a spectral mapping theorem for perturbed ornstein uhlenbeck operators on l2 rd abstract we consider ornstein uhlenbeck operators on l 2 r d perturbed by a radial potential v under weak assumptions on v we prove a spectral mapping theorem for the generated semigroup the proof relies on a perturbative construction of the resolvent based on angular separation and the gearhart pruss theorem

products in hochschild cohomology and grothendieck rings of group crossed products abstract we give a general construction of rings graded by the conjugacy classes of a finite group some examples of our construction are the hochschild cohomology ring of a finite group algebra the grothendieck ring of the drinfel d double of a group and the orbifold cohomology ring for a global quotient we generalize the first two examples by deriving product formulas for the hochschild cohomology ring of a group crossed product and for the grothendieck ring of an abelian extension of hopf algebras our results account for similarities in the product structures among these examples

on the lp theory of c0 semigroups associated with second order elliptic operators with complex singular coefficients we study lp theory of second order elliptic divergence type operators with complex measurable coefficients the major aspect is that we allow complex coefficients in the main part of the operator too we investigate generation of analytic c0 semigroups under very general conditions on the coefficients related to the notion of form boundedness we determine an interval j in the lp scale not necessarily containing p 2 in which one obtains a consistent family of quasi contractive semigroups this interval is close to optimal as shown by several examples in the case of uniform ellipticity we construct a family of semigroups in an extended range of lp spaces and we prove p independence of the analyticity sector and of the spectrum of the generators

hochschild duality localization and smash products abstract in this work we study the class of algebras satisfying a duality property with respect to hochschild homology and cohomology as in proc amer math soc 126 1998 1345 1348 more precisely we consider the class of algebras a such that there exists an invertible bimodule u and an integer number d with the property h a m h d a u a m for all a bimodules m we show that this class is closed under localization and under smash products with respect to hopf algebras satisfying also the duality property we also illustrate the subtlety on dualities with smash products developing in detail the example s v g the crossed product of the symmetric algebra on a vector space and a finite group acting linearly on v

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

some classes of non analytic markov semigroups we deal with markov semigroups tt corresponding to second order elliptic operators au u du f where f is an unbounded locally lipschitz vector field on rn we obtain new conditions on f under which tt is not analytic in cb rn in particular we prove that the one dimensional operator au u x3u with domain u c2 r u u x3u cb r is not sectorial in cb r under suitable hypotheses on the growth of f we introduce a class of non analytic markov semigroups in lp rn where is an invariant measure for tt

estimates of the derivatives for parabolic operators with unbounded coefficients we consider a class of second order uniformly elliptic operators a with unbounded coefficients in r n using a bernstein approach we provide several uniform estimates for the semigroup t t generated by the realization of the operator a in the space of all bounded and continuous or holder continuous functions in r n as a consequence we obtain optimal schauder estimates for the solution to both the elliptic equation u au f 0 and the nonhomogeneous dirichlet cauchy problem d t u au g then we prove two different kinds of pointwise estimates of t t that can be used to prove a liouville type theorem finally we provide sharp estimates of the semigroup t t in weighted l p spaces related to the invariant measure associated with the semigroup

functional calculus for the ornstein uhlenbeck operator let be the gauss measure on rd and l the ornstein uhlenbeck operator which is self adjoint in l2 for every p in 1 p 2 set p arc sin 2 p 1 and consider the sector s p z c arg z p the main result of this paper is that if m is a bounded holomorphic function on s p whose boundary values on s p satisfy suitable hormander type conditions then the spectral operator m l extends to a bounded operator on lp and hence on lq for all q such that 1 q 1 2 1 p 1 2 the result is sharp in the sense that l does not admit a bounded holomorphic functional calculus in a sector smaller than s p

spectral sequences for the cohomology rings of a smash product abstract stefan and guichardet have provided lyndon hochschild serre type spectral sequences which converge to the hochschild cohomology and ext groups of a smash product we show that these spectral sequences carry natural multiplicative structures and that these multiplicative structures can be used to calculate the cup product on hochschild cohomology and the yoneda product on an ext algebra

gaussian bounds for propagators perturbed by potentials abstract we develop the perturbation theory for propagators with the objective to prove gaussian bounds let u be a strongly continuous propagator i e a family of operators describing the solutions of a non autonomous evolution equation on an l p space and assume that u is positive and satisfies gaussian upper and lower bounds let v be a time dependent potential satisfying certain miyadera conditions with respect to u we show that then the perturbed propagator enjoys gaussian upper and lower bounds as well to prepare the necessary tools we extend the perturbation theory of strongly continuous propagators and the theory of absorption propagators

poisson homology in degree 0 for some rings of symplectic invariants abstract let g be a finite dimensional semi simple lie algebra h a cartan subalgebra of g and w its weyl group the group w acts diagonally on v h h as well as on c v the purpose of this article is to study the poisson homology of the algebra of invariants c v w endowed with the standard symplectic bracket to begin with we give general results about the poisson homology space in degree 0 denoted by hp 0 c v w in the case where g is of type b n c n or d n results which support alev s conjecture then we are focusing the interest on the particular cases of ranks 2 and 3 by computing the poisson homology space in degree 0 in the cases where g is of type b 2 so 5 d 2 so 4 then b 3 so 7 and d 3 a 3 so 6 sl 4 in order to do this we make use of a functional equation introduced by y berest p etingof and v ginzburg we recover by a different method the result established by j alev and l foissy according to which the dimension of hp 0 c v w equals 2 for b 2 then we calculate the dimension of this space and we show that it is equal to 1 for d 2 we also calculate it for the rank 3 cases we show that it is equal to 3 for b 3 c 3 and 1 for d 3 a 3

analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations abstract we consider elliptic operators associated with discrete groups of quantized canonical transformations in order to be able to apply results from algebraic index theory we define the localized algebraic index of the complete symbol of an elliptic operator with the help of a calculus of semiclassical quantized canonical transformations a version of egorov s theorem and a theorem on trace asymptotics for semiclassical fourier integral operators we show that the localized analytic index and the localized algebraic index coincide as a corollary we express the fredholm index in terms of the algebraic index for a wide class of groups in particular for finite extensions of abelian groups

on maximal regularity of type lp lq under minimal assumptions for elliptic non divergence operators we prove maximal regularity of type l p l q for operators in non divergence form with complex valued measurable coefficients on r n for a certain range of q which depends on dimension and the order of the operators this is done under the sole assumption that they generate an analytic semigroup in l q thus we give for this class of operators and this range of q a positive answer to brezis question whether generation of an analytic semigroup entails maximal l p regularity for other values of q we give several additional assumptions the proof relies on a result on maximal regularity under the assumption of suitable off diagonal bounds due to s blunck and the author which we improve here these off diagonal bounds are obtained by a modification of davies technique suited to cope with operators in non divergence form and they also imply new results on the scale of l q spaces in which a given operator generates an analytic semigroup we thus obtain a completely new approach to maximal l p regularity for operators of this kind in particular for those whose highest order coefficients belong to vmo moreover we obtain extensions of recent results due to kim and krylov for operators with measurable coefficients depending on one coordinate

schrodinger operators with ll 2w rl potentials we consider the schrodinger operators v with v in the weak lq class with q 1 2 the underlying dimension which is the borderline for a definition to be possible we concentrate first on optimal bounds on how large the weak norm of v can be and then on spectral properties on lp spaces

the absolute continuity of the integrated density of states for magnetic schrodinger operators with certain unbounded random potentials the object of the present study is the integrated density of states of a quantum particle in multi dimensional euclidean space which is characterized by a schrodinger operator with magnetic field and a random potential which may be unbounded from above and below in case that the magnetic field is constant and the random potential is ergodic and admits a so called one parameter decomposition we prove the absolute continuity of the integrated density of states and provide explicit upper bounds on its derivative the density of states this local lipschitz continuity of the integrated density of states is derived by establishing a wegner estimate for finite volume schrodinger operators which holds for rather general magnetic fields and different boundary conditions examples of random potentials to which the results apply are certain alloy type and gaussian random potentials besides we show a diamagnetic inequality for schrodinger operators with neumann boundary conditions

a t 1 theorem for non integral operators let x be a space of homogeneous type and let l be a sectorial operator with bounded holomorphic functional calculus on l 2 x we assume that the semigroup e tl t 0 satisfies davies gaffney estimates associated with l are certain approximations of the identity we call an operator t a non integral operator if compositions involving t and these approximations satisfy certain weighted norm estimates the davies gaffney and the weighted norm estimates are together a substitute for the usual kernel estimates on t in calderon zygmund theory in this paper we show under the additional assumption that a vertical littlewood paley stein square function associated with l is bounded on l 2 x that a non integral operator t is bounded on l 2 x if and only if t 1 in bmo l x and t 1 in bmo l x here bmo l x and bmo l x denote the recently defined bmo x spaces associated with l that generalize the space bmo x of john and nirenberg generalizing a recent result due to f bernicot we show a second version of a t 1 theorem under weaker off diagonal estimates which gives a positive answer to a question raised by him as an application we prove l 2 x boundedness of a paraproduct operator associated with l we moreover study criterions for a t b theorem to be valid

weak type p p estimates for riesz transforms we consider the problem of l p boundedness of higher order riesz transforms associated to elliptic operators l of order 2m on as an application of the recently solved kato conjecture we show for all this generalizes the result of auscher and tchamitchian restricted to the case d 2m

fixed rings of the weyl algebra c abstract a complete classification up to isomorphism is given of the fixed rings a1 c g of the weyl algebra a1 c with respect to the action of a finite group g the quillen higher k groups ki a1 c g and in most cases the trace group or zeroth homology h0 a1 c g a1 c g a1 c g a1 c g are calculated for these rings

poisson deformations of symplectic quotient singularities abstract we establish a connection between smooth symplectic resolutions and symplectic deformations of a possibly singular affine poisson variety in particular let v be a finite dimensional complex symplectic vector space and g sp v a finite subgroup our main result says that the so called calogero moser deformation of the orbifold v g is in an appropriate sense a versal poisson deformation that enables us to determine the algebra structure on the cohomology h x c of any smooth symplectic resolution x v g multiplicative mckay correspondence we prove further that if g gl h is an irreducible weyl group and v h h then no smooth symplectic resolution of v g exists unless g is of types a b c

on the ornstein uhlenbeck operator in spaces of continuous functions we study the realization of the ornstein uhlenbeck operator a in the space of the uniformly continuous and bounded functions in rn we prove that it generates a semigroup which is neither strongly continuous nor analytic but enjoys nice smoothing properties such properties are used to prove a schauder type theorem for the elliptic equation u au f

absorption semigroups their generators and schrodinger semigroups on presente des resultats de perturbations pour des c 0 semi groupes on considere le probleme aux valeurs initiales pour l equation de la chaleur avec absorption avec une solution dans l p r v avec une mauvaise fonction v r r on considere le meme probleme dans l 2 r pour l equation de schrodinger

gaussian bounds for higher order elliptic differential operators with kato type potentials abstract let p d be a nonnegative homogeneous elliptic operator of order 2m with real constant coefficients on r n and v be a suitable real measurable function in this paper we are mainly devoted to establish the gaussian upper bound for schrodinger type semigroup e t h generated by h p d v with kato type perturbing potential v which naturally generalizes the classical result for schrodinger semigroup e t v as v k 2 r n the famous kato potential class our proof significantly depends on the analyticity of the free semigroup e t p d on l 1 r n as a consequence of the gaussian upper bound the l p spectral independence of h is concluded

ultracontractivity and the heat kernel for schrodinger operators and dirichlet laplacians abstract abstract connections between integral kernels of positivity preserving semigroups and suitable lp contractivity properties are established then these questions are studied for the semigroups generated by v and h the dirichlet laplacian for an open connected region as an application under a suitable hypothesis sobolev estimates are proved valid up to of the form x c 0 x h k 2 where 0 is the unique positive l2 eigenfunction of h

gaussian estimates for elliptic operators with unbounded drift we consider a strictly elliptic operator au ij di aij dj u b u div c u vu

equivariant lefschetz number of differential operators let g be a compact lie group acting on a compact complex manifold m by holomorphic transformations we prove a trace density formula for the g lefschetz number of a holomorphic differential operator on m we generalize the recent results of engeli and the first author to orbifolds

on the asymptotic s n structure of invariant differential operators on symplectic manifolds abstract we consider the space of polydifferential operators on n functions on symplectic manifolds invariant under symplectic automorphisms whose study was initiated by mathieu in 1995 permutations of inputs yield an action of s n which extends to an action of s n 1 we study this structure viewing n as a parameter in the sense of deligne s category for manifolds of dimension 2d we show that the isotypic part of this space of 2 d 1 th tensor powers of the reflection representation h c n of s n 1 is spanned by poisson polynomials we also prove a partial converse and compute explicitly the isotypic part of 4 th tensor powers of the reflection representation we give generating functions for the isotypic parts corresponding to young diagrams which only differ in the length of the top row and prove that they are rational fractions whose denominators are related to hook lengths of the diagrams obtained by removing the top row this also gives such a formula for the same isotypic parts of induced representations from z n 1 to s n 1 where n is viewed as a parameter we show that the space of invariant operators of order 2m has polynomial dimension in n of degree equal to 2m while the part not coming from poisson polynomials has polynomial dimension of degree 2 m 3 we use this to compute asymptotics of the dimension of invariant operators we also give new bounds on the order of invariant operators for a fixed n we apply this to the poisson and hochschild homology associated to the singularity c 2 d n s n 1 namely the canonical surjection from hp 0 o c 2 d n s n 1 o c 2 d n to gr hh 0 weyl c 2 d n s n 1 weyl c 2 d n the brylinski spectral sequence in degree zero restricts to an isomorphism in the aforementioned isotypic part h 2 d 1 and also in h 4 we prove a partial converse finally the kernel of the entire surjection has dimension on the order of 1 n 3 times the dimension of the homology group

suites spectrales a la hochschild serre pour les produits croises d algebres et de groupes resume etant donne le produit croise b g a d une algebre a par un groupe d automorphismes g et un b bimodule x on construit une filtration du complexe standard hom b x calculant la cohomologie de hochschild h b x on montre ensuite que la suite spectrale associee a cette filtration verifie e p q 2 h p g h q a x ceci generalise la methode directe utilisee par hochschild et serre 1953 dans le cas des extensions de groupes on applique cela a certains automorphismes des tores t d on prend pour g le groupe z pour a l algebre des polynomes trigonometriques sur t d et on construit des bases des divers espaces h n b b au sein du complexe standard hom b b given the crossed product b g a of an algebra a by a group of automorphisms g and a b bimodule x we construct a filtration of the standard complex hom b x which computes the hochschild cohomology h b x then we show that the associated spectral sequence satisfies e p q 2 h p g h q a x this generalizes the direct method used by hochschild and serre 1953 in the case of a group extension we apply this to certain automorphisms of the tori t d where g is the group z and a is the algebra of trigonometric polynomials on t d and we construct bases of the spaces h n b b inside the standard complex hom b b

representing measures and infinite dimensional holomorphy we consider some applications of the bishop de leeuw theorem about representing measures for some algebras of analytic functions on unit balls of banach spaces in particular we investigate hardy spaces h2 associated with corresponding algebras some examples are considered

generalized double affine hecke algebras of rank 1 and quantized del pezzo surfaces abstract let d be a simply laced dynkin diagram of rank r whose affinization has the shape of a star i e d 4 e 6 e 7 e 8 to such a diagram one can attach a group g whose generators correspond to the legs of the affinization have orders equal to the leg lengths plus 1 and the product of the generators is 1 the group g is then a 2 dimensional crystallographic group g z l z 2 where l is 2 3 4 and 6 respectively in this paper we define a flat deformation h t q of the group algebra c g of this group by replacing the relations saying that the generators have prescribed orders by their deformations saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots which are deformation parameters the algebra h t q for d 4 is the cherednik algebra of type c c 1 which was studied by noumi sahi and stokman and controls askey wilson polynomials we prove that h t q is the universal deformation of the twisted group algebra of g and that this deformation is compatible with certain filtrations on c g we also show that if q is a root of unity then for generic t the algebra h t q is an azumaya algebra and its center is the function algebra on an affine del pezzo surface for generic q the spherical subalgebra e h t q e provides a quantization of such surfaces we also discuss connections of h t q with preprojective algebras and painleve vi

on the lp theory of c0 semigroups associated with second order elliptic operators ii abstract we study positive c 0 semigroups on l p associated with second order uniformly elliptic divergence type operators with singular lower order terms subject to a wide class of boundary conditions we obtain an interval p min p max in the l p scale where these semigroups can be defined including the case 2 p min p max we present an example showing that the result is optimal we also show that the semigroups are analytic with angles of analyticity and spectra of the generators independent of p for the whole range of p where the semigroups are defined

ultraboundedness for parabolic equations in convex domains without boundary conditions abstract we consider the operator a u 1 2 u d u d u where u is a convex real function defined in a convex open set o r n and lim x u x lim x o u x we prove that the associated markov semigroup is ultrabounded with respect to the gibbs measure e 2 u x d x

local existence and regularity for a class of degenerate parabolic equations on etudie des equations paraboliques scalaires a une variable d espace de la forme u t f u u x uu xx ou f f u p s est une fonction lisse de u p s r 3 avec f s strictement positive

an algebraic index theorem for orbifolds abstract using the concept of a twisted trace density on a cyclic groupoid a trace is constructed on a formal deformation quantization of a symplectic orbifold an algebraic index theorem for orbifolds follows as a consequence of a local riemann roch theorem for such densities in the case of a reduced orbifold this proves a conjecture by fedosov schulze and tarkhanov finally it is shown how the kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem

l1 properties of intrinsic schrodinger semigroups abstract we investigate the l 1 properties of the intrinsic markov semigroup associated with a schrodinger operator on r n which possesses a positive ground state we discover cases for which this semigroup is norm analytic for positive times and others for which the semigroup is norm discontinuous in the strongest possible sense in the case of the harmonic oscillator we show that the generator of the intrinsic semigroup has totally different spectrum depending on whether one works in l 1 r e x 2 dx or l 2 r e x 2 dx in more general cases we show that the equality of the l 1 and l 2 spectrum is closely related to whether the schrodinger semigroup is intrinsically ultracontractive

conditional transformation of drift formula and potential theory for 1 2 b using conditional brownian motion and the transformation of drift formula of cameron martin girsarov maruyama we give integral conditions on a vector fieldb which imply the harmonic measures and green functions for 1 2 and 1 2 b on a bounded lipschitz domaind are equivalent by equivalent we mean there exist two sided inequalities with constants depending only onb andd this enables one to conclude the potential theory for 1 2 b ond and 1 2 ond are the same

a diamagnetic inequality for semigroup differences the diamagnetic inequality for the magnetic schrodinger semigroup is extended to the difference of the semigroups of magnetic schrodinger operators with neumann and dirichlet boundary conditions on arbitrary open domains and rather general magnetic vector potentials a and potentials v in particular this bound renders moot all the technical issues in the recent proofs of the independence of the boundary conditions for the integrated density of states for magnetic schrodinger operators independence of the boundary conditions for the free case that is for vanishing potentials and vector potentials immediately implies independence of the boundary conditions of the integrated density of states for a large class of magnetic schrodinger operators

l homologie cyclique des algebres enveloppantes for any lie algebra g we compute the hochschild and cyclic homology groups of its enveloping algebra in terms of the canonical lie poisson structure on the dual g we also discuss the collapsing of connes spectral sequence for cyclic homology particularly in the case of semisimple lie algebras

hochschild lefschetz class for mathcal d modules we introduce a notion of hochschild lefschetz class for a good coherent mathcal d module on a compact complex manifold and prove that this class is compatible with the direct image functor we prove an orbifold riemann roch formula for a mathcal d module on a compact complex orbifold

homologie des invariants d une algebre de weyl sous l action d un groupe fini resume soit g un sous groupe fini de sp 2 n c operant par automorphismes dans l algebre de weyl a n c nous calculons les groupes d homologie et de cohomologie de hochschild de l algebre d invariants a n c g let g be a finite subgroup of sp 2 n c acting by automorphisms in the weyl algebra a n c we compute the hochschild homology and cohomology groups of the invariant algebra a n c g

non symmetric perturbations of symmetric dirichlet forms abstract we provide a path space integral representation of the semigroup associated with the quadratic form obtained by lower order perturbation of a symmetric local dirichlet form the representation is a combination of feynman kac and girsanov formulas and extends previously known results in the framework of symmetric diffusion processes through the use of the hardy class of smooth measures which contains the kato class of smooth measures

hardy type spaces associated with compact unitary groups abstract we investigate hilbertian hardy type spaces of complex analytic functions of infinite many variables associated with compact unitary groups and the corresponding invariant haar s measures for such analytic functions we establish a cauchy type integral formula and describe natural domains also we show some relations between constructed spaces of analytic functions and the symmetric fock space

a dominated type convergence theorem for the feynman integral a dominated type convergence theorem is proved for the operator valued feynman integral defined via the trotter product formula this definition is intimately related to the one of feynman and the physical setting is the same as in his original paper the convergence result given here provides the final piece of a unifying and rather satisfactory picture of three approaches to the feynman integral

product hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type the aim of this article is to develop the theory of product hardy spaces associated with operators which possess the weak assumption of davies gaffney heat kernel estimates in the setting of spaces of homogeneous type we also establish a calderon zygmund decomposition on product spaces which is of independent and use it to study the interpolation of these product hardy spaces we then show that under the assumption of generalized gaussian estimates the product hardy spaces coincide with the lebesgue spaces for an appropriate range of p

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

cyclic cocycles on deformation quantizations and higher index theorems abstract we construct a nontrivial cyclic cocycle on the weyl algebra of a symplectic vector space using this cyclic cocycle we construct an explicit local quasi isomorphism from the complex of differential forms on a symplectic manifold to the complex of cyclic cochains of any formal deformation quantization thereof we give a new proof of nest tsygan s algebraic higher index theorem by computing the pairing between such cyclic cocycles and the k theory of the formal deformation quantization furthermore we extend this approach to derive an algebraic higher index theorem on a symplectic orbifold as an application we obtain the analytic higher index theorem of connes moscovici and its extension to orbifolds

a new proof of moser s parabolic harnack inequality using the old ideas of nash in 1958 nash published his fundamental work on the local holder continuity of solutions of second order parabolic equations with coefficients which need not be smooth 8 the primary purpose of that work was to study the properties of the fundamental solution corresponding to the parabolic operator and from these properties to derive regularity for a general solution though the work is often cited in the literature about weak solutions of elliptic and parabolic equations one feels that nash s ideas were never fully understood and maybe still are not and that because of this the more understandable and seemingly more fruitful ideas of de giorgi 4 and moser 6 7 were subsequently adopted

long time behavior of heat kernels of operators with unbounded drift terms abstract given a second order elliptic operator on r d with bounded diffusion coefficients and unbounded drift which is the generator of a strongly continuous semigroup on l 2 r d represented by an integral we study the time behavior of the integral kernel and prove estimates on its decay at infinity if the diffusion coefficients are symmetric a local lower estimate is also proved

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

algebraic index theorem we prove the atiyah singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold

sharp spectral multipliers for operators satisfying generalized gaussian estimates abstract let l be a non negative self adjoint operator acting on l 2 x where x is a space of homogeneous type assume that l generates a holomorphic semigroup e t l which satisfies generalized m th order gaussian estimates in this article we study singular and dyadically supported spectral multipliers for abstract self adjoint operators we show that in this setting sharp spectral multiplier results follow from plancherel or stein tomas type estimates these results are applicable to spectral multipliers for a large class of operators including m th order elliptic differential operators with constant coefficients biharmonic operators with rough potentials and laplace type operators acting on fractals

gaussian estimates for second order operators with unbounded coefficients abstract we study second order differential operators a with lower order coefficients in some lq l we prove the generation of positive quasi contractive c0 semigroups on lp for all p 1 if the second order coefficients are in some lq l we get upper pseudo gaussian bounds of the heat kernel maximal regularity spectral independence on lp and analyticity of the generated semigroup on l1 are studied for these operators

dominated semigroups with singular complex potentials abstract we develop the perturbation and approximation theory for dominated c 0 semigroups on l p 1 p

integral representation of holomorphic functions on banach spaces abstract in this paper we discuss the problem of integral representation of analytic functions over a complex banach space e we obtain for a wide class of functions integral representations of the form f x e e x f 1 d w and f x e 1 1 x f 2 d w where w is an abstract wiener measure on e and f 1 f 2 are transformations of f involving the covariance operator of w

kernel estimates and lp spectral independence of generators of c0 semigroups abstract after the appearance of w arendt s result that gaussian estimate of a semigroup implies the l p spectral independence of the generator various generalizations have been obtained this paper shows that a certain kernel estimate of a semigroup implies the l p spectral independence of the generator generalizing the case of upper gaussian estimate and gaussian estimate of order 0 1 s miyajima h shindoh gaussian estimates of order and l p spectral independence of generators of c 0 semigroups positivity 11 1 2007 15 39 definition 3 1 the proof uses s karrmann s result about the l p spectral independence and b a barnes theorem about the spectrum of integral operators as an application the l p spectral independence of v 0 1 for a suitable v is proved with the help of a recent result by v liskevich h vogt and j voigt v liskevich h vogt j voigt gaussian bounds for propagators perturbed by potentials j funct anal 238 2006 245 277

global properties of generalized ornstein uhlenbeck operators on lp rn rn with more than linearly growing coefficients we show that the realization ap of the elliptic operator au div q u f u vu in lp rn rn p 1 generates a strongly continuous semigroup and we determine its domain d ap u w2 p rn rn f u vu lp rn rn if 1 p the diffusion coefficients q qij are uniformly elliptic and bounded together with their first order derivatives the drift coefficients f can grow as x log x and v can grow logarithmically our approach relies on the monniaux pruss theorem on the sum of noncommuting operators we also prove lp lq estimates and under somewhat stronger assumptions we establish pointwise gradient estimates and smoothing of the semigroup in the spaces w p rn rn 0 1 where 1 p