completely bounded modules and associated extremal problems in this paper we continue our study of certain finite dimensional hilbert modules over the function algebra a cm we show that these modules are always completely bounded with the bound obtained as the matrix valued analogue of a certain scalar valued extremal problem in particular we obtain a necessary and sufficient condition for our module to be completely contractive we produce a contractive module cnm over a bm such that it is completely bounded with the complete bound equal to m that is cnm is not completely contractive

analyzing optima in the exploration of multiple response surfaces a method is presented for testing the equality of some or all constrained or unconstrained optima in a response surface analysis an estimator of a common location of stationary points is obtained by a standard multivariate testing procedure and a confidence region associated with the common optimum is derived the procedure is illustrated by the estimation of a common optimum in a multiple response experiment the multivariate approach facilitates a more efficient estimation of the optimum than the usual univariate response surface analysis and provides additional tests of the response surface model

confidence regions around the ridge of optimal response on fitted second order response surfaces ridge analysis is a technique useful in connection with the fitting of second order response surfaces it enables a path of maximum predicted values maximum on a sphere of radius r to be specified and followed out from the origin of the experimental region as r increases alternatively a minimum path can be followed out this article discusses the addition of a measure of uncertainty to the selected path thus providing an assessment of the reliability of the ridge analysis as a path progresses the utility of this method is illustrated by applications to two datasets

commutants and reflexivity of multiplication tuples on vector valued reproducing kernel hilbert spaces abstract motivated by the theory of weighted shifts on directed trees and its multivariable counterpart we address the question of identifying commutant and reflexivity of the multiplication d tuple m z on a reproducing kernel hilbert space h of e valued holomorphic functions on where e is a separable hilbert space and is a bounded domain in c d admitting bounded approximation by polynomials in case e is a finite dimensional cyclic subspace for m z under some natural conditions on the b e valued kernel associated with h the commutant of m z is shown to be the algebra h b e of bounded holomorphic b e valued functions on provided m z satisfies the matrix valued von neumann s inequality this generalizes a classical result of shields and wallen the case of dim e 1 and d 1 as an application we determine the commutant of a bergman shift on a leafless locally finite rooted directed tree t of finite branching index as the second main result of this paper we show that a multiplication d tuple m z on h satisfying the von neumann s inequality is reflexive this provides several new classes of examples as well as recovers special cases of various known results in one and several variables we also exhibit a family of tri diagonal b c 2 valued kernels for which the associated multiplication operators m z are non hyponormal reflexive operators with commutants equal to h b c 2 d

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

confidence regions for constrained optima in response surface experiments the precision of the estimated optimum from a response surface experiment is often indicated via a confidence region about the optimum sometimes because of associated secondary responses unconstrained optima produce unrealistic operating conditions even when the true response surface is known we consider confidence intervals for constrained optima for which the constraint function is known or separately estimated an example from a cancer combination chemotherapy experiment illustrates the construction of such a region

unitary equivalence of operator valued multishifts abstract we systematically study various aspects of operator valued multishifts beginning with basic properties we show that the class of multishifts on the directed cartesian product of rooted directed trees is contained in that of operator valued multishifts further we establish circularity analyticity and wandering subspace property of these multishifts in the rest part of the paper we study the function theoretic behaviour of operator valued multishifts we determine the bounded point evaluation reproducing kernel structure and the unitary equivalence of operator valued multishifts with invertible operator weights in contrast with a result of lubin it appears that the set of all bounded point evaluations of an operator valued multishift may be properly contained in the joint point spectrum of the adjoint of underlying multishift

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

similarity quasisimilarity and operator factorizations we introduce and illustrate an operator factorization technique to study similarity and quasisimilarity of hilbert space operators the technique allows one to generate in a systematic way families of test operators and to check for similarity and quasisimilarity with a given model in the case of the unilateral shift u we obtain a one parameter family of nonhyponormal noncontractive shift like operators in the similarity orbit of u we also obtain new characterizations of quasisimilarity and similarity in terms of invariant operator ranges and conditions for spectral and essential spectral inclusions

on the sum of two subnormal kernels abstract we show by means of a class of examples that if k 1 and k 2 are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the corresponding reproducing kernel hilbert space is subnormal then the multiplication operator on the hilbert space determined by their sum k 1 k 2 need not be subnormal this settles a recent conjecture of gregory t adams nathan s feldman and paul j mcguire in the negative we also discuss some cases for which the answer is affirmative

curvature invariant and generalized canonical operator models ii one can view contraction operators given by a canonical model of sz nagy and foias as being defined by a quotient module where the basic building blocks are hardy spaces i n this note we generalize this framework to allow the bergman and weighted bergman spaces as building blocks but restricting attention to the case in which the operator obtained is in the cowen douglas class and requiring the multiplicity to be one w e view the classification of such operators in the context of complex geometry and obtain a complete classification up to unitary equivalence of them in terms of their associated vector bundles and their curvatures

manifolds of hilbert space projections the hardy space h2 for the upper half plane together with a multiplicative group of unimodular functions u exp i 11 nn with n gives rise to a manifold of orthogonal projections for the subspaces u h2 of l2 for classes of admissible functions i the strong operator topology closures of and are determined explicitly as various n balls and n spheres the arguments used are direct and rely on the analysis of oscillatory integrals e m stein harmonic analysis real variable methods orthogonality and oscillatory integrals princeton mathematical series 43 princeton university press princeton nj 1993 and hilbert space geometry some classes of these closed projection manifolds are classified up to unitary equivalence in particular the fourier plancherel 2 sphere and the hyperbolic 3 sphere of katavolos and power a katavolos and s c power translation and dilation invariant subspaces of l2 j reine angew math 552 2002 101 129 appear as distinguished special cases admitting non trivial unitary automorphism groups which are explicitly described

on a method of atkinson for evaluating domain integrals in the boundary element method we have shown how to couple a numerical method due to atkinson for computing particular solutions to a class of elliptic differential equations with a variety of boundary element methods which alleviates the problem of domain discretization for solving inhomogeneous equations when the inhomogeneous term is of the form typically used in the dual reciprocity method atkinson s formula is such that only boundary integrals need to be approximated numerically if this method is coupled with the method of potentials it results in a computational technique which requires neither boundary nor domain discretization some numerical results are given validating our approach

toeplitz operators and weighted wiener hopf operators pseudoconvex reinhardt and tube domains the notion of weighted wiener hopf operators is introduced their relationship with toeplitz operators acting on the space of holomorphic functions which are square integrable with respect to a given symmetric measure is discussed the groupoid approach is used in order to present a general program for studying the c algebra generated by weighted wiener hopf operators associated with a solid cone of a second countable locally compact hausdorff group this is applied to the case when the group is the dual of a connected locally compact abelian lie group and the measure is well behaved in order to produce a geometric groupoid which is independent of the representation

classification of quasi homogeneous holomorphic curves and operators in the cowen douglas class abstract in this paper we study quasi homogeneous operators which include the homogeneous operators in the cowen douglas class we give two separate theorems describing canonical models with respect to equivalence under unitary and invertible operators respectively for these operators using techniques from complex geometry this considerably extends the similarity and unitary classification of homogeneous operators in the cowen douglas class obtained recently by the last author and a koranyi in a significant generalization of the properties of the homogeneous operators we show that quasi homogeneous operators are irreducible and determine which of them are strongly irreducible applications include the equality of the topological and algebraic k group of a quasi homogeneous operator and an affirmative answer to a well known question of halmos

on reducing submodules of hilbert modules with g n invariant kernels fix a bounded domain omega subset of c n and a positive definite kernel k on omega both invariant under g n the permutation group on n symbols let h subset of hol omega be the hilbert module determined by k we show that h splits into orthogonal direct sum of subspaces pph indexed by the partitions p of n we prove that each submodule pph is a locally free hilbert module of rank equal to square of the dimension chi p 1 of the irreducible representation corresponding to p given two partitions p and q we show that if chi p 1 not equal chi q 1 then the sub modules pph and pqh are not unitarily equivalent we prove that if h is a contractive analytic hilbert module on omega then the taylor joint spectrum of the n tuple of multiplication operators by elementary symmetric polynomials on pph is clos s omega where s c n c n is the symmetrization map it is then shown that this commuting tuple of operators defines a contractive homomorphism of the ring of symmetric polynomials cz gn in n variables equipped with the sup norm on clos s omega c 2018 elsevier inc all rights reserved

radial basis collocation methods for elliptic boundary value problems this paper introduces radial basis functions rbf into the collocation methods and the combined methods for elliptic boundary value problems first the ritz galerkin method rgm is chosen using the rbf and the integration approximation leads to the collocation method of rbf for poisson s equation next the combinations of rbf with finite element method fem finite difference method fdm etc can be easily formulated by following li 1 and hu and li 2 3 but more analysis of inverse estimates is explored in this paper since the rbfs have the exponential convergence rates and since the collocation nodes may be scattered in rather arbitrary fashions in various applications the rbf may be competitive to orthogonal polynomials for smooth solutions moreover for singular solutions we may use some singular functions and rbfs together numerical examples for smooth and singularity problems are provided to display effectiveness of the methods proposed and to support the analysis made

moment problems and subnormality abstract we investigate the connection between certain algebraic conditions on a subnormal tuple s and the support of the representing measure s for s

optimization of dual response systems a comprehensive procedure for degenerate and nondegenerate problems most dual response systems drss arising in response surface modeling can be approximated using a nonlinear and typically nonconvex mathematical program involving two quadratic functions one of the quadratic functions is used as the objective function the other for imposing a target constraint this paper describes an effective heuristic for computing global or near global optimal solutions for this type of problem the first part of the paper addresses the special case of degeneracy a condition that makes the system more difficult to solve included are means for detecting degeneracy as well as issues relating to its likelihood in practice the subsequent part of the paper describes our new procedure axis which rotates a degenerate problem and then decomposes it into a finite sequence of nondegenerate subproblems of lower dimension the nondegenerate subproblems are solved using the algorithm drsalg developed earlier in the final parts of the paper the axis and drsalg algorithms are integrated into a single dual response solver termed dr2 dr2 is tested against two nonlinear optimization procedures that have been used frequently in dual response applications the new solver proves to be extremely effective at locating best practice operating conditions

an approximation theorist s view on solving operator equations with special attention to trefftz mfs mps and drm methods abstract when an approximation theorist looks at well posed pde problems or operator equations and standard solution algorithms like finite elements rayleigh ritz or trefftz techniques methods of fundamental or particular solutions and their combinations they boil down to approximation problems and stability issues these two can be handled by approximation theory and this paper shows how with special applications to the aforementioned algorithms the intention is that the approximation theorist s viewpoint is helpful for readers who are somewhat away from that subject

rigidity of the flag structure for a class of cowen douglas operators the explicit description of irreducible homogeneous operators in the cowen douglas class and the localization of hilbert modules naturally leads to the definition of a smaller class possessing a flag structure these operators are shown to be irreducible it is also shown that the flag structure is rigid that is the unitary equivalence class of the operator and the flag structure determine each other a complete set of unitary invariants which are somewhat more tractable than those of an arbitrary operator in the cowen douglas class is obtained c 2017 elsevier inc all rights reserved

bounded modules extremal problems and a curvature inequality abstract in this paper we study certain finite dimensional hilbert modules over the function algebra a c n these modules appear as localizations of a cowen douglas operator we show that these modules are always bounded where the bound is related to the solution of an extremal problem in particular we obtain necessary sufficient conditions for such a module to be contractive we apply the above results to produce an example of a contractive module over a b 2 which is not completely contractive

recent developments in the numerical evaluation of particular solutions in the boundary element method abstract we survey recent work on the numerical evaluation of particular solutions in the boundary elements method bem particularly rbf approximations and related mathematical convergence theory current research suggests at least in r 2 that the best choice for bases is the generalized multiquadrics numerical results are presented to support this observation

the curvature invariant for a class of homogeneous operators for an operator t in the class b n introduced by cowen and douglas the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle e t determine the unitary equivalence class of the operator t in a subsequent paper the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator t is an element of b n here we show that some of the covariant derivatives are necessary our examples consist of homogeneous operators in b n for homogeneous operators the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0 this shows that it is enough to calculate all the invariants and compare them at just one point say 0 these calculations are then carried out in number of examples one of our main results is that the curvature along with its covariant derivative of order 0 1 at 0 determines the equivalence class of generic homogeneous hermitian holomorphic vector bundles over the unit disc

unitary invariants for hilbert modules of finite rank we associate a sheaf model to a class of hilbert modules satisfying a natural finiteness condition it is obtained as the dual to a linear system of hermitian vector spaces in the sense of grothendieck a refined notion of curvature is derived from this construction leading to a new unitary invariant for the hilbert module a division problem with bounds originating in douady s privilege is related to this framework a series of concrete computations illustrate the abstract concepts of the paper

representations of function algebras abstract operator spaces and banach space geometry let g be the closed unit ball of some norm on cn and let a g be the closure of the polynomials in the sup norm we prove that if n 5 then there is a contractive representation of a g as operators on a hilbert space which is not completely contractive our technique involves introducing a numerical invariant x for a normed space x which measures the difference between the minimal operator space structure which can be assigned to x min x and the maximal structure max x we estimate x using banach space techniques we also prove that if x is any infinite dimensional subspace of the space of continuous functions on a compact hausdorff space then there exists a bounded linear map on x which is not completely bounded

fredholm and invertible tuples of operators the deformation problem using j l taylor s definition of joint spectrum we study fredholm and invertible tuples of operators on a hilbert space we give the foundations for a several variables theory including a natural generalization of atkinson s theorem and an index which well behaves we obtain a characterization of joint invertibility in terms of a single operator and study the main examples at length we then consider the deformation problem and solve it for the class of almost doubly commuting fredholm pairs with a semi fredholm coordinate 1 introduction 1 let t be a bounded linear operator on a banach space t is said to be invertible if there exists an operator s on such that ts st 1 the identity operator on 9c by the open mapping theorem this is equivalent to ker t 0 and r t range of t the last formulation does not rely upon the existence of an inverse for t but rather on the action of the operator t when t is replaced by an tuple of commuting operators several definitions of nonsingular ity exist j l taylor 19 has obtained one which reflects the actions of the operators by considering the koszul complex associated with the tuple 2 in this paper we develop a general several variables theory on the basis of taylor s work and study commuting and almost commuting commuting mod ulo the compacts tuples of operators on a hilbert space we obtain a characterization of joint invertibility in terms of the invertibility of a single operator which is essential for our approach from that we get a number of corollaries which generalize nicely the known elementary results in one variable at the same time the referred characterization allows us to define a continuous invariant under compact perturbations integer valued index on the class of fred holm tuples those almost commuting tuples which are invertible in the calkin algebra this index extends the classical one for fredholm operators we prove that an almost commuting tuple of essentially normal operators with all commu tators in trace class has index zero 2 and that a natural generalization of atkinson s theorem holds for tuples

generalized ridge analysis under linear restrictions with particular applications to mixture experiments problems to investigate the behavior of a response y over a specified region of interest by fitting a secondorder response surface standard ridge analysis provides a way of following the locus of for example a maximum response moving outward from the origin of the predictor variable space because this approach does not require one to view the fitted regression surface as a whole this important technique may be applied even when visualization of the surface is difficult in several dimensions the ridge trace view enables practitioners to assess and understand the typically complex interplay between the input variables as the response improves to explore a subspace defined by a linear restriction on the predictors a situation discussed infrequently in the literature and never in the context of mixture experiments we show how a modification of ridge regression can be used generally to investigate second order mixture surfaces with many ingredients particularly when the experimental mixture space is itself l

the application of ridge techniques to mixture data ridge analysis the response surface technique ridge analysis was developed within the context of unconstrained or nonmixture explanatory variables it has apparently been generally considered nonapplicable to mixture data in this discussion two methods are introduced for analyzing quadratic mixture response surfaces with ridge analysis the first may be useful with standard response surface designs e g draper and lawrence 1965a b thompson and myers 1968 and the second offers an alternative method of examining the effects of individual components in constrained designs both methods are demonstrated on real data

multiquadric interpolation improved abstract our concern in this paper is the improvement of localization properties of multiquadric interpolation on a multivariate integer grid

toeplitz algebras subnormal tuples and rigidity on reproducing c z1 zd modules this paper mainly considers toeplitz algebras subnormal tuples and rigidity concerning reproducing c z1 zd modules by making use of arveson s boundary representation theory we find there is more rigidity in several variables than there is in single variable we specialize our attention to reproducing c z1 zd modules with u invariant kernels by examining the spectrum and the essential spectrum of the d tuple mz1 mzd and deducing an exact sequence of c algebras associated with toeplitz algebra finally we deal with toeplitz algebras defined on arveson submodules and rigidity of arveson submodules

miscellaneous error bounds for multiquadric and related interpolators we establish several types of a a priori error bounds for multiquadric and related interpolators the results are stated and proven in the general multivariate case these estimates show for example that in many cases such interpolators converge very quickly and can be used in the recovery of band limited functions from discrete data we also include numerical experiments which illustrate the theoretical results

a general approach to ridge analysis with confidence intervals in response surface methodology ridge analysis is a graphical technique for interpreting response surfaces particularly those of three or more dimensions standard ridge analysis techniques employ a second order polynomial regression model an approach to ridge analysis is presented here that generalizes its current scope this approach allows the use of a general regression model for the response surface within the class of linear models conservative or approximate simultaneous confidence intervals about the optimal mean responses for varying radii can be obtained these simultaneous confidence intervals form a guidance band to aid the experimenter in determining optimal levels of operation a variety of explanatory variable constraints including mixture constraints can also be imposed for the standard quadratic model these confidence intervals can be easily modified to obtain confidence bounds about the maximum or minimum eigenvalues of b the matrix of second order regression coefficients

solving partial differential equations by collocation using radial basis functions after a series of application papers have proven the approach to be numerically effective this paper gives the first theoretical foundation for methods solving partial differential equations by collocation with possibly radial basis functions

on intertwining operators via reproducing kernels abstract in this note we investigate operators intertwining the coordinate multiplication between functional hilbert spaces in terms of their matrix valued reproducing kernel functions which extends the work of curto and salinas 1984 4 on unitary intertwining operators

confidence sets for optimal factor levels of a response surface construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology in wan et al 2015 an exact 1 confidence set has been provided for a maximum or minimum point i e an optimal factor level of a univariate polynomial function in a given interval in this article the method has been extended to construct an exact 1 confidence set for the optimal factor levels of response surfaces the construction method is readily applied to many parametric and semiparametric regression models involving a quadratic function a conservative confidence set has been provided as an intermediate step in the construction of the exact confidence set two examples are given to illustrate the application of the confidence sets the comparison between confidence sets indicates that our exact confidence set is better than the only other confidence set available in the statistical literature that guarantees the 1 confidence level

subnormal operators whose adjoints have rich point spectrum a generalized version of the glauber klauder basic formula of quantum optics is shown to be valid for any cyclic subnormal operator s whose adjoint has a rich point spectrum p s in the sense that a semispectral measure of s vanishes on c p s it is exhibited that such operators always have analytic models the point spectrum of the adjoint of a subnormal operator which satisfies a generalized version of the glauber klauder formula is proved to be rich in the above sense

some thoughts on ando s theorem and parrott s example in this short note we present an elementary proof of ando s theorem within a restricted class p of homomorphisms modeled after parrott s example we also show by explicit estimation that the cb norm of the contractive homomorphism of the tri disc algebra induced by the commuting triple of parrott exceeds 1 indeed we construct a polynomial p with matrix coefficients with the property p p in particular we show that there are contractive homomorphisms of the tri disc algebra which are not even 2 contractive