the schwarz lemma at the boundary of the symmetrized bidisc abstract the symmetrized bidisc g 2 is defined by g 2 z 1 z 2 z 1 z 2 c 2 z 1 1 z 2 1 z 1 z 2 c it is a bounded inhomogeneous pseudoconvex domain without c 1 boundary and especially the symmetrized bidisc hasn t any strongly pseudoconvex boundary point and the boundary behavior of both caratheodory and kobayashi metrics over the symmetrized bidisc is hard to describe precisely in this paper we study the boundary schwarz lemma for holomorphic self mappings of the symmetrized bidisc g 2 and our boundary schwarz lemma in the paper differs greatly from the earlier related results

rigidity of holomorphic mappings and a new schwarz lemma at the boundary a rigidity theorem for holomorphic mappings in the nature of the uniqueness statement of the classical one variable schwarz lemma is proved at the boundary of a strongly pseudoconvex domain the result reduces to an interesting and apparently new result even in one complex dimension the theorem has a variety of geometric and analytic interpretations department of mathematics university of michigan ann arbor michigan 48109 department of mathematics box 1146 washington university in st louis st louis missouri 63130 this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 04 utc all use subject to http about jstor org terms

bayesian analysis of switching regression models abstract the paper considers a class of switching regression models where the change of regime is represented by a min operator after reviewing a maximum likehood method a local identification criterion is proposed contrary to classical analysis it is shown that bayesian analysis requires here local identification everywhere on the parameter space the paper then proposes a monte carlo procedure to compute posterior moments with an importance function based on an approximate posterior density of the model feasibility of the method is shown in a numerical example and then in an economic example

schwarz lemma at the boundary of strongly pseudoconvex domain in mathbb c n in this paper we establish a new type of the classical boundary schwarz lemma for holomorphic self mappings of strongly pseudoconvex domain in mathbb c n

the automorphism group and limit set of a bounded domain i the finite type case abstract for bounded pseudoconvex domains with finite type we give a precise description of the automorphism group if an orbit of the automorphism group accumulates on at least two different points of the boundary then the automorphism group has finitely many components and is the almost direct product of a compact group and connected lie group locally isomorphic to aut b k further the limit set is a smooth submanifold diffeomorphic to the sphere of dimension 2 k 1 as applications we prove a new finite jet determination theorem and a tits alternative theorem the geometry of the kobayashi metric plays an important role in the paper

a burns krantz type theorem for domains with corners in their pioneering paper bk94 burns andkrantzhave established a boundary version of the classical cartan s uniqueness theorem if f is holomorphic self map of a smoothly bounded strongly pseudoconvex domain d c such that f z z o z p 3 as z p for some p d then f z z furthermore they give an example showing that the exponent 3 in the above statement cannot be decreased the goal of this paper is twofold first to give purely local boundary uniqueness results for maps defined only on one side as germs at a boundary point and hence not necessarily sending any domain to itself and also under the weaker assumption that f z z o z p 3 holds only for z in a proper cone in d with vertexp such results have no analogues in one complex variable in contrast with the situation when a domain is preserved our second goal is to extend the above results from boundaries of domains to real submanifolds m c of higher codimension recall that m is called generic if its tangent space tpm at every point p m spans tpc over c i e tpc n tpm itpm here the usual replacement for a one sided neighborhood of a boundary point is a wedge with edgem at a pointp m in the direction of an open cone npm tpc tpm i e a domain w c such that for any pair of open cones npm with 0 and 0 there exists a neighborhood u of p in c such that m u u w and m u u contains a neighborhood of p in w where we identify npm with a fixed complement of tpm in tpc c furthermore we extend the notion of strong pseudoconvexity to wedges as follows we call a wedge w with edge m at p in the direction of strongly

integer solution for linear complementarity problem we consider the problem of finding an integer solution to a linear complementarity problem we introduce the class i of matrices for which the corresponding linear complementarity problem has an integer complementary solution for every vector q for which it has a solution strong principal unimodularity forms a sufficient condition for inclusion in the class i it is also shown to be necessary for some well known classes of matrices including the class of positive semidefinite matrices this is used in deriving necessary and sufficient conditions for a convex quadratic program to have an integer optimal solution for all b and c for which it has an optimal solution characterizations are also derived for some other well known classes of matrices in linear complementarity to belong to the class i in the end a peeling algorithm for finding integer solution for linear complementarity problems is given and related results are derived

econometric illustrations of novel numerical integration strategies for bayesian inference abstract recent progress with numerical techniques for implementing bayesian methods for irregular multi parameter likelihoods is reviewed and illustrated with two econometric examples the numerical integration strategies involve novel iterative adaptive uses of cartesian product and spherical rule quadrature formulae together with importance sampling techniques

julia theory for slice regular functions the theory of slice regular functions is nowadays widely studied and has found elegant applications to functional calculus for quaternionic linear operators and schur analysis however much less is known about their boundary behaviors in this paper we initiate the study of julia theory for slice regular functions more precisely we establish the quaternionic versions of the julia lemma the julia caratheodory theorem the boundary schwarz lemma the hopf lemma and the burns krantz rigidity theorem for slice regular self mappings of the open unit ball b h and of the right half space h we provide an explicit example to show that in quaternionic hopf lemma the slice derivative of a slice regular function f at the boundary fixed point may not be real in contrast to the complex version our result implies that the commonly believed version of the hopf lemma turns out to be totally wrong this new quaternionic version of the hopf lemma also improves osserman estimate even in the complex setting and is essentially the first significant theorem belonging to the theory of quaternions itself other than the theory of complex analysis since the result involves the lie brackets which reflect the non commutative feature of quaternions

boundary behavior of infinitesimal generators in the unit ball we prove a julia wolff caratheodory type theorem for infinitesimal generators on the unit ball in n moreover we study jets expansions at the boundary and give necessary and sufficient conditions on such jets for an infinitesimal generator to generate a group of automorphisms of the ball

almost n matrices and linear complementarity abstract an almost n matrix a is one with real entries whose determinant is positive and proper principal minors are negative in this paper we obtain some characterization results for almost n matrices that are similar to n matrices among other things we show that an almost n matrix of first category with n 4 belongs to the class of q matrices as an application we derive a new univalence result

discontinuous decision processes and threshold autoregressive time series modelling where p is a smooth function suppose that we approximate 4u x by 0 a constant for all x in subsequent discussion we suppress the argument x whenever this may be done without obscuring the context clearly this approximation will incur some errors on the other hand as argued by tong lim 1980 we could approximate arbitrarily closely by a step function at first sight it seems that this could pose a horrendous computational problem indeed this is the case from a purely deterministic point of view however we usually approximate the true model with some purpose in mind e g forecasting control filtering thus we should really specify what we mean by approximating u arbitrarily closely bayesian decision theory seems a natural approach to this problem in particular the recent general results of smith et al 1981 provide the necessary framework

stationary holomorphic discs and finite jet determination problems we construct a family of small analytic discs attached to levi non degenerate hypersurfaces in mathbb c n 1 which is globally biholomorphically invariant we then apply this technique to study unique determination problems along levi non degenerate hypersurfaces that are merely of class mathcal c 4 this method gives 2 jet determination results for germs of biholomorphisms cr diffeomorphisms as well as in the almost complex setting

boundary jets of holomorphic maps between strongly pseudoconvex domains abstract in this paper we consider jets taken at a fixed boundary point of germs of holomorphic diffeomorphisms which send one strongly pseudoconvex domain into another we completely describe possible first and second jets and conditions of extremality in terms of the chern moser normal forms of the domains

extension operators via semigroups abstract the roper suffridge extension operator and its modifications are powerful tools to construct biholomorphic mappings with special geometric properties the first purpose of this paper is to analyze common properties of different extension operators and to define an extension operator for biholomorphic mappings on the open unit ball of an arbitrary complex banach space the second purpose is to study extension operators for starlike spirallike and convex in one direction mappings in particular we show that the extension of each spirallike mapping is a spirallike for a variety of linear operators a our approach is based on a connection of special classes of biholomorphic mappings defined on the open unit ball of a complex banach space with semigroups acting on this ball

on singular n0 matrices and the class q abstract the class of n and n 0 matrices arises in the theory of global univalence of functions multivariate analysis and in complementarity theory in this paper we study singular n 0 matrices with q property

an improved version of the quandt ramsey mgf estimator for mixtures of normal distributions and switching regressions quandt and ramsey have suggested an estimator for normal mixtures and switching regressions which minimizes a sum of squared differences between empirical and theoretical values of the moment generating function this paper demonstrates how their estimator can be improved by minimizing a generalized sum of squares rather than an ordinary sum of squares when this is done more points of evaluation moments are unambiguously better than less most of the results presented are also applicable to method of moments estimators in general

superfluous matrices in linear complementarity superfluous matrices were introduced by howe 1983 in linear complementarity in general producing examples of this class is tedious a few examples can be found in chapter 6 of cottle pang and stone 1992 to overcome this problem we define a new class of matrices bar z and establish that in bar z superfluous matrices of any ordern 4 can easily be constructed for every integerk an example of a superfluous matrix of degreek is exhibited in the end

boundary schwarz lemma for solutions to poisson s equation abstract let d be the closure of the unit disk d in c and g a continuous function of d in this paper we establish the schwarz lemma at the boundary for solutions to the poisson s equation f g

on the inverses of general tridiagonal matrices in this work the sign distribution for all inverse elements of general tridiagonal h matrices is presented in addition some computable upper and lower bounds for the entries of the inverses of diagonally dominant tridiagonal matrices are obtained based on the sign distribution these bounds greatly improve some well known results due to ostrowski 1952 23 shivakumar and ji 1996 26 nabben 1999 21 22 and recently given by peluso and politi 2001 24 peluso and popolizio 2008 25 and so forth it is also stated that the inverse of a general tridiagonal matrix may be described by 2n 2 parameters k k 2n and k k 1n 1 instead of 2n 2 ones as given by el mikkawy 2004 3 el mikkawy and karawia 2006 4 and huang and mccoll 1997 10 according to these results a new symbolic algorithm for finding the inverse of a tridiagonal matrix without imposing any restrictive conditions is presented which improves some recent results finally several applications to the preconditioning technology the numerical solution of differential equations and the birth death processes together with numerical tests are given

the n matrix completion problem under digraphs assumptions fundacao para a ciencia e a tecnologia fct programa operacional ciencia tecnologia inovacao pocti spanish dgi grant number bfm2001 0081 c03 02

schwarz lemma and rigidity theorem at the boundary for holomorphic mappings on the unit polydisk in cn abstract this article is devoted to a deep study of holomorphic self mappings of the unit polydisk via not only establishing a new type of the classical schwarz lemma at the boundary but also giving the boundary version of the rigidity theorem

the degree of an exact order matrix the classes of exact order k matrices for any positive integer k were defined and studied by mohan parthasarathy and sridhar mohan s r t parthasarathy r sridhar 1994 the linear complementarity problem with exact order matrices math oper res 19 618 644 here we prove results on the linear complementarity problem lcpq m for m belonging to the class of exact order k k 3 using the concepts of degree theory our main result in this paper consists in proving that a matrix m rn n of exact order k for any positive integer n k 3 belongs to the class q if and only if the degree of m is either 1 or 1 also a complete characterization of exact order 2 matrices is presented in terms of their inverse structure

a new maximum likelihood algorithm for piecewise regression abstract this paper presents a piecewise regression method for continuous models containing max or min operators or both this method does not require knowledge of the zone in which a shift in regimes occurs moreover it allows the application of analytical derivatives to maximize the likelihood function which greatly simplifies the estimation of the model the method proposed exhibits fast convergence and can be used for an arbitrary number of regimes and variables

weighted composition operators between fock type spaces in cn motivated by quite recent results by ueki 22 the boundedness and compactness of the weighted composition operators acting between some fock type spaces in c n are characterized we also study weighted composition operators on little weighted fock type spaces norm of some of these operators is calculated in some cases we give some estimates for the essential norm of some of these operators

bounded composition operators on weighted bergman spaces abstract we answer two questions asked by t l kriete 1998 in contemp math vol 213 pp 73 91 amer math soc providence concerning bounded composition operators on weighted bergman spaces of the unit disk the main result is the following if gi e hi for i 1 2 are weight functions in a certain range for which h 1 r h 2 r as r 1 then there is a self map of the unit disk such that the induced composition operator c maps a2g2 boundedly into itself but does not map a2g1 into itself

the symmetric n matrix completion problem abstract an n n matrix is called an n matrix if all its principal minors are negative in this paper we are interested in the symmetric n matrix completion problem that is when a partial symmetric n matrix has a symmetric n matrix completion here we prove that a partial symmetric n matrix has a symmetric n matrix completion if the graph of its specified entries is chordal furthermore if this graph is not chordal then examples exist without symmetric n matrix completions necessary and sufficient conditions for the existence of a symmetric n matrix completion of a partial symmetric n matrix whose associated graph is a cycle are given

testing and modeling threshold autoregressive processes abstract the threshold autoregressive model is one of the nonlinear time series models available in the literature it was first proposed by tong 1978 and discussed in detail by tong and lim 1980 and tong 1983 the major features of this class of models are limit cycles amplitude dependent frequencies and jump phenomena much of the original motivation of the model is concerned with limit cycles of a cyclical time series and indeed the model is capable of producing asymmetric limit cycles the threshold autoregressive model however has not received much attention in application this is due to a the lack of a suitable modeling procedure and b the inability to identify the threshold variable and estimate the threshold values the primary goal of this article therefore is to suggest a simple yet widely applicable model building procedure for threshold autoregressive models based on some predictive residuals a simple statistic is proposed to test for threshold nonlinearity and specify the

identity principles for commuting holomorphic self maps of the unit disc abstract let f g be two commuting holomorphic self maps of the unit disc if f and g agree at the common wolff point up to a certain order of derivatives no more than 3 if the wolff point is on the unit circle then f g

a bayesian analysis of some threshold switching models abstract this paper presents a bayesian analysis of various threshold switching regression models including simple time series models where the change of regime is governed by a known function of exogenous variables some special features arising from the choice of a two dimensional linear dichotomy function are then discussed and the concepts of concurrency and duality introduced within this framework we compare the maximum likelihood and bayesian methodologies for inference and prediction in particular we show that the bayesian approach solves the non uniqueness problem which affects maximum likelihood prediction in certain situations these results are illustrated with two numerical examples

applications of degree theory to linear complementarity problems in this paper we consider two applications of degree theory to linear complementarity problems in the first application we study the stability of an lcp at a solution point specifically we prove the stability of an lcp corresponding to a p0 matrix at an isolated solution using a recent degree formula due to stewart 1991 we strengthen a stability result of gowda and pang 1992 in the second application we use the same degree formula of stewart to describe the number of solutions of lcpm q when m is a negative almost n matrix this analysis leads to a lipschitzian characterization of the solution map i q solm q corresponding to a nondegenerate negative matrix

n matrix completion problem abstract an n n matrix is called an n matrix if all principal minors are negative in this paper we are interested in n matrix completion problems that is when a partial n matrix has an n matrix completion in general a combinatorially or non combinatorially symmetric partial n matrix does not have an n matrix completion here we prove that a combinatorially symmetric partial n matrix has an n matrix completion if the graph of its specified entries is a 1 chordal graph we also prove that there exists an n matrix completion for a partial n matrix whose associated graph is an undirected cycle

the generalized linear complementarity problem revisited given a vertical block matrixa we consider in this paper the generalized linear complementarity problem vlcp q a introduced by cottle and dantzig we formulate this problem as a linear complementarity problem with a square matrixm a formulation which is different from a similar formulation given earlier by lemke our formulation helps in extending many well known results in linear complementarity to the generalized linear complementarity problem we also show that the class of vertical block matrices which cottle and dantzig s algorithm can process is the same as the class of equivalent square matrices which lemke s algorithm can process we also present some degree theoretic results on a vertical block matrix

comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains we prove that for a strongly pseudoconvex domain d subset mathbb c n the infinitesimal caratheodory metric g c z v and the infinitesimal kobayashi metric g k z v coincide if z is sufficiently close to bd and if v is sufficiently close to being tangential to bd also we show that every two close points of d sufficiently close to the boundary and whose difference is almost tangential to bd can be joined by a unique up to reparameterization complex geodesic of d which is also a holomorphic retract of d the same continues to hold if d is a worm domain as long as the points are sufficiently close to a strongly pseudoconvex boundary point we also show that a strongly pseudoconvex boundary point of a worm domain can be globally exposed this has consequences for the behavior of the squeezing function

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

ky fan s n matrices and linear complementarity problems we consider the linear complementarity problem lcp w az q w 0 z 0 wtz 0 when all the off diagonal entries ofa are nonpositive the class of z matrices all the proper principal minors ofa are positive and the determinant ofa is negative the class of almost p matrices we shall call this the class of f matrices we show that ifa is a z matrix thena is an f matrix if and only if lcp q a has exactly two solutions for anyq 0 q 0 and has at most two solutions for any otherq

on characterizing n matrices using linear complementarity we show that a square matrix a with at least one positive entry and all principal minors negative can be characterized in terms of the number of solutions the linear complementarity problem q a with the matrix a has for different vectors q such a matrix can also be characterized in terms of a sign nonreversal property these results complement the known results for a square matrix a 0 with all its principal minors negative

structure properties of w matrices abstract we continue an investigation of the class w of real square matrices a matrix belongs to w if and only if certain pairs of its complementary cones intersect in the zero vector only we show that a w matrix with no zero diagonal entries is a p 0 matrix each principal minor is nonnegative and a w matrix with no nonzero diagonal entries is a nonnegative matrix which either is monomial or has a zero column lastly we show how these two results impose certain necessary conditions on the structure of a w matrix

parametrization of local cr automorphisms by finite jets and applications the goal of this work is to study the structure of the group of all local realanalytic cr automorphisms of a germ of a real analytic hypersurface m p in c or equivalently of all local biholomorphisms h c p c p mapping the germ m p into itself we also deal with the more general situation of a realanalytic cr manifold of arbitrary codimension see 2 for every fixed point p m we refer to this group of local biholomorphisms as the stability group of m p and denote it by aut m p endowed with the topology of uniform convergence on compact neighbourhoods of p it becomes a topological group this natural inductive limit topology can be described in the following way a sequence of germs of biholomorphisms hj aut m p converges to another such germ h aut m p if there exists a neighbourhood u of p in c to which all mappings hj extend holomorphically and such that hj h uniformly on u this group arises in a variety of different circumstances one of the most important ones where it naturally appears is the biholomorphic equivalence problem which consists in deciding whether two given germs of real analytic hypersurfaces are biholomorphically equivalent the biholomorphic equivalence problem has been studied since the beginning of the last century when poincare 37 observed probably for the first time that two real hypersurfaces in c for n 2 are not necessarily locally equivalent via a holomorphic transformation though they are via a c transformation today the biholomorphic equivalence problem for strongly pseudoconvex or levi nondegenerate hypersurfaces is pretty well understood based on the works of e cartan 14 15 in dimension two and the results of tanaka 42 and chern moser 17 in arbitrary dimension thanks to the works initiated in the 1970s a number of remarkable properties of the stability group of strongly pseudoconvex real analytic hypersurfaces have been discovered see e g the surveys by vitushkin 45 huang 30 and baouendi ebenfelt and rothschild 5 for complete discussions on this matter these properties depend on whether the germ m p can be biholomorphically mapped onto a piece of the unit sphere if there exists such a biholomorphism one says that m p is spherical for instance if m p is not spherical the group aut m p is

linear sums of two composition operators on the fock space abstract linear sums of two composition operators of the multi dimensional fock space are studied we show that such an operator is bounded only when both composition operators in the sum are bounded so cancelation phenomenon is not possible on the fock space in contrast to what have been known on other well known function spaces over the unit disk we also show the analogues for compactness and for membership in the schatten classes for linear sums of more than two composition operators the investigation is left open

nonlinear interest rate dynamics and implications for the term structure this paper explores nonlinear dynamics in the time series of the short term interest rate in the united states the proposed model is an autoregressive threshold model augmented by conditional heteroskedasticity the performance of the model is evaluated by considering its implications for the term structure of interest rates the nonlinear dynamics imply a form of nonlinearity in the levels relation between the long and the short rate

n0 completions on partial matrices an nxn matrix is called an n 0 matrix if all its principal minors are non positive in this paper we are interested in n 0 matrix completion problems that is when a partial n 0 matrix has an n 0 matrix completion in general a combinatorially or non combinatorially symmetric partial n 0 matrix does not have an n 0 matrix completion here we prove that a combinatorially symmetric partial n 0 matrix with no null main diagonal entries has an n 0 matrix completion if the graph of its specified entries is a 1 chordal graph or a cycle we also analyze the mentioned problem when the partial matrix has some null main diagonal entries

composition operators on hilbert spaces of entire functions with analytic symbols abstract composition operators with analytic symbols on some reproducing kernel hilbert spaces of entire functions on a complex hilbert space are studied the questions of their boundedness seminormality and positivity are investigated it is proved that if such an operator is bounded then its symbol is a polynomial of degree at most 1 i e it is an affine mapping fock s type model for composition operators with linear symbols is established as a consequence explicit formulas for their polar decomposition aluthge transform and powers with positive real exponents are provided the theorem of carswell maccluer and schuster is generalized to the case of segal bargmann spaces of infinite order some related questions are also discussed

on suboperators with codimension one domains the question of the existence of a proper closed densely defined suboperator whose domain contains a given linear space is answered such suboperators with codimension one domains are described the motivation for studying this topic comes from the theory of extremal extensions of non densely defined positive operators

second angular derivatives and parabolic iteration in the unit disk in this paper we deal with second angular derivatives at denjoy wolff points for parabolic functions in the unit disc namely we study and analyze the existence and the dynamical meaning of this second angular derivative for instance we provide several characterizations of that existence in terms of the so called koenigs function it is worth pointing out that there are two quite different classes of parabolic iteration those with positive hyperbolic step and those with zero hyperbolic step in the first case the koenigs function is in the caratheodory class but in the second case it is even unknown if it is normal therefore the ideas and techniques to approach these two cases are really different in the end we also present several rigidity results related to the second angular derivatives at denjoy wolff points

almost p 0 matrices and the class q this paper demonstrates that within the class of thosen n real matrices each of which has a negative determinant nonnegative proper principal minors and inverse with at least one positive entry the class ofq matrices coincides with the class of regular matrices each of these classes of matrices plays an important role in the theory of the linear complementarity problem lastly analogous results are obtained for nonsingular matrices which possess only nonpositive principal minors

finite jet determination of cr mappings abstract we prove the following finite jet determination result for cr mappings given a smooth generic submanifold m c n n 2 that is essentially finite and of finite type at each of its points for every point p m there exists an integer l p depending upper semicontinuously on p such that for every smooth generic submanifold m c n of the same dimension as m if h 1 h 2 m p m are two germs of smooth finite cr mappings with the same l p jet at p then necessarily j p k h 1 j p k h 2 for all positive integers k in the hypersurface case this result provides several new unique jet determination properties for holomorphic mappings at the boundary in the real analytic case in particular it provides the finite jet determination of arbitrary real analytic cr mappings between real analytic hypersurfaces in c n of d angelo finite type it also yields a new boundary version of h cartan s uniqueness theorem if c n are two bounded domains with smooth real analytic boundary then there exists an integer k depending only on the boundary such that if h 1 h 2 are two proper holomorphic mappings extending smoothly up to near some point p and agreeing up to order k at p then necessarily h 1 h 2

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

algorithmic detection and construction of n matrices abstract n matrices are real n n matrices all of whose principal minors are negative we provide i an o 2 n test to detect whether or not a given matrix is an n matrix and ii a characterization of n matrices leading to the recursive construction of every n matrix