nonlinear quantum fields in 4 dimensions and cohomology of the infinite heisenberg group aspects of the cohomology of the infinite dimensional heisenberg group as represented on the free boson field over a given hilbert space are treated the 1 cohomology is shown to be trivial in certain spaces of generalized vectors from this derives a canonical quantization mapping from classical unquantized forms to generalized operators on the boson field an example applied here to scalar relativistic fields is the quantization of a given classical interaction lagrangian or hamiltonian i e the establishment and characterization of corresponding boson field operators for example if q denotes the free massless scalar field in d dimensional minkowski space d 4 even and if q is an even integer greater than or equal to 4 then f smo x q dx exists as a nonvanishing poincare invariant hermitian selfadjointly extendable operator where o x q denotes the wick power applications are also made to the rigorous establishment of basic symbolic operators in heuristic quantum field theory including certain massive field theories to a class of pseudo interacting fields obtained by substituting the free field into desingularized expressions for the total hamiltonian in the conformally invariant case d q 4 and to corresponding scattering theory

holomorphic dirichlet forms on complex manifolds a complete description of all holomorphic dirichlet forms on complex hyperbolic space is given they are classified in terms of the lie algebra of the automorphism group which we take to act in the unit ball of n we show that the measure defining the holomorphic dirichlet form is finite if and only if the real part of the associated holomorphic vector field points outward at the boundary of the unit ball a logarithmic sobolev inequality is proven to hold whenever this measure is finite all holomorphic dirichlet forms over complex hyperbolic space complex projective space and n are now known

on uniqueness for nonlinear elliptic equation involving the pucci s extremal operator abstract in this article we study uniqueness of positive solutions for the nonlinear uniformly elliptic equation m d 2 u u u p 0 in r n lim r u r 0 where m d 2 u denotes the pucci s extremal operator with parameters 0 and p 1 it is known that all positive solutions of this equation are radially symmetric with respect to a point in r n so the problem reduces to the study of a radial version of this equation however this is still a nontrivial question even in the case of the laplacian the pucci s operator is a prototype of a nonlinear operator in no divergence form this feature makes the uniqueness question specially challenging since two standard tools like pohozaev identity and global integration by parts are no longer available the corresponding equation involving m is also considered

on complex hypercontractivity abstract we give a new proof of a hypercontractivity theorem for the mehler transform with a complex parameter earlier proved by weissler 1979 j funct anal 32 102 121 and epperson 1989 j funct anal 87 1 30 the proof uses stochastic integrals and ito calculus the method also yields new proofs of some related results

hypersingular quarter point boundary elements for crack problems the present paper deals with the study and effective implementation for stress intensity factor computation of a mixed boundary element approach based on the standard displacement integral equation and the hypersingular traction integral equation expressions for the evaluation of the hypersingular integrals along general curved quadratic line elements are presented the integration is carried out by transformation of the hypersingular integrals into regular integrals which are evaluated by standard quadratures and simple singular integrals which are integrated analytically the generality of the method allows for the modelling of curved cracks and the use of straight line quarter point elements the stress intensity factors can be computed very accurately from the crack opening displacement at collocation points extremely close to the crack tip several examples with different crack geometries are analyzed the computed results show that the proposed approach for stress intensity factors evaluation is simple produces very accurate solutions and has little dependence on the size of the elements near the crack tip

solution of inverse problems by boundary integral equations without residual minimization in this paper the solution of some inverse problems for potential fields is tackled the aim is to compute the position and shape of an unknown flaw within a body using some experimental measures as additional data by the linearization of the difference between the boundary integral equation for the actual configuration and the same equation for an assumed configuration an integral equation for the variations is deduced this integral equation is carried to the boundary by a limiting process and a solution procedure is devised to compute an approximation to the actual flaw the solution method proceeds iteratively solving a direct and an inverse problem in every step but no minimization algorithm is involved the performance of the method is shown in several numerical examples

strong hypercontractivity and strong logarithmic sobolev inequalities for log subharmonic functions on stratified lie groups abstract on a stratified lie group g equipped with hypoelliptic heat kernel measure we study the behavior of the dilation semigroup on l p spaces of log subharmonic functions we consider a notion of strong hypercontractivity and a strong logarithmic sobolev inequality and show that these properties are equivalent for any group g moreover if g satisfies a classical logarithmic sobolev inequality then both properties hold this extends similar results obtained by graczyk kemp and loeb in the euclidean setting

on the stress wave imaging of cavities in a semi infinite solid the problem of mapping underground cavities from surface seismic measurements is investigated within the framework of a regularized boundary integral equation bie method with the ground modeled as a uniform elastic half space the inverse analysis of elastic waves scattered by a three dimensional void is formulated as a task of minimizing the misfit between experimental observations and theoretical predictions for an assumed void geometry for an accurate treatment of the gradient search technique employed to solve the inverse problem sensitivities of the predictive bie model with respect to cavity parameters are evaluated semi analytically using an adjoint problem approach and a continuum kinematics description several key features of the formulation including the rigorous treatment of the radiation condition for semi infinite solids modeling of an illuminating seismic wave field and treatment of the prior information are highlighted a set of numerical examples with spherical and ellipsoidal cavity geometries is included to illustrate the performance of the method it is shown that the featured adjoint problem approach reduces the computational requirements by an order of magnitude relative to conventional finite difference estimates thus rendering the three dimensional elastic wave imaging of solids tractable for engineering applications

uniqueness of positive radial solutions of δu f u 0 in rn n 2 abstract we study the uniqueness of radially symmetric ground states for the semilinear elliptic partial differential equation u f u 0 in r n n 2 assuming that f t 0 t f s d s is negative in 0 u 1 and positive in u 1 u we obtain the uniqueness of nonnegative solutions with u 0 sup u 0 u in the case where s u u f u f u is monotonically decreasing in u 1 u

strong hypercontractivity and relative subharmonicity abstract a hermitian metric g on a complex manifold m together with a smooth probability measure on m determine minimal and maximal dirichlet forms q d and q max given by q f m g grad f z grad f z d z q d is the form closure of q on c c m and q max is the form closure of q on c 1 b m the corresponding operators a d and a max generate semigroups having standard hypercontractivity properties in the scale of l p spaces p 1 when the corresponding form q satisfies a logarithmic sobolev inequality it was shown by the author 1999 acta math 182 159 206 that the semigroup e ta d has even stronger hypercontractivity properties when restricted to certain holomorphic subspaces of l p these results are extended here to a max when m g is not complete it is necessary that the elliptic differential operator a max degenerate on the boundary of m a second proof of these strong hypercontractive inequalities for both a d and a max is given which depends on an extension of the submean value property of subharmonic functions the riemann surface for z 1 n and the weighted bergman spaces in the unit disc are given as examples

non perturbative deformation quantization of cartan domains abstract we construct families of non commuting c algebras of quantized functions for bounded irreducible hermitian symmetric spaces for this procedure we use algebras of toeplitz operators defined with respect to a perturbation of the ordinary bergman metric we prove the deformation quantization conditions for these algebras

the contractivity of the free hamiltonian semigroup in the lp space of entire functions abstract a semigroup of operators t t t 0 generated by the number operator in the complex wave representation is given by t t z e t z for any entire function on c n the problem is to find all possible r p 1 such that t t hlr cn dgn cn dgn is contractive or bounded it turns out that t t hlr cn dgn cn dgn is contractive if and only if p 1 re2t and is unbounded if and only if p re2t furthermore all maximizers are identified they are constant functions if p 1 re2t and exponential functions if p re2t t 0

a boundary element formulation for the inverse elastostatics problem iesp of flaw detection a boundary integral formulation is presented for the detection of flaws in planar structural members from the displacement measurements given at some boundary locations and the applied loading such inverse problems usually start with an initial guess for the flaw location and size and proceed towards the final configuration in a sequence of iterative steps a finite element formulation will require a remeshing of the object corresponding to the revised flaw configuration in each iteration making the procedure computationally expensive and cumbersome no such remeshing is required for the boundary element approach the inverse problem is written as an optimization problem with the objective function being the sum of the squares of the differences between the measured displacements and the computed displacements for the assumed flaw configuration the geometric condition that the flaw lies within the domain of the object is imposed using the internal penalty function approach in which the objective function is augmented by the constraint using a penalty parameter a first order regularization procedure is also implemented to modify the objective function in order to minimize the numerical fluctuations that may be caused in the numerical procedure due to errors in the experimental measurements for displacements the flaw configuration is defined in terms of geometric parameters and the sensitivities with respect to these parameters are obtained in the boundary element framework using the implicit differentiation approach a series of numerical examples involving the detection of circular and elliptical flaws of various sizes and orientations are solved using the present approach good predictions of the flaw shape and location are obtained

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

function theory on cartan domains and the berezin toeplitz symbol calculus cn with dv z normalized lebesgue measure on 9 we let l l2 q dv be the usual space of lebesgue square integrable complex valued functions on 9 by h2 h2 q dv we denote the bergman subspace of l2 consisting of holomorphic functions the orthogonal projection operator from l2 onto h2 is denoted by p forf in l q the space of essentially bounded measurable functions on 9 we will consider the multiplication operator

contractive inequalities for bergman spaces and multiplicative hankel forms we consider sharp inequalities for bergman spaces of the unit disc establishing analogues of the inequality in carleman s proof of the isoperimetric inequality and of weissler s inequality for dilations by contractivity and a standard tensorization procedure the unit disc inequalities yield corresponding inequalities for the bergman spaces of dirichlet series we use these results to study weighted multiplicative hankel forms associated with the bergman spaces of dirichlet series reproducing most of the known results on multiplicative hankel forms associated with the hardy spaces of dirichlet series in addition we find a direct relationship between the two type of forms which does not exist in lower dimensions finally we produce some counter examples concerning carleson measures on the infinite polydisc

erratum to a nonlinear elliptic system for maps from hermitian to riemannian manifolds and rigidity theorems in hermitian geometry it is the purpose of this paper to introduce and study a nonlinear elliptic system of equations imposed on a map from a hermitian into a riemannian manifold which seems to be more appropriate to hermitian geometry than the harmonic map system thus let x be a complex manifold with hermitian metric 7 in local coordinates n a riemannian manifold with metric gij and christoffel symbols f k a harmonic map f x n then has to satisfy

quantum riemann surfaces i the unit disc we construct a non commutative algebra c mu bar u which is a quantum deformation of the algebra of continuous functions on the closed unit disc bar u c mu bar u is generated by the toeplitz operators on a suitable hilbert space of holomorphic functions onu

hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n sphere a logarithmic sobolev inequality with respect to the probability measure a 1 x2 12 dx on 1 1 is proved for all 12 from this inequality sharp hypercontractive estimates are derived for the heat semigroups for ultraspherical polynomials and on the n sphere

shape design sensitivity analysis via material derivative adjoint variable technique for 3 d and 2 d curved boundary elements a general approach to shape design sensitivity analysis of three and two dimensional elastic solid objects is developed using the material derivative adjoint variable technique and boundary element method the formulation of the problem is general and first order sensitivities in the form of boundary integrals for the effect of boundary shape variations are derived for an arbitrary performance functional second order quadrilateral surface elements for 3 d problems and quadratic boundary elements for 2 d problems are employed in the solution of primary and adjoint systems and discretization of the boundary integral expressions for sensitivities the accuracy of sensitivity information is studied for selected global performance functionals and also for boundary state fields at discrete points numerical results are presented to demonstrate the accuracy and efficiency of this approach

hypersingular shape sensitivity boundary integral equation for crack identification under harmonic elastodynamic excitation abstract model based nondestructive testing ndt requires fast and accurate solutions of the response of the mechanical model including the defect as well as the sensitivity of this response to the variation of the parameters describing the defect for modelling crack type defects under dynamic conditions like vibration analysis or ultrasonics the boundary element method bem is especially well suited in particular due to the hypersingular formulation the present work presents the stress sensitivity boundary integral equation q bie and its use for the solution of the inverse problem when coupled to gradient based minimization algorithms the capability of solving numerically a ndt problem such as the location and characterization of cracks by measuring the dynamic response at an accessible boundary of the specimen is evaluated for that the accuracy and convergence of the sensitivity from the q bie is verified then comprehensive convergence tests are made for the initial guess the amount of supplied measurements and simulated errors on measurements geometry elastic constants and frequency

sensitivity analysis for shape perturbation of cavity or internal crack using bie and adjoint variable approach this paper deals with the application of the adjoint variable approach to sensitivity analysis of objective functions used for defect detection from knowledge of supplementary boundary data in connection with the use of bie bem formulations for the relevant forward problem the main objective is to establish expressions for crack shape sensitivity based on the adjoint variable approach that are suitable for bem implementation in order to do so it is useful to consider first the case of a cavity defect for which such boundary only sensitivity expressions are obtained for general initial geometry and shape perturbations the analysis made in the cavity defect case is then seen to break down in the limiting case of a crack however a closer analysis reveals that sensitivity formulas suitable for bem implementation can still be established first particular sensitivity formulas are obtained for special shape transformations translation rotation or expansion of the crack for either two or three dimensional geometries which except for the case of crack expansion together with dynamical governing equations are made only of surface integrals three dimensional geometries or line integrals two dimensional geometries next arbitrary shape transformations are accommodated by using an additive decomposition of the transformation velocity over a tubular neighbourhood of the crack front which leads to sensitivity formulas this leads to sensitivity formulas involving integrals on the crack the tubular neighbourhood and its boundary finally the limiting case of the latter results when the tubular neighbourhood shrinks around the crack front is shown to yield a sensitivity formula involving the stress intensity factors of both the forward and the adjoint solutions classical path independent integrals are recovered as special cases the main exposition is done in connection with the scalar transient wave equation the results are then extended to the linear time domain elastodynamics framework linear static governing equations are contained as obvious special cases numerical results for crack shape sensitivity computation are presented for two dimensional time domain elastodynamics

some integral identities and inequalities for entire functions and their application to the coherent state transform let be an entire function on cn and for any h 0 and r 0 define fr z r e 2 z 2h let d h denote h n times lebesgue measure on cn frs2 2 d h n sh frsd h from this and a logarithmic sobolev inequality we easily deduce qnq fr q pnp fr p for all 0 p q t8 where the lp norms are taken with respect to the measure d h above we apply these results to the study of the spaces ap consisting of all entire functions satisfying z pe 2 z 2h d h obtaining sharp bounds for some associated operators and proving denseness of analytic polynomials in ap for 1 p we then apply our results to the coherent state transform extending and simplifying some previously known results

uniqueness of positive solutions of δu f u 0 in ℝn n 3 we study the uniqueness of radial ground states for the semilinear elliptic partial differential equation delta u f u 0 eqno in n we assume that the function f has two zeros the origin and u 0 0 above u 0 the function f is positive is locally lipschitz continuous and satisfies convexity and growth conditions of a superlinear nature below u 0 f is assumed to be non positive non identically zero and merely continuous our results are obtained through a careful analysis of the solutions of an associated initial value problem and the use of a monotone separation theorem it is known that for a large class of functions f the ground states of are radially symmetric in these cases our result implies that possesses at most one ground state

flaw identification using the boundary element method in this paper a new boundary element formulation is presented for the identification of the location and size of internal flaws in two dimensional structures an introduction to inverse analysis is given with special reference to methods of flaw identification along with a brief review of the optimization methods employed both the standard boundary element and the dual boundary element method are presented with the dual boundary element method proposed as the basis for the new formulation the flaw identification method is presented along with the computation of the boundary displacement and traction derivatives and the specialized analytical integration used for cracked boundaries examples are given to demonstrate the accuracy of the sensitivity values and the performance of flaw location

some notes on singular integral techniques in boundary element analysis the paper presented here reviews the numerical techniques used currently to calculate the singular integrals and nearly singular integrals in the boundary element analysis some incorrect algorithms published before are discussed and a new numerical technique to calculate the nearly singular integral is developed the numerical results show a significant improvement in both accuracy and efficiency compared to the traditional adaptive gaussian quadrature and subdivision techniques

uniqueness of non negative solutions of semilinear equations in rn on etudie l unicite des solutions positives classiques u x du probleme u f u 0 dans r n u x 0 quand x avec n 1 et x x 1 x n

an inequality for fourier laplace transforms of entire functions and the existence of exponential frames in fock space abstract we study mapping properties of the fourier laplace transform between certain spaces of entire functions we introduce a variant of the classical fock space by integrating against the monge ampere measure of the weight function and show that the norm of the fourier laplace transform in a dual fock space dominates the norm of the function equality holds when the weight function is an hermitean form as an application we get a criterium for the existence of frames of exponential functions in fock space

on the existence of sign changing bound state solutions of a quasilinear equation abstract in this paper we establish the existence of bound state solutions having a prescribed number of sign changes for p m u f u 0 x r n n m 1 where m u u m 2 u our result is new even for the case of the laplacian m 2

regularization of hypersingular and nearly singular integrals in the potential theory and elasticity both the hypersingular and nearly singular integrals which appear in the hypersingular boundary integralequations and integral representations of the secondary fields respectively are regularized by the application of the superposition principle two kinds of the non singular formulations namely those with the strongly singular and weakly singular kernels are presented in this paper the formulations are given in terms of the relevant boundary quantities and the collocation at element junctions is possible two and three dimensional problems are analysed simultaneously in a unique way for either internal or external problems of the potential theory and elasticity

non degeneracy of positive solutions of kirchhoff equations and its application abstract a non degeneracy theorem for positive solutions of the standard kirchhoff model is proved in all cases except for n 5 and b r n q 2 d x 2 n 4 n 4 2 n 2 n 2 2 in particular for dimensions n 5 and b r n q 2 d x 2 n 4 n 4 2 n 2 n 2 2 we show that there exist two non degenerate positive solutions of the kirchhoff equations which seem to be completely different from the result of the standard schrodinger equation the effects of the non local term on the positive solution set are also studied we show that the non local term has no effect on the structure of the positive solution set for dimensions 1 n 3 and the effects eventually appear for dimensions n 4 with the non degeneracy property of positive solutions of the limit problem we construct concentrated solutions of a singularly perturbed kirchhoff problem via the well known lyapunov schmidt reduction method for dimensions n 5 the existence result of concentrated solutions is completely new and is not implied by the main result of g m figueiredo et al in 19 where a generalized singularly perturbed kirchhoff problem was considered

internal variables and their sensitivities in three dimensional linear elasticity by the boundary contour method a variant of the usual boundary element method bem called the boundary contour method bcm has been presented in the literature in recent years in the bcm in three dimensions surface integrals on boundary elements of the usual bem are transformed through an application of stokes theorem into line integrals on the bounding contours of these elements a new formulation for design sensitivities in three dimensional linear elasticity based on the bcm has been recently presented in ref 12 this challenging derivation is carried out by first taking the material derivative of the regularized boundary integral equation bie with respect to a shape design variable and then converting the resulting equation into its boundary contour version the focus of 12 is the boundary problem i e evaluation of displacements stresses and their sensitivities on the bounding surface of a body the focus of the present paper is the corresponding internal problem i e analogous calculations at points inside a body numerical results for internal variables and their sensitivities are presented here for selected examples

singular operators on boson fields as forms on spaces of entire functions on hilbert space abstract invariant scales of entire analytic functions on hilbert space are introduced and applied singular operators represented by sesquilinear forms on spaces of regular vectors are given explicit integral representations via kernels that are entire functions on the direct sum of the hilbert space with its dual the weyl or exponentiated boson field operators act smoothly and irreducibly on corresponding spaces of entire functions arbitrary symplectic operators on a single particle hilbert space are shown to be implementable on the corresponding boson field by appropriate generalized operators

strictly pseudoconvex domains in c n the theory which we have developed so far will be expanded in two ways 1 in this chapter we shall use the cauchy fantappie calculus to transform the bochner martinelli kernel into a kernel adapted to strictly pseudoconvex domains in n and prove a number of finiteness and vanishing theorems for these domains 2 in the next chapter we shall pass from n to arbitrary hermitian manifolds and establish the analogue of the bmk formula in that context obtaining along the way the hodge decomposition theorem on compact manifolds both lines of thought will merge in the subsequent chapters and lead to a solution of the levi problem and finiteness theorems for strictly pseudoconvex manifolds as well as to a solution of the overline partial neumann problem to be formulated later

deformation estimates for the berezin toeplitz quantization deformation estimates for the berezin toeplitz quantization ofcn are obtained these estimates justify the description of ccr k as a first order quantum deformation of ap c0 where ccr is the usualc algebra of boson canonical commutation relations k is the full algebra of compact operators ap is the algebra of almost periodic functions andc0 is the algebra of continuous functions which vanish at infinity

shape optimization of peristaltic pumping transport is a fundamental aspect of biology and peristaltic pumping is a fundamental mechanism to accomplish this it is also important to many industrial processes we present a variational method for optimizing the wave shape of a peristaltic pump specifically we optimize the wave profile of a two dimensional channel containing a navier stokes fluid with no assumption on the wave profile other than it is a traveling wave e g we do not assume it is the graph of a function hence this is an infinite dimensional optimization problem the optimization criteria consists of minimizing the input fluid power due to the peristaltic wave subject to constraints on the average flux of fluid and area of the channel sensitivities of the cost and constraints are computed variationally via shape differential calculus and we use a sequential quadratic programming sqp method to find a solution of the first order kkt conditions we also use a merit function based line search in order to balance between decreasing the cost and keeping the constraints satisfied when updating the channel shape our numerical implementation uses a finite element method for computing a solution of the navier stokes equations adjoint equations as well as for the sqp method when computing perturbations of the channel shape the walls of the channel are deformed by an explicit front tracking approach in computing functional sensitivities with respect to shape we use l 2 type projections for computing boundary stresses and for geometric quantities such as the tangent field on the channel walls and the curvature we show error estimates for the boundary stress and tangent field approximations as a result we find optimized shapes that are not obvious and have not been previously reported in the peristaltic pumping literature specifically we see highly asymmetric wave shapes that are far from being sine waves many examples are shown for a range of fluxes and reynolds numbers up to re 500 which illustrate the capabilities of our method

uniqueness of the ground state solutions of quasilinear schrodinger equations abstract we are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics we convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity we also investigate the non degeneracy of a positive radial solution for a converted semilinear elliptic equation

correspondence principle for the quantized annulus romanovski polynomials and morse potential abstract a general theory of quantization has been proposed by berezin see e g his survey in comm math phys 40 1975 153 174 in this paper we establish a weak form of the correspondence principle for the annulus quantized according to berezin more precisely we show that b i as 0 where i is the identity operator and b the berezin transform we consider also spectral analysis on the annulus in particular we express the eigenfunctions of the relevant laplacian in terms of certain romanovski polynomials finally we write down the expression for the analogue of the morse potential in this case we remark that similar considerations can be made in principle on any circular domain in the presence of a radial hermitian metric of constant curvature

function spaces and reproducing kernels on bounded symmetric domains there are several natural hilbert spaces of holomorphic functions on a bounded symmetric domain such are the bergman type spaces on which the holomorphic discrete series operates and the hardy type spaces which are related to the analytic continuation of the holomorphic discrete series also closely related is the bergmann space of entire functions on the ambient which arises as the closure of the polynomials with respect to a natural inner product the space of holomorphic polynomials decomposes into irreducible subspaces under the action of the isotropy group k of the domain the main facts about this decomposition were proved by schmid 21 for another proof see 22 each irreducible subspace contains a unique normalized l invariant spherical polynomial where l is the isotropy group of the shilov boundary in k our first main result is the explicit computation of the norms of the spherical polynomials with respect to each of the hilbert spaces considered for the domains of classical type they were considered by hua 9 and for some of the hilbert spaces this was done before by upmeier 24 using different methods for certain others there are partial results in 22 we are able to do this in a fairly simple unified way by making strong use of gindikin s generalized gamma function s next we obtain a description of the reproducing kernels of the k irreducible subspaces in each of our hilbert spaces and an expansion in terms of these for

toeplitz operators on the segal bargmann space in this paper we give a complete characterization of those functions on 2n dimensional euclidean space for which the berezin toeplitz quantizations admit a symbol calculus modulo the compact operators the functions in question are characterized by a condition of small oscillation at infinity

existence and uniqueness of fast decay entire solutions of quasilinear elliptic equations we prove the existence and uniqueness of fast decay solutions and clarify the structure of positive radial solutions of the quasilinear elliptic equation mu f u 0 in rn where m denotes the m laplace operator and f has a supercritical growth for small u 0 and a subcritical growth for large u our proofs use only elementary arguments based on several variational identities and a maximum principle of peletier and serrin

hypercontractivity for log subharmonic functions abstract we prove strong hypercontractivity shc inequalities for logarithmically subharmonic functions on r n and different classes of measures gaussian measures on r n symmetric bernoulli and symmetric uniform probability measures on r as well as their convolutions surprisingly a slightly weaker strong hypercontractivity property holds for any symmetric measure on r a log sobolev inequality lsi is deduced from the shc for compactly supported measures on r n still for log subharmonic functions an analogous lsi is proved for gaussian measures on r n and for other measures for which we know the shc holds our log sobolev inequality holds in the log subharmonic category with a constant smaller than the one for gaussian measure in the classical context