simple finite element method in vorticity formulation for incompressible flows a very simple and efficient finite element method is introduced for two and three dimensional viscous incompressible flows using the vorticity formulation this method relies on recasting the traditional finite element method in the spirit of the high order accurate finite difference methods introduced by the authors in another work optimal accuracy of arbitrary order can be achieved using standard finite element or spectral elements the method is convectively stable and is particularly suited for moderate to high reynolds number flows

toeplitz operators and solvable c algebras on hermitian symmetric spaces bounded symmetric domains cartan domains and exceptional domains are higher dimensional generalizations of the open unit disc in this note we give a structure theory for the c algebra t generated by all toeplitz operators tf h p fh with continuous symbol function g c s on the shilov boundary 5 of a bounded symmetric domain d of arbitrary rank r here h belongs to the hardy space h s and p l s h s is the szego projection for domains of rank 1 and tube domains of rank 2 the structure of t has been determined in 1 2 in these cases toeplitz operators are closely related to pseudodifferential operators for the open unit disc t is the c algebra generated by the unilateral shift the structure theory for the general case 12 is based on the fact that d can be realized as the open unit ball of a unique jordan triple system z 7 theorem 4 1 denoting the jordan triple product by uv w a tripotent e g z satisfies ee e e tripotents generalize the partial isometries of matrix algebras and determine the boundary structure of d c z cf 7 theorem 6 3 our principal result 12 cf also 3 4 8 is the following

hua operators poisson transform and relative discrete series on line bundles over bounded symmetric domains let d g k be a bounded symmetric domain and s k l be its shilov boundary we consider the action of g with weight nu in mathbb z on functions on d viewed as sections the line bundle and the corresponding eigenspace of g invariant di erential operators the poisson transform maps hyperfunctions on the s to the eigenspaces we characterize the image in terms of hua operators on the sections of the line bundle for some special parameter the poisson transform is of szego type mapping into the relative discrete series we compute the corresponding elements in the discrete series

on the transport diffusion algorithm and its applications to the navier stokes equations this paper deals with an algorithm for the solution of diffusion and or convection equations where we mixed the method of characteristics and the finite element method globally it looks like one does one step of transport plus one step of diffusion or projection but the mathematics show that it is also an implicit time discretization of thepde in lagrangian form we give an error bound h t h h t in the interesting case that holds also for the navier stokes equations even when the reynolds number is infinite euler equation

c algebras of multiplication operators on bergman spaces soit un domaine borne dans c soit a 2 l espace de bergman de toutes les fonctions analytiques sur qui sont de carre integrable par rapport a la mesure volumetrique et soit c la c algebre engendree par les operateurs de multiplication par les fonctions coordonnee sur on etudie les proprietes de c

homogeneous vector bundles and intertwining operators for symmetric domains the main features of homogeneous cowen douglas operators well known for the unit disk are generalised to the setting of hermitian bounded symmetric domains of arbitrary rank c 2016 elsevier inc all rights reserved

homogeneous multiplication operators on bounded symmetric domains let d g k be an irreducible bounded symmetric domain of dimension d and let h d be the analytic continuation of the weighted bergman spaces of holomorphic functions on d we consider the d tuple m m1 md of multiplication operators by coordinate functions and consider its spectral properties we find those parameters for which the tuple m is subnormal and we answer some open questions of bagchi and misra in particular we prove that when d bd is the unit ball in cd then bd is a k spectral set of m if and only if h bd is the hardy space or a weighted bergman space

finite element solution of the 3d compressible navier stokes equations by a velocity vorticity method this paper presents an alternative formulation to the primitive variable form of the navier stokes equations the approach is based on the use of the velocity and vorticity variables as a logical extension of the stream function vorticity method which is quite effective for two dimensional flows second order equations are obtained for the variables and discretization is through a weak galerkin finite element method followed by newton linearization the velocity and vorticity components are solved simultaneously by a direct solver the scheme is demonstrated for two dimensional and three dimensional incompressible and subsonic internal enclosed flow problems

analytic models for commuting operator tuples on bounded symmetric domains for a domain in c d and a hilbert space h of analytic functions on which satisfies certain conditions we characterize the commuting d tuples t t 1 t d of operators on a separable hilbert space h such that t is unitarily equivalent to the restriction of m to an invariant subspace where m is the operator d tuple z i on the hilbert space tensor product h h for the unit disc and h the hardy space h 2 this reduces to a well known theorem of sz nagy and foias for h a reproducing kernel hilbert space on c c d such that the reciprocal 1 k x y of its reproducing kernel is a polynomial in x and y this is a recent result of ambrozie muller and the second author in this paper we extend the latter result by treating spaces h for which 1 k ceases to be a polynomial or even has a pole namely the standard weighted bergman spaces or rather their analytic continuation h h on a cartan domain corresponding to the parameter v in the continuous wallach set and reproducing kernel hilbert spaces h for which 1 k is a rational function further we treat also the more general problem when the operator m is replaced by m w w being a certain generalization of a unitary operator tuple for the case of the spaces h on cartan domains our results are based on an analysis of the homogeneous multiplication operators on which seems to be of an independent interest

mixed finite element approximation of the vector potential we consider a mixed finite element approximation of the three dimensional vector potential which plays an important role in the simulation of perfect fluids and in the calculation of rotational corrections to transonic potential flows the central point of our approach is a saddlepoint formulation of the essential boundary conditions in particular this avoids the wellknown babuska paradox when approximating smooth domains by polyhedrons using piecewise linear piecewise constant elements for the vector potential the boundary terms we obtain optimal error estimates under minimal regularity assumptions for the solution of the continuous problem

non vanishing functions and toeplitz operators on tube type domains abstract we prove an index theorem for toeplitz operators on irreducible tube type domains and we extend our results to toeplitz operators with matrix symbols in order to prove our index theorem we proved a result asserting that a non vanishing function on the shilov boundary of a tube type bounded symmetric domain not necessarily irreducible is equal to a unimodular function defined as the product of powers of generic norms times an exponential function

degenerate principal series representations and their holomorphic extensions let x h l be an irreducible real bounded symmetric domain realized as a real form in an hermitian symmetric domain d g k the intersection s of the shilov boundary of d with x defines a distinguished subset of the topological boundary of x and is invariant under h it can be realized as s h p for certain parabolic subgroup p of h we study the spherical representations of h induced from p we find formulas for the spherical functions in terms of the macdonald hypergeometric function this generalizes the earlier result of faraut koranyi for hermitian symmetric spaces d we consider a class of h invariant integral intertwining operators from the representations on l2 s to the holomorphic representations of g restricted to h we construct a new class of complementary series for the groups h so n m su n m with n m 2 and sp n m with n m 1 we realize them as discrete components in the branching rule of the analytic continuation of the holomorphic discrete series of g su n m su n m su n m and su 2n 2m respectively

a variational approach for the vector potential formulation of the stokes and navier stokes problems in three dimensional domains abstract a few well posed variational problems are constructed whose solutions are vector potentials of the velocity field of the three dimensional stokes problem a choice of the adequate boundary conditions to be imposed is performed in a systematic manner even in the case of not simply connected domains the test functions do not have to be divergence free in the formulations given here it is then seen that a similar approach is well suited to the treatment of the non linear navier stokes problem

reproducing kernel functions and asymptotic expansions on jordan kepler manifolds abstract we study the complex geometry of generalized kepler manifolds defined in jordan theoretic terms introduce hilbert spaces of holomorphic functions defined by radial measures and find the complete asymptotic expansion of the corresponding reproducing kernels for kahler potentials both in the flat and bounded setting

laplace and segal bargmann transforms on hermitian symmetric spaces and orthogonal polynomials let d g k be a complex bounded symmetric domain of tube type in a complex jordan algebra v and let dr j d d be its real form in a formally real euclidean jordan algebra j v dr h l is a bounded realization of the symmetric cone in j we consider representations of h that are gotten by the generalized segal bargmann transform from a unitary g space of holomorphic functions on d to an l2 space on dr we prove that in the unbounded realization the inverse of the unitary part of the restriction map is actually the laplace transform we find the extension to d of the spherical functions on dr and find their expansion in terms of the l spherical polynomials on d which are jack symmetric polynomials we prove that the coefficients are orthogonal polynomials in an l2 space the measure being the harish chandra plancherel measure multiplied by the symbol of the berezin transform we prove the difference equation and recurrence relation for those polynomials by considering the action of the lie algebra and the cayley transform on the polynomials on d finally we use the laplace transform to study generalized laguerre functions on symmetric cones

dixmier trace for toeplitz operators on symmetric domains abstract for toeplitz operators on bounded symmetric domains of higher rank there is no obvious way to define the dixmier trace within the toeplitz c algebra since commutators are in general not compact in this paper we solve this problem by constructing a hilbert quotient module corresponding to partitions of length 1 which leads to commutators in the macaev class l n we also obtain an explicit formula for the dixmier trace of such commutators in terms of the underlying boundary geometry which involves a new type of flag manifold defined in jordan theoretic terms

the berezin transform and invariant differential operators the berezin calculus is important to quantum mechanics creation annihilation operators and operator theory toeplitz operators we study the basic berezin transform linking the contravariant and covariant symbol for all bounded symmetric domains and express it in terms of invariant differential operators

toeplitz quantization and asymptotic expansions for real bounded symmetric domains an analogue of the star product familiar from deformation quantization is studied in the setting of real bounded symmetric domains the analogue turns out to be a certain invariant operator which one might call star restriction from functions on the hermitification of the domain into functions on the domain itself in particular we establish the usual i e semiclassical asymptotic expansion of this star restriction and further obtain a real variable analogue of a theorem of arazy and orsted concerning the analogous expansion for the berezin transform

toeplitz operators on bounded symmetric domains in this paper jordan algebraic methods are applied to study toeplitz operators on the hardy space h2 s associated with the shilov boundary s of a bounded symmetric domain d in c of arbitrary rank the jordan triple system z c associated with d is used to determine the relationship between toeplitz operators and differential operators further it is shown that each jordan triple idempotent e e z induces an irreducible representation e symbol of the c algebra generated by all toeplitz operators tf with continuous symbol function f 0 introduction toeplitz operators on the boundary t aa of the open unit disc a c c play an important role in function theory of one complex variable cf 9 chapter 7 in several dimensions toeplitz operators have been mainly studied for strictly pseudo convex domains d c c 4 13 14 24 28 in particular for the hilbert ball 7 using the relationship with pseudo differential operators another class of domains in c generalizing the unit disc is the class of bounded symmetric domains cartan domains and exceptional domains which have a more complicated boundary structure compared to the strictly pseudo convex case the aim of this paper is the study of toeplitz operators t1 with continuous symbol functionf e c s on the shilov boundary s of a bounded symmetric domain d of arbitrary rank r in the special cases of the hilbert ball r 1 and the lie ball r 2 the structure of the operators ti and of the toeplitz c algebra

index theory for toeplitz operators on bounded symmetric domains in this note we give an index theory for toeplitz operators on the hardy space of the shilov boundary of an arbitrary bounded symmetric domain our results generalize earlier work of gohberg krein and venugopalkrishna 12 for domains of rank 1 and of berger coburn koranyi 1 for domains of rank 2 bounded symmetric domains cartan domains classical or exceptional are the natural higher dimensional analogues of the open unit disk each such domain is homogeneous under a semisimple lie group of biholomorphic transformations and has an essentially unique realization as a convex circular domain which is conveniently described in jordan algebraic terms the underlying vector space z c n carries a jordan triple product denoted by uyv w uv w and the bounded symmetric domain d is the open unit ball of z with respect to the spectral norm 7 the basic example is the space z c of rectangular matrices with jordan triple product uv w uv w wv u 2 giving rise to the hyperbolic matrix ball d z g z spectrum z z 1 the symmetric domains of rank 1 are the smooth hilbert balls in c n for domains d of higher rank r the boundary dd forms a nonsmooth stratified space in jordan algebraic terms the structure of dd can be described as follows an element e z satisfying ee e e is called a tripotent for matrices the tripotents are just the partial isometries every tripotent e induces a splitting of z into the peirce spaces z e z g z ee z xz for a 0 1 the set

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

stream vectors in three dimensional aerodynamics this work deals with the decomposition of a vector fieldu intou non homogeneous boundary conditions on or are investigated applications to the computation of inviscid flows are given finally a conforming finite element implementation is studied and tested