometry of connes the paper obtains better pointwise upper bounds on the heat kernels than those previously known by the use of a novel metric on the graph in certain cases it is shown that the new estimates are optimal of their type the metric is investigated at some length and compared with other known metrics on graphs

dirac operators and the calculation of the connes metric on arbitrary infinite graphs as an outgrowth of our investigation of non regular spaces within the context of quantum gravity and non commutative geometry we develop a graph hilbert space framework on arbitrary infinite graphs and use it to study spectral properties of graph laplacians and graph dirac operators we define a spectral triplet sharing most of the properties of what connes calls a spectral triple with the help of this scheme we derive an explicit expression for the connes distance function on general directed or undirected graphs we derive a series of a priori estimates and calculate it for a variety of examples of graphs as a possibly interesting side we show that the natural setting for approaching such problems may be the framework of non linear programming or optimization we compare our results arrived at within our particular framework with those of other authors and show that the seeming differences depend on the use of different graph geometries and or dirac operators

dirac and magnetic schrodinger operators on fractals abstract in this paper we define local dirac operators and magnetic schrodinger hamiltonians on fractals and prove their essential self adjointness to do so we use the concept of 1 forms and derivations associated with dirichlet forms as introduced by cipriani and sauvageot and further studied by the authors jointly with rockner ionescu and rogers for simplicity our definitions and results are formulated for the sierpinski gasket with its standard self similar energy form we point out how they may be generalized to other spaces such as the classical sierpinski carpet

a paley wiener theorem for reductive symmetric spaces let x g h be a reductive symmetric space and k a maximal compact subgroup of g the image under the fourier transform of the space of k finite compactly supported smooth functions on x is characterized

intrinsic metrics for non local symmetric dirichlet forms and applications to spectral theory we present a study of what may be called an intrinsic metric for a general regular dirichlet form for such forms we then prove a rademacher type theorem for strongly local forms we show existence of a maximal intrinsic metric under a weak continuity condition and for dirichlet forms with an absolutely continuous jump kernel we characterize intrinsic metrics by bounds on certain integrals we then turn to applications on spectral theory and provide for measure perturbation of general regular dirichlet forms an allegretto piepenbrinck type theorem which is based on a ground state transform and a shnol type theorem our setting includes laplacian on manifolds on graphs and stable processes

dirac operators and spectral triples for some fractal sets built on curves abstract we construct spectral triples and in particular dirac operators for the algebra of continuous functions on certain compact metric spaces the triples are countable sums of triples where each summand is based on a curve in the space several fractals like a finitely summable infinite tree and the sierpinski gasket fit naturally within our framework in these cases we show that our spectral triples do describe the geodesic distance and the minkowski dimension as well as more generally the complex fractal dimensions of the space furthermore in the case of the sierpinski gasket the associated dixmier type trace coincides with the normalized hausdorff measure of dimension log 3 log 2

fourier transforms on a semisimple symmetric space let g h be a semisimple symmetric space that is g is a connected semisimple real lie group with an involution and h is an open subgroup of the group of xed points for in g the main purpose of this paper is to study an explicit fourier transform on g h in terms of general representation theory the abstract fourier transform of a compactly supported smooth function f 2 c 1 c g h is given by see 5 1 f f zg h f x x dx for h a unitary irreducible representation of g and 2 h an h invariant distribution vector for here dx is the invariant measure on g h thus f isa smooth vector for h depending linearly on our goal is to obtain an explicit version of the restriction of this fourier transform to representations h in the minimal unitary principal series h for g h under the assumption that the center of g is nite in a sequel 9 to this paper it will be proved that a function f 2 c 1 c g h is uniquely determined by the restriction of f to this series a priori it is known that f is determined by f