a class of complex symmetric toeplitz operators on hardy and bergman spaces abstract an operator t b h is complex symmetric if there exists a conjugation c on h so that c t c t in this paper we characterize the complex symmetric toeplitz operator on the hardy and bergman space in particular we show that the toeplitz operator induced by the berezin transform of a complex symmetric operator on hardy space is also complex symmetric with the same conjugation however we see that this is not true for bergman space by providing some examples

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

approximation in the mean by polynomials for a positive measure al with compact support in the complex plane c and for 1 t co let pt i denote the closure in lt i of the polynomials in one complex variable the purpose of this paper is to describe pt a the main results are the following first there exists a borel partition ail of the support of al such that for i 1 the space pt t laai contains no nontrivial characteristic functions and

semi lagrangian schemes for hamilton jacobi equations discrete representation formulae and godunov methods we study a class of semi lagrangian schemes which can be interpreted as a discrete version of the hopf lax oleinik representation formula for the exact viscosity solution of first order evolutive hamilton jacobi equations that interpretation shows that the scheme is potentially accurate to any prescribed order we discuss how the method can be implemented for convex and coercive hamiltonians with a particular structure and how this method can be coupled with a discrete legendre trasform we also show that in one dimension the first order semi lagrangian scheme coincides with the integration of the godunov scheme for the corresponding conservation laws several test illustrate the main features of semi lagrangian schemes for evolutive hamilton jacobi equations

ranks of complex skew symmetric operators and applications to toeplitz operators abstract we study the rank of complex skew symmetric operators on separable hilbert spaces we prove that a finite rank complex skew symmetric operator can t have an odd rank as applications we show that any finite rank commutator of two toeplitz operators on the pluriharmonic bergman space of the ball can t have an odd rank we also show that for any positive even integer n there are two toeplitz operators whose commutator is exactly of rank n also we obtain the similar result for certain truncated toeplitz operators

on an example of a complex symmetric composition operator on h2 d abstract in the article 8 an example of a composition operator c on the hardy space h 2 d is discovered that is claimed to be complex symmetric but not normal the purpose of this note is to highlight a mistake in the example that makes the result incorrect

a variational approach for continuous supply chain networks we consider a continuous supply chain network consisting of buffering queues and processors first proposed by d armbruster p degond and c ringhofer siam j appl math 6 6

complex symmetric generators of c algebras abstract this paper gives necessary and sufficient conditions for an essentially normal operator t to have its c algebra c t generated by a complex symmetric operator also it is completely determined when c t is isomorphic to a c algebra singly generated by complex symmetric operators these both depend only on the singular part of t

complex symmetric operators and isotropic vectors on banach spaces abstract in this paper we generalize the concepts of isotropic vectors and complex symmetric operators from hilbert spaces to banach spaces via their dual spaces with this extension we show the existence of isotropic vectors on banach spaces whose dimension is at least two and the relation between the simplicity of an eigenvalue and the non existence of its isotropic eigenvectors

norm estimates of complex symmetric operators applied to quantum systems this paper communicates recent results in the theory of complex symmetric operators and shows through two non trivial examples their potential usefulness in the study of schrodinger operators in particular we propose a formula for computing the norm of a compact complex symmetric operator this observation is applied to two concrete problems related to quantum mechanical systems first we give sharp estimates on the exponential decay of the resolvent and the single particle density matrix for schrodinger operators with spectral gaps second we provide new ways of evaluating the resolvent norm for schrodinger operators appearing in the complex scaling theory of resonances

lax hopf based incorporation of internal boundary conditions into hamilton jacobi equation part i theory this article proposes a new approach for computing a semi explicit form of the solution to a class of hamilton jacobi hj partial differential equations pdes using control techniques based on viability theory we characterize the epigraph of the value function solving the hj pde as a capture basin of a target through an auxiliary dynamical system called characteristic system the properties of capture basins enable us to define components as building blocks of the solution to the hj pde in the barron jensen frankowska sense these components can encode initial conditions boundary conditions and internal boundary conditions which are the topic of this article a generalized lax hopf formula is derived and enables us to formulate the necessary and sufficient conditions for a mixed initial and boundary conditions problem with multiple internal boundary conditions to be well posed we illustrate the capabilities of the method with a data assimilation problem for reconstruction of highway traffic flow using lagrangian measurements generated from next generation simulation ngsim traffic data

observability and controllability of piecewise affine and hybrid systems we prove in a constructive way the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics automata and propositional logic by focusing our investigation on the former class we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems instead we propose practical numerical tests based on mixed integer linear programming

j self adjoint operators with mathcal c symmetries an extension theory approach a well known tool in conventional von neumann quantum mechanics is the self adjoint extension technique for symmetric operators it is used e g for the construction of dirac hermitian hamiltonians with point interaction potentials here we reshape this technique to allow for the construction of pseudo hermitian j self adjoint hamiltonians with complex point interactions we demonstrate that the resulting hamiltonians are bijectively related to the so called hypermaximal neutral subspaces of the defect krein space of the symmetric operator this symmetric operator is allowed to have arbitrary but equal deficiency indices n n general properties of the operators for these hamiltonians are derived a detailed study of operator parametrizations and krein type resolvent formulae is provided for j self adjoint extensions of symmetric operators with deficiency indices 2 2 the technique is exemplified on 1d pseudo hermitian schr dinger and dirac hamiltonians with complex point interaction potentials

matrix representations of truncated toeplitz operators abstract in this paper we describe matrix representations of truncated toeplitz operators on the model space k b where b is an infinite blaschke product satisfying some additional conditions our results are extensions of that obtained by cima ross and wogen in 2008

complex symmetric weighted composition operators in several variables abstract in this paper we study the complex symmetric weighted composition operators on the hilbert space h s of analytic functions over the open unit ball with reproducing kernels k w s z 1 z w s where s n we completely characterize complex symmetric weighted composition operators with respect to two important conjugations j v and j which include hermitian weighted composition operators and normal weighted composition operators appeared in 17 surprisingly they are essential representatives of general conjugations of the form c j where c is unitary and j symmetric indeed these complex symmetric weighted composition operators can only be divided into two classes the size estimates and some other properties of these complex symmetric weighted composition operators are obtained moreover involutive weighted composition operators are completely characterized too as an application we construct concrete conjugations for the involutive composition operators which solves a problem raised by garcia and hammond in a general case

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

a time dependent hamilton jacobi formulation of reachable sets for continuous dynamic games we describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game the algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time dependent hamilton jacobi isaacs partial differential equation while alternative techniques for computing the reachable set have been proposed the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters because the time dependent equation s solution is continuous and defined throughout the state space methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions a numerical implementation of our formulation is described and has been released on the web its correctness is verified through a two vehicle three dimensional collision avoidance example for which an analytic solution is available

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 the boundary conditions characterizing j selfadjoint extensions of j symmetric operators the study of boundary value problems involving linear differentiai equations with real valued coefficients is by now a well established area of analysis on the other hand much less is known about the solvability of such problems when the coefficients or boundary conditions are known to be complex examples of this latter type arise naturally for example in nuclear physics e g the so called optical mode1 for low energy scattering 1 p ijo electromagnetic field theory dielectric waveguides with heat loss c f 19 i or the propagation of radio waves through inhomogeneous media s and elsewhere in cases like these the relevant differential expressions are no longer formally symmetric and hence the powerful methods associated with the spectral theory of selfadjoint operators are not available to facilitate the study of such problems glazman introduced in 4 the concept of a j symmetric operator in a complex hilbert space r let j be a given conjugation operator on 2 i e j is a conjugate linear involution with jx 3 u x for all x and y in 2 a closed densely defined linear operator t in 3 is said to be j symmetric if

unitary equivalence to a complex symmetric matrix low dimensions abstract a matrix t m n c is uecsm if it is unitarily equivalent to a complex symmetric i e self transpose matrix we develop several techniques for studying this property in dimensions three and four among other things we completely characterize 4 4 nilpotent matrices which are uecsm and we settle an open problem which has lingered in the 3 3 case we conclude with a discussion concerning a crucial difference which makes dimension three so different from dimensions four and above

algebraic geometric codes and multidimensional cyclic codes a unified theory and algorithms for decoding using grobner bases it is proved that any algebraic geometric ag code can be expressed as a cross section of an extended multidimensional cyclic code both ag codes and multidimensional cyclic codes are described by a unified theory of linear block codes defined over point sets ag codes are defined over the points of an algebraic curve and an m dimensional cyclic code is defined over the points in m dimensional space the power of the unified theory is in its description of decoding techniques using grobner bases in order to fit an ag code into this theory a change of coordinates must be applied to the curve over which the code is defined so that the curve is in special position for curves in special position all computations can be performed with polynomials and this also makes it possible to use the theory of grobner bases next a transform is defined for ag codes which generalizes the discrete fourier transform the transform is also related to a grobner basis and is useful in setting up the decoding problem in the decoding problem a key step is finding a grobner basis for an error locator ideal for ag codes multidimensional cyclic codes and indeed any cross section of an extended multidimensional cyclic code sakata s algorithm can be used to find linear recursion relations which hold on the syndrome array in this general context the authors give a self contained and simplified presentation of sakata s algorithm and present a general framework for decoding algorithms for this family of codes in which the use of sakata s algorithm is supplemented by a procedure for extending the syndrome array

time reversal frameness and superselection we show that appropriate superpositions of motional states are a reference frame resource that enables breaking of time reversal superselection so that two parties lacking knowledge about the other s direction of time can still communicate we identify the time reversal reference frame resource states and determine the corresponding frameness monotone which connects time reversal frameness to entanglement in contradistinction to other studies of reference frame quantum resources this is the first analysis that involves an antiunitary rather than unitary representation

p mathcal t symmetric non self adjoint operators diagonalizable and non diagonalizable with a real discrete spectrum consider in the operator family h0 a 1a1 a dad d 2 is the quantum harmonic oscillator with rational frequencies w is a symmetric bounded potential and g is a real coupling constant we show that if g being an explicitly determined constant the spectrum of h g is real and discrete moreover we show that the operator has a real discrete spectrum but is not diagonalizable

complex symmetric monomial toeplitz operators on the unit ball abstract monomial toeplitz operators t z p z q on the weighted bergman space of the unit ball in c n are natural extension of the weighted shift operators in higher dimensions dim ker t z p z q may occur for non trivial case thus complex symmetric phenomena will appear in this paper we completely characterize when the monomial toeplitz operator t z p z q on the weighted bergman space is j a symmetric where j a f z f a z with the symmetric unitary n n matrix a moreover we also determine all possible forms of a such that t z p z q is j a symmetric as an application we construct the weakly closed unital commutative algebra generated by complex symmetric toeplitz operators

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

complex symmetric differential operators on fock space abstract the space of entire functions which are integrable with respect to the gaussian weight known also as the fock space is one of the preferred functional hilbert spaces for modeling and experimenting harmonic analysis quantum mechanics or spectral analysis phenomena this space of entire functions carries a three parameter family of canonical isometric involutions we characterize the linear differential operators acting on fock space which are complex symmetric with respect to these conjugations in parallel as a basis of comparison we discuss the structure of self adjoint linear differential operators the computation of the point spectrum of some of these operators is carried out in detail

complex symmetric composition operators on h2 abstract in this paper we find complex symmetric composition operators on the classical hardy space h 2 whose symbols are linear fractional but not automorphic in doing so we answer a recent question of noor and partially answer the original problem posed by garcia and hammond

lax hopf based incorporation of internal boundary conditions into hamilton jacobi equation part ii computational methods this article presents a new method for explicitly computing solutions to a hamilton jacobi partial differential equation for which initial boundary and internal conditions are prescribed as piecewise affine functions based on viability theory a lax hopf formula is used to construct analytical solutions for the individual contribution of each affine condition to the solution of the problem the results are assembled into a lax hopf algorithm which can be used to compute the solution to the partial differential equation at any arbitrary time at no other cost than evaluating a semi analytical expression numerically the method being semi analytical it performs at machine accuracy compared to the discretization error inherent to finite difference schemes the performance of the method is assessed with benchmark analytical examples the running time of the algorithm is compared with the running time of a godunov scheme

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

j self adjointness of a class of dirac type operators in this note we prove that the maximally defined operator associated with the dirac type differential expression m q iddxim q q ddxim where q represents a symmetric m m matrix i e q x q x a e with entries in l1loc r is j self adjoint where j is the antilinear conjugation defined by j 1c 1 0imim0 and c a1 am b1 bm a1 am b1 bm the differential expression m q is of significance as it appears in the lax formulation of the non abelian matrix valued focusing nonlinear schrodinger hierarchy of evolution equations

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 linear maps preserving complex symmetry abstract an operator t on a complex hilbert space h is said to be complex symmetric if there exists a conjugate linear isometric involution c h h so that c t c t this paper is devoted to describing which linear maps leave the class of complex symmetric operators invariant complete characterizations are obtained for several classes of linear maps including similarity transformations surjective linear isometries multiplication operators and certain completely positive maps

the orthogonal lie algebra of operators ideals and derivations abstract we study in this paper the infinite dimensional orthogonal lie algebra o c which consists of all bounded linear operators t on a separable infinite dimensional complex hilbert space h satisfying c t c t where c is a conjugation on h by employing results from the theory of complex symmetric operators and skew symmetric operators we determine the lie ideals of o c and their dual spaces we study derivations of o c and determine their spectra these results complete some results of p de la harpe and provide interesting contrasts between o c and the algebra b h of all bounded linear operators on h

complex symmetry of weighted composition operators on the fock space abstract with the techniques of weighted composition operators we introduce a new concept of general weighted composition conjugations on the fock space f 2 c and completely solve the following problems the description of weighted composition operators which are conjugations the criteria for weighted composition operators to be complex symmetric the spectrum and the point spectrum of complex symmetric operators and the criteria for schatten class membership as well as for normality of such operators

convex formulations of data assimilation problems for a class of hamilton jacobi equations this article proposes a new method for data assimilation and data reconciliation problems applicable to systems modeled by conservation laws the problem is solved directly in the equivalent format of a hamilton jacobi partial differential equation for which the solution is fully characterized by a lax hopf formula using properties of the solution we prove that when the data of the problem is prescribed in piecewise affine form the resulting constraints which consist of the partial differential equation in data assimilation and reconciliation problems are convex and can be instantiated explicitly this property enables us to identify a class of data assimilation and data reconciliation problems that can be formulated using convex programs in standard form we illustrate the capabilities of the method for reconstruction of highway traffic flow using experimental data generated from the mobile century experiment

complex symmetric toeplitz operators on the dirichlet space abstract we study when a toeplitz operator t on the dirichlet space of the unit disk is complex symmetric with respect to a class of conjugations and find surprisingly that the case of complex symmetries of toeplitz operators according to these conjugations is very few we also show that if t is complex symmetric then the curve t t must be nowhere winding furthermore the spectrum and invertibility of complex symmetric toeplitz operators are described

on sequential data assimilation for scalar macroscopic traffic flow models a b s t r a c t we consider the problem of sequential data assimilation for transportation networks using optimal filtering with a scalar macroscopic traffic flow model properties of the distribution of the uncertainty on the true state related to the specific nonlinearity and non differentiability inherent to macroscopic traffic flow models are investigated derived analytically and analyzed we show that nonlinear dynamics by creating discontinuities in the traffic state affect the performances of classical filters and in particular that the distribution of the uncertainty on the traffic state at shock waves is a mixture distribution the non differentiability of traffic dynamics around stationary shock waves is also proved and the resulting optimality loss of the estimates is quantified numerically the properties of the estimates are explicitly studied for the godunov scheme and thus the cell transmission model leading to specific conclusions about their use in the context of filtering which is a significant contribution of this article analytical proofs and numerical tests are introduced to support the results presented a java implementation of the classical filters used in this work is available on line at http traffic berkeley edu for facilitating further efforts on this topic and fostering reproducible research

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

lower semicontinuous solutions of hamilton jacobi bellman equations the value function of mayer s problem arising in optimal control is investigated and lower semicontinuous solutions of the associated hamilton jacobi bellman equation are defined in three equivalent ways under quite weak assumptions about the control system the value function is the unique solution moreover it is stable with respect to perturbations of the control system and the cost it coincides with the viscosity solution whenever it is continuous

the reducibility of c0 2 operators abstract in this paper we give a necessary and sufficient condition for the reducibility of a c 0 2 operator by using its characteristic function moreover we obtain the number of reducing subspaces of a c 0 2 operator as an application we will restudy the reducibility of the truncated toeplitz operator a z 2

complex symmetric composition operators on the newton space abstract a conjecture posed by macdonald and rosenthal states the composition operator c acting on the newton space n 2 p induced by z m z m 1 2 is bounded where m 0 1 our first result is proving that the aforementioned conjecture holds we investigate complex symmetry of composition operators acting on the newton space which is different from that on the hardy space in addition normality and co isometry of composition operators are studied finally we consider complex symmetric weighted composition operators

complex symmetric composition operators on a hilbert space of dirichlet series abstract on the hilbert space of dirichlet series with square summable coefficients there are no non normal complex symmetric composition operators induced by non constant symbols this is in sharp contrast with the phenomenon on the classical hardy space over the unit disk

complex symmetric c0 semigroups on the fock space abstract in this paper we introduce a new concept in dynamical systems the complex symmetric operator c 0 semigroups groups acting on hilbert space using techniques of weighted composition operators we study these semigroups on the fock space f 2 and show in particular that complex symmetric operator c 0 semigroups contain the familiar unitary semigroups as a proper subclass

complex symmetric weighted composition operators on hγ d abstract we study the complex symmetric structure of weighted composition operators of the form w on the hilbert space h d of holomorphic functions over the open unit disk d with reproducing kernels k w 1 w z where n first we consider conjugations on h d of the form a u v f u f v such conjugations are also known as weighted composition conjugations and characterize them into two classes denoted by c 1 and c 2 then we obtain explicit conditions for w when it is c 1 symmetric and c 2 symmetric respectively

fast legendre fenchel transform and applications to hamilton jacobi equations and conservation laws we are interested in the study of a fast algorithm introduced by brenier computing the discrete legendre fenchel transform of a real function we present convergence results and show how the order of convergence grows with the regularity of the function to be transformed applications to hamilton jacobi equations for front propagation problems and conservation laws are presented

viability kernels and capture basins of sets under differential inclusions this paper provides a characterization of viability kernels and capture basins of a target viable in a constrained subset as a unique closed subset between the target and the constrained subset satisfying tangential conditions or by duality normal conditions it is based on a method devised by helene frankowska for characterizing the value function of an optimal control problem as generalized contingent or viscosity solutions to hamilton jacobi equations these abstract results interesting by themselves can be applied to epigraphs of functions or graphs of maps and happen to be very efficient for solving other problems such as stopping time problems dynamical games boundary value problems for systems of partial differential equations and impulse and hybrid control systems which are the topics of other companion papers

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

approximation of complex symmetric operators an operator t on a complex hilbert space mathcal h is called a complex symmetric operator if there exists a conjugate linear isometric involution c mathcal h rightarrow mathcal h so that ctc t in this paper we study the approximation of complex symmetric operators by virtue of an intensive analysis of compact operators in singly generated c algebras we obtain a complete characterization of norm limits of complex symmetric operators and provide a classification of complex symmetric operators up to approximate unitary equivalence this gives a general solution to the norm closure problem for complex symmetric operators as an application we provide a concrete description of partial isometries which are norm limits of complex symmetric operators

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

complex symmetry of invertible composition operators abstract a bounded operator t on a separable hilbert space h is said to be complex symmetric if there exists an orthonormal basis for h with respect to which t has a self transpose matrix representation in this paper we study the complex symmetry of composition operators c f f induced on the hardy space h 2 by holomorphic self maps of the open unit disk d for any holomorphic self map of d we establish that if c is complex symmetric then must fix a point in d thus among the automorphisms of d only the elliptic ones may induce complex symmetric composition operators for an elliptic automorphism we prove that if is not a rotation or of order 3 then c is complex symmetric if and only if z z 1 z for some d 0