real analytic sets in complex spaces and cr maps if r is a real analytic set in mathbb c n viewed as mathbb r 2n then for any point p r there is a uniquely defined germ xp of the smallest complex analytic variety which contains rp the germ of r at p it is shown that if r is irreducible of constant dimension then the function p dim xp is constant on a dense open subset of r as an application it is proved that a continuous map from a real analytic cr manifold m into mathbb c n which is cr on some open subset of m and whose graph is a real analytic set in m times mathbb c n is necessarily cr everywhere on m

on scalar extensions and spectral decompositions of complex symmetric operators abstract in this paper we prove that a complex symmetric operator with property is subscalar as a corollary we get that such operators with rich spectra have nontrivial invariant subspaces we also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints

some new classes of complex symmetric operators we say that an operator t e b h is complex symmetric if there exists a conjugate linear isometric involution c so that t ct c we prove that binormal operators operators that are algebraic of degree two including all idempotents and large classes of rank one perturbations of normal operators are complex symmetric from an abstract viewpoint these results explain why the compressed shift and volterra integration operator are complex symmetric finally we attempt to describe all complex symmetric partial isometries obtaining the sharpest possible statement given only the data dim ker t dim ker t

mixed finite elements for second order elliptic problems in three variables two families of mixed finite elements one based on simplices and the other on cubes are introduced as alternatives to the usual raviart thomas nedelec spaces these spaces are analogues of those introduced by brezzi douglas and marini in two space variables error estimates inl2 andh s are derived

on nash approximation of complex analytic sets in runge domains abstract we prove that every complex analytic set x in a runge domain can be approximated by nash sets on any relatively compact subdomain 0 of moreover for every nash subset y of with y x the approximating sets can be chosen so that they contain y 0 as a consequence we derive a necessary and sufficient condition for a complex analytic set x to admit a nash approximation which coincides with x along its arbitrary given subset

on m complex symmetric weighted shift operators on cn abstract in this paper we study m complex symmetric weighted shift operators on c n let t be the backward weighted shift on c n for some n 2 we consider when t and t a the matrix of entries the moduli of those of t are both m complex symmetric with the same standard conjugation c give as well some unitary operators useful in the study and generalize to upper triangular matrices also we show that if t is 2k complex symmetric with the standard conjugation c for some k n with k n then t is 2 k 1 complex symmetric with the conjugation c

on local spectral properties of complex symmetric operators abstract in this paper we study properties of complex symmetric operators in particular we prove that every complex symmetric operator having property or is decomposable moreover we show that complex symmetric operator t has dunford s property c and it satisfies weyl s theorem if and only if its adjoint does

on complex symmetric operator matrices abstract an operator t l h is said to be complex symmetric if there exists a conjugation j on h such that t j t j in this paper we find several kinds of complex symmetric operator matrices and examine decomposability of such complex symmetric operator matrices and their applications in particular we consider the operator matrix of the form t a b 0 j a j where j is a conjugation on h we show that if a is complex symmetric then t is decomposable if and only if a is furthermore we provide some conditions so that a weyl s theorem holds for the operator matrix t

natural superconvergence points in three dimensional finite elements a systematic and analytic process is conducted to identify natural superconvergence points of high degree polynomial c 0 finite elements in a three dimensional setting this identification is based upon explicitly constructing an orthogonal decomposition of local finite element spaces derivative and function value superconvergence points are investigated for both the poisson and the laplace equations superconvergence results are reported for hexahedral pentahedral and tetrahedral elements up to certain degrees

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

means of unitaries conjugations and the friedrichs operator abstract if c is a conjugation an isometric conjugate linear involution on a separable complex hilbert space h then t b h is called c symmetric if t c t c in this note we prove that each c symmetric contraction t is the mean of two c symmetric unitary operators we discuss several corollaries and an application to the friedrichs operator of a planar domain

complex symmetric weighted composition operators on h2 d abstract in this paper we study complex symmetric weighted composition operators on the hardy space we provide some characterizations of and when a weighted composition operator w is complex symmetric we investigate which combinations of weights and maps of the open unit disk give rise to complex symmetric weighted composition operators with a special conjugation as some applications we obtain several examples for nonnormal complex symmetric operators in addition we give spectral properties of complex symmetric weighted composition operators we examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is hilbert schmidt finally we consider cyclicity hypercyclicity and the single valued extension property for complex symmetric weighted composition operators

on the holomorphic closure dimension of real analytic sets given a real analytic or more generally semianalytic set r in cn viewed as r2n there is for every p r a unique smallest complex analytic germ xp that contains the germ rp we call dimc xp the holomorphic closure dimension of r at p we show that the holomorphic closure dimension of an irreducible r is constant on the complement of a closed proper analytic subset of r and we discuss the relationship between this dimension and the cr dimension of r

tameness of holomorphic closure dimension in a semialgebraic set given a semianalytic set s in mathbb c n and a point p in bar s there is a unique smallest complex analytic germ x p which contains s p called the holomorphic closure of s p we show that if s is semialgebraic then x p is a nash germ for every p and s admits a semialgebraic filtration by the holomorphic closure dimension as a consequence every semialgebraic subset of a complex vector space admits a semialgebraic stratification into cr manifolds

finite element differential forms on cubical meshes we develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions the family contains elements of all polynomial degrees and all form degrees in two dimensions these include the serendipity finite elements and the rectangular bdm elements in three dimensions they include a recent generalization of the serendipity spaces and new h curl and h div finite element spaces spaces in the family can be combined to give finite element subcomplexes of the de rham complex which satisfy the basic hypotheses of the finite element exterior calculus and hence can be used for stable discretization of a variety of problems the construction and properties of the spaces are established in a uniform manner using finite element exterior calculus

complex symmetric partial isometries an operator t b h is complex symmetric if there exists a conjugate linear isometric involution c h h so that t ct c we provide a concrete description of all complex symmetric partial isometries in particular we prove that any partial isometry on a hilbert space of dimension 4 is complex symmetric

on complex symmetric toeplitz operators abstract in this paper we give a characterization of a complex symmetric toeplitz operator t on the hardy space h 2 moreover if t is a complex symmetric toeplitz operator we provide a necessary and sufficient condition for t to be normal finally we investigate these t with finite symbols

on the closure of the complex symmetric operators compact operators and weighted shifts abstract we study the closure cso of the set cso of all complex symmetric operators on a separable infinite dimensional complex hilbert space among other things we prove that every compact operator in cso is complex symmetric using a construction of kakutani as motivation we also describe many properties of weighted shifts in cso cso in particular we show that weighted shifts which demonstrate a type of approximate self similarity belong to cso cso as a byproduct of our treatment of weighted shifts we explain several ways in which our result on compact operators is optimal