isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

additive units of product systems we introduce the notion of additive units or addits of a pointed arveson system and demonstrate their usefulness through several applications by a pointed arveson system we mean a spatial arveson system with a fixed normalised reference unit we show that the addits form a hilbert space whose codimension one subspace of roots is isomorphic to the index space of the arveson system and that the addits generate the type i part of the arveson system consequently the isomorphism class of the hilbert space of addits is independent of the reference unit the addits of a pointed inclusion system are shown to be in natural correspondence with the addits of the generated pointed product system the theory of amalgamated products is developed using addits and roots and an explicit formula for the amalgamation of pointed arveson systems is given providing a new proof of its independence of the particular reference units this independence justifies the terminology spatial product of spatial arveson systems finally a cluster construction for inclusion subsystems of an arveson system is introduced and we demonstrate its correspondence with the action of the cantor bendixson derivative in the context of the random closed set approach to product systems due to tsirelson and liebscher

tensor algebras overc correspondences representations dilations andc envelopes tensor algebras overc correspondences are noncommutative generalizations of the disk algebra they contain as special cases analytic crossed products semi crossed products and popescu s noncommutative disk algebras in this paper a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved these are used to show that for certainc correspondences thec envelopes in the sense of arveson of the tensor algebras are the cuntz pimsner algebras of the correspondences

complements to models for noncommuting operators abstract this paper develops a dilation theory for two noncommutative operators many of the results and techniques in dilation theory for one operator are extended to this setting this is done by extending the schaffer construction for one operator to the fock space setting a new wold decomposition for two isometrics with orthogonal range is obtained this wold decomposition and the schaffer construction is used to extend the sz nagy foias lifting theorem and the characteristic function theory to the noncommutative setting the characteristic function is operator valued and defined in a fock space

explicit simplicial discretization of distributed parameter port hamiltonian systems simplicial dirac structures as finite analogues of the canonical stokes dirac structure capturing the topological laws of the system are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators these finite dimensional dirac structures offer a framework for the formulation of standard input output finite dimensional port hamiltonian systems that emulate the behavior of distributed parameter port hamiltonian systems this paper elaborates on the matrix representations of simplicial dirac structures and the resulting port hamiltonian systems on simplicial manifolds employing these representations we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port hamiltonian systems on simplicial manifolds

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

discrete product systems and twisted crossed products by semigroups a product systemeover a semigrouppis a family of hilbert spaces es s p together with multiplicationses et est we vieweas a unitary valued cocycle onp and consider twisted crossed productsa e pinvolvingeand an action ofpby endomorphisms of ac algebraa whenpis quasi lattice ordered in the sense of nica we isolate a class of covariant representations ofe and consider a twisted crossed productbp e pwhich is universal for covariant representations ofewhenehas finite dimensional fibres and in general is slightly larger in particular whenp nand dim e1 our algebrabn e n is a new infinite analogue of the toeplitz cuntz algebras ton our main theorem is a characterisation of the faithful representations ofbp e p

e0 dilation of strongly commuting cp0 semigroups abstract we prove that every strongly commuting pair of cp 0 semigroups has a minimal e 0 dilation this is achieved in two major steps interesting in themselves 1 we show that a strongly commuting pair of cp 0 semigroups can be represented via a two parameter product system representation 2 we prove that every fully coisometric product system representation has a fully coisometric isometric dilation in particular we obtain that every commuting pair of cp 0 semigroups on b h h finite dimensional has an e 0 dilation

the index of a quantum dynamical semigroup a numerical index is introduced for semigroups of completely positive maps of b h which generalizes the index ofe0 semigroups it is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to ane0 semigroup provided that the dilation isminimal

dirac structures and boundary control systems associated with skew symmetric differential operators associated with a skew symmetric linear operator on the spatial domain a b we define a dirac structure which includes the port variables on the boundary of this spatial domain this dirac structure is a subspace of a hilbert space naturally associated with this dirac structure is an infinite dimensional system we parameterize the boundary port variables for which the c 0 semigroup associated with this system is contractive or unitary furthermore this parameterization is used to split the boundary port variables into inputs and outputs similarly we define a linear port controlled hamiltonian system associated with the previously defined dirac structure and a symmetric positive operator defining the energy of the system we illustrate this theory on the example of the timoshenko beam

weak form of stokes dirac structures and geometric discretization of port hamiltonian systems we present the mixed galerkin discretization of distributed parameter port hamiltonian systems due to the inherent definition of boundary interconnection ports this system representation is particularly useful for the modeling of interconnected multi physics systems and control at the prototypical example of a system of two conservation laws in arbitrary spatial dimension we derive the main contributions i a weak formulation of the underlying geometric stokes dirac structure ii its geometric approximation by a finite dimensional dirac structure using a mixed galerkin approach and power preserving maps on the space of discrete power variables and iii the approximation of the hamiltonian to obtain finite dimensional port hamiltonian state space models the power preserving maps on the discrete bond space offer design degrees of freedom for the discretization which is illustrated at the example whitney finite elements on a 2d simplicial triangulation the resulting schemes can be considered as trade offs between centered approximations and upwinding

on c algebras of irreversible algebraic dynamical systems abstract extending the work of cuntz and vershik we develop a general notion of independence for commuting group endomorphisms based on this concept we initiate the study of irreversible algebraic dynamical systems which can be thought of as irreversible analogues of the dynamical systems considered by schmidt to each irreversible algebraic dynamical system we associate a universal c algebra and show that it is a uct kirchberg algebra under natural assumptions moreover we discuss the structure of the core subalgebra which turns out to be closely related to generalized bunce deddens algebras in the sense of orfanos we also construct discrete product systems of hilbert bimodules for irreversible algebraic dynamical systems which allow us to view the associated c algebras as cuntz nica pimsner algebras besides we prove a decomposition theorem for semigroup crossed products of unital c algebras by semidirect products of discrete left cancellative monoids

operators affiliated to the free shift on the free hardy space abstract the smirnov class for the classical hardy space is the set of ratios of bounded analytic functions in the open complex unit disk with outer denominators this definition extends naturally to the commutative and non commutative multi variable settings of the drury arveson space and the full fock space over c d identifying the fock space with the free multi variable hardy space of non commutative or free holomorphic functions in a non commutative open unit ball in several matrix variables we prove that any closed densely defined operator affiliated to the right free multiplier algebra of the full fock space acts as right multiplication by a non commutative function in the right free smirnov class and analogously replacing right with left

energy based lyapunov functions for forced hamiltonian systems with dissipation in this paper we propose a constructive procedure to modify the hamiltonian function of forced hamiltonian systems with dissipation in order to generate lyapunov functions for nonzero equilibria a key step in the procedure which is motivated from energy balance considerations standard in network modeling of physical systems is to embed the system into a larger hamiltonian system for which a series of casimir functions can be easily constructed interestingly enough for linear systems the resulting lyapunov function is the incremental energy thus our derivations provide a physical explanation to it an easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given some examples that illustrate the method are given

an index theory for quantum dynamical semigroups w arveson showed a way of associating continuous tensor product systems of hilbert spaces with endomorphism semigroups of type i factors we do the same for general quantum dynamical semigroups through a dilation procedure the product system so obtained is the index and its dimension is a numerical invariant for the original semigroup

finitely correlated representations of product systems of c correspondences over nk abstract we study isometric representations of product systems of correspondences over the semigroup n k which are minimal dilations of finite dimensional fully coisometric representations we show the existence of a unique minimal cyclic coinvariant subspace for all such representations the compression of the representation to this subspace is shown to be a complete unitary invariant for a certain class of graph algebras the nonself adjoint wot closed algebra generated by these representations is shown to contain the projection onto the minimal cyclic coinvariant subspace this class includes free semigroup algebras this result extends to a class of higher rank graph algebras which includes higher rank graphs with a single vertex

solving index 1 daes in matlab and simulink this paper describes mathematical and software developments needed for the effective solution of differential algebraic equations of index 1 in the integrated computing environment matlab and the dynamic simulation package simulink the developments are applicable to other problem solving environments and some are applicable to general scientific computation

models for noncommuting operators abstract this paper develops a model theory for a pair of noncommuting operators using backward shift operators on a fock space rota s theorem is generalized i e it is shown that any two bounded operators on a hilbert space are simultaneously similar to part of a pair of backward shift operators on a fock space these shift operators and the fock space framework are also used to develop a dilation theory for two noncommuting operators

simulating ising spin glasses on a quantum computer a linear time algorithm is presented for the construction of the gibbs distribution of configurations in the ising model on a quantum computer the algorithm is designed so that each run provides one configuration with a quantum probability equal to the corresponding thermodynamic weight the partition function is thus approximated efficiently the algorithm neither suffers from critical slowing down nor gets stuck in local minima the algorithm can be applied in any dimension to a class of spin glass ising models with a finite portion of frustrated plaquettes diluted ising models and models with a magnetic field

dilations wandering subspaces and inner functions the objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on hilbert spaces it is shown that for a large class of analytic functional hilbert spaces h k on the unit ball in c n wandering subspaces for restrictions of the multiplication tuple m z m z1 m zn can be described in terms of suitable h k inner functions we prove that h k inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi homogeneous polynomials as an application along the way we prove a refinement of a result of arveson on the uniqueness of minimal dilations of pure row contractions c 2017 elsevier inc all rights reserved

dirac structures on hilbert spaces and boundary control of distributed port hamiltonian systems abstract aim of this paper is to show how the dirac structure properties can be exploited in the development of energy based boundary control laws for distributed port hamiltonian systems usually stabilization of non zero equilibria has been achieved by looking at or generating a set of structural invariants namely casimir functions in closed loop since this approach fails when an infinite amount of energy is required at the equilibrium dissipation obstacle this paper illustrates a novel approach that enlarges the class of stabilizing controllers the starting point is the parametrization of the dynamics provided by the image representation of the dirac structure that is able to show the effects of the boundary inputs on the state evolution in this way energy balancing and control by state modulated source methodologies are extended to the distributed parameter scenario and a geometric interpretation of these control techniques is provided the theoretical results are discussed with the help of a simple but illustrative example i e a transmission line with an rlc load in both serial and parallel configurations in the latter case energy balancing controllers are not able to stabilize non zero equilibria because of the dissipation obstacle the problem is solved thanks to a boundary state modulated source

operator algebras and subproduct systems arising from stochastic matrices we study subproduct systems in the sense of shalit and solel arising from stochastic matrices on countable state spaces and their associated operator algebras we focus on the non self adjoint tensor algebra and viselter s generalization of the cuntz pimsner c algebra to the context of subproduct systems suppose that x and y are arveson stinespring subproduct systems associated to two stochastic matrices over a countable set and let t x and t y be their tensor algebras we show that every algebraic isomorphism from t x onto t y is automatically bounded furthermore t x and t y are isometrically isomorphic if and only if x and y are unitarily isomorphic up to a automorphism of l when is finite we prove that t x and t y are algebraically isomorphic if and only if there exists a similarity between x and y up to a automorphism of l moreover we provide an explicit description of the cuntz pimsner algebra o x in the case where is finite and the stochastic matrix is essential

on representations and integrability of mathematical structures in energy conserving physical systems in the present paper we elaborate on the underlying hamiltonian structure of interconnected energy conserving physical systems it is shown that a power conserving interconnection of port controlled generalized hamiltonian systems leads to an implicit generalized hamiltonian system and a power conserving partial interconnection to an implicit port controlled hamiltonian system the crucial concept is the notion of a generalized dirac structure defined on the space of energy variables or on the product of the space of energy variables and the space of flow variables in the port controlled case three natural representations of generalized dirac structures are treated necessary and sufficient conditions for closedness or integrability of dirac structures in all three representations are obtained the theory is applied to implicit port controlled generalized hamiltonian systems and it is shown that the closedness condition for the dirac structure leads to strong conditions on the input vector fields

absolutely continuous representations and a kaplansky density theorem for free semigroup algebras we introduce notions of absolutely continuous functionals and representations on the non commutative disk algebra an absolutely continuous functionals are used to help identify the type l part of the free semigroup algebra associated to a extendible representation a extendible representation of an is regular if the absolutely continuous part coincides with the type l part all known examples are regular absolutely continuous functionals are intimately related to maps which intertwine a given extendible representation with the left regular representation a simple application of these ideas extends reflexivity and hyper reflexivity results moreover the use of absolute continuity is a crucial device for establishing a density theorem which states that the unit ball of an is weak dense in the unit ball of the associated free semigroup algebra if and only if is regular we provide some explicit constructions related to the density theorem for specific representations a notion of singular functionals is also defined and every functional decomposes in a canonical way into the sum of its absolutely continuous and singular parts

representations of product systems over semigroups and dilations of commuting cp maps we prove that every pair of commuting cp maps on a von neumann algebra m can be dilated to a commuting pair of endomorphisms on a larger von neumann algebra to achieve this we first prove that every completely contractive representation of a product system of c correspondences over the semigroup n2 can be dilated to an isometric or toeplitz representation

achievable casimirs and its implications on control of port hamiltonian systems in this paper we extend results on interconnections of port hamiltonian systems to infinite dimensional port hamiltonian systems and to mixed finite and infinite dimensional port hamiltonian systems the problem of achievable dirac structures is now studied for systems with dissipation in the finite dimensional infinite dimensional and the mixed finite and infinite dimensional case we also characterize the set of achievable casimirs and study its application for the control of port hamiltonian systems

renormalization group approach to exact sampling in this letter we use a general renormalization group algorithm to implement propp and wilson s coupling from the past approach to complex physical systems our algorithm follows the evolution of the entire configuration space under the markov chain monte carlo dynamics from parts of the configurations patches on increasing length scales and it allows us to generate exact samples of the boltzmann distribution which are rigorously proven to be uncorrelated with the initial condition we validate our approach in the two dimensional ising spin glass on lattices of size 64 ifmmode times else texttimes fi 64

operator algebras of monomial ideals in noncommuting variables abstract we study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables through the apparatus of subproduct systems and c correspondences we provide a full comparison amongst the related operator algebras for our analysis we isolate a partially defined dynamical system to which we refer as the quantised dynamics of the monomial ideal in addition we revisit several previously considered constructions these include matsumoto s subshift c algebras as well as the tensor and the pimsner algebras associated with dynamical systems or graphs we sort out the various relations by giving concrete conditions and counterexamples that orientate the operator algebras of our context it appears that the boundary c algebras do not arise as the quotient with the compact operators unconditionally we establish a dichotomy to this effect by examining the resulting tensor algebras we identify their boundary representations we analyse their c envelopes and we give criteria for hyperrigidity moreover we completely classify them in terms of the data provided by the monomial ideals for tensor algebras of c correspondences and bounded isomorphisms this is achieved up to the level of local conjugacy in the sense of davidson and roydor for the quantised dynamics for tensor algebras of subproduct systems and algebraic isomorphisms this is achieved up to the level of equality of monomial ideals modulo permutations of the variables in the process we accomplish more in different directions most notably we show that tensor algebras form a complete invariant for isomorphic resp similar subproduct systems of homogeneous ideals up to isometric resp bounded isomorphisms the results on local conjugacy are obtained via an alternative proof of the breakthrough result of davidson and katsoulis on piecewise conjugate systems for our purposes we use appropriate compressions of the fock representation we then apply this alternative proof locally for the partially defined quantised dynamics in this way we avoid the topological graphs machinery and pave the way for further applications these include operator algebras of dynamical systems over commuting contractions or over row commuting contractions

modeling and control of the timoshenko beam the distributed port hamiltonian approach the purpose of this paper is to show how the timoshenko beam can be fruitfully described within the framework of distributed port hamiltonian dph systems so that rather simple and elegant considerations can be drawn regarding both the modeling and control of this mechanical system after the dph model of the beam is introduced the control problem is discussed in particular it is shown how control approaches already presented in the literature can be unified and a new control methodology is presented and discussed this control methodology relies on the generalization to infinite dimensions of the concept of structural invariant casimir function and on the extension to distributed systems of the so called control by interconnection methodology in this way finite dimensional passive controllers can stabilize distributed parameter systems by shaping their total energy i e by assigning a new minimum in the desired equilibrium configuration that can be reached if a dissipative effect is introduced

on the product system of a completely positive semigroup abstract given a w continuous semigroup of unital normal completely positive maps of b h we introduce its continuous tensor product system e if is a minimal dilation e 0 semigroup of with arveson product system f then e is canonically isomorphic to f we apply this construction to a class of semigroups of b l 2 r arising from a modified weyl moyal quantization of convolution semigroups of borel probability measures on r 2 this class includes the heat flow on the ccr algebra studied recently by arveson we prove that the minimal dilations of all such semigroups are completely spatial and additionally we prove that the minimal dilation of the heat flow is cocyle conjugate to the car ccr flow of index two

dilating covariant representations of the non commutative disc algebras let be an isometric automorphism of the non commutative disc algebra an for n 2 we show that every contractive covariant representation of an dilates to a unitary covariant representation of on hence the c envelope of the semicrossed product an z is on z

hardy algebras w correspondences and interpolation theory given a von neumann algebra m and a w correspondence e over m we construct an algebra h e that we call the hardy algebra of e when m open image in new window e h e is the classical hardy space h open image in new window of bounded analytic functions on the unit disc when m open image in new window and e open image in new window h e is the free semigroup algebra studied by popescu davidson and pitts and many others we show that given any faithful normal representation of m on a hilbert space h there is a natural correspondence e over the commutant m called the dual of e and that h e can be realized in terms of b h valued functions on the open unit ball open image in new window e in the space of adjoints of elements in e we prove analogues of the nevanlinna pick theorem in this setting and discover other aspects of the value distribution theory for elements in h e we also analyze the boundary behavior of elements in h e and obtain generalizations of the sz nagy foias functional calculus and the functional calculus of popescu for c n c row contractions the correspondence e has a dual that is naturally isomorphic to e and the commutants of certain so called induced representations of h e can be viewed as induced representations of h e for these induced representations a double commutant theorem is proved

energy shaping of distributed parameter port hamiltonian systems based on finite element approximation the main contribution of this paper is a procedure for the control by energy shaping via casimir generation of infinite dimensional port hamiltonian systems based on a particular finite element approximation the proposed approach is justified by the fact that the adopted spatial discretization technique is able to preserve casimir functions in the closed loop system when going from the distributed to the approximated lumped parameter system besides the intrinsic difficulties related to the large number of state variables the finite element model is generally given in terms of a dirac structure and is completely a causal which implies that the plant dynamics is not given in standard input state output form but as a set of daes consequently the classical energy casimir method has to be extended in order to deal with dynamical systems with constraints usually appearing in the form of lagrangian multipliers the general methodology is illustrated with the help of an example in which the distributed parameter system is a lossless transmission line

quantum algorithm for exact monte carlo sampling we build a quantum algorithm which uses the grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems the algorithm is based on recently developed exact monte carlo sampling methods and yields a polynomial gain compared to classical procedures

quantum speedup of monte carlo methods monte carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically one important example is the use in statistical physics of rapidly mixing markov chains to approximately compute partition functions in this work we describe a quantum algorithm which can accelerate monte carlo methods in a very general setting the algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance achieving a near quadratic speedup over the best possible classical algorithm combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions which use multiple stage markov chain monte carlo techniques the quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently

operator algebras associated with unitary commutation relations abstract we define nonselfadjoint operator algebras with generators l e 1 l e n l f 1 l f m subject to the unitary commutation relations of the form l e i l f j k l u i j k l l f l l e k where u u i j k l is an n m n m unitary matrix these algebras which generalise the analytic toeplitz algebras of rank 2 graphs with a single vertex are classified up to isometric isomorphism in terms of the matrix u

characteristic function for polynomially contractive commuting tuples abstract in this note we develop the theory of characteristic function as an invariant for n tuples of operators the operator tuple has a certain contractivity condition put on it this condition and the class of domains in c n that we consider are intimately related a typical example of such a domain is the open euclidean unit ball given a polynomial p in c z 1 z 2 z n whose constant term is zero all the coefficients are nonnegative and the coefficients of the linear terms are nonzero one can naturally associate a reinhardt domain with it which we call the p ball definition 1 1 using the reproducing kernel hilbert space h p c associated with this reinhardt domain in c n s pott constructed the dilation for a polynomially contractive commuting tuple definition 1 2 s pott standard models under polynomial positivity conditions j operator theory 41 1999 365 389 mr 2000j 47019 given any polynomially contractive commuting tuple t we define its characteristic function t which is a multiplier we construct a functional model using the characteristic function exploiting the model we show that the characteristic function is a complete unitary invariant when the tuple is pure the characteristic function gives newer and simpler proofs of a couple of known results one of them is the invariance of the curvature invariant and the other is a beurling theorem for the canonical operator tuple on h p c it is natural to study the boundary behaviour of t in the case when the domain is the euclidean unit ball we do that and here essential differences with the single operator situation are brought out

hamiltonian discretization of boundary control systems a fundamental problem in the simulation and control of complex physical systems containing distributed parameter components concerns finite dimensional approximation numerical methods for partial differential equations pdes usually assume the boundary conditions to be given while more often than not the interaction of the distributed parameter components with the other components takes place precisely via the boundary on the other hand finite dimensional approximation methods for infinite dimensional input output systems e g in semi group format are not easily relatable to numerical techniques for solving pdes and are mainly confined to linear pdes in this paper we take a new view on this problem by proposing a method for spatial discretization of boundary control systems based on a particular type of mixed finite elements resulting in a finite dimensional input output system the approach is based on formulating the distributed parameter component as an infinite dimensional port hamiltonian system and exploiting the geometric structure of this representation for the choice of appropriate mixed finite elements the spatially discretized system is again a port hamiltonian system which can be treated as an approximating lumped parameter physical system of the same type in the current paper this program is carried out for the case of an ideal transmission line described by the telegrapher s equations and for the two dimensional wave equation

local unitary cocycles of e0 semigroups abstract this paper concerns the structure of the group of local unitary cocycles also called the gauge group of an e 0 semigroup the gauge group of a spatial e 0 semigroup has a natural action on the set of units by operator multiplication arveson has characterized completely the gauge group of e 0 semigroups of type i and as a consequence it is known that in this case the gauge group action is transitive in fact if the semigroup has index k then the gauge group action is transitive on the set of k 1 tuples of appropriately normalized independent units an action of the gauge group having this property is called k 1 fold transitive we construct examples of e 0 semigroups of type ii and index 1 which are not 2 fold transitive these new examples also illustrate that an e 0 semigroup of type ii k need not be a tensor product of an e 0 semigroup of type ii 0 and another of type i k

on the exact evaluation of certain instances of the potts partition function by quantum computers we present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti ferromagnetic q state potts partition function z for a family of graphs related to irreducible cyclic codes this problem is related to the evaluation of the jones and tutte polynomials we consider the connection between the weight enumerator polynomial from coding theory and z and exploit the fact that there exists a quantum algorithm for efficiently estimating gauss sums in order to obtain the weight enumerator for a certain class of linear codes in this way we demonstrate that for a certain class of sparse graphs which we call irreducible cyclic cocycle code iccce graphs quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph and an exponential speed up in q over the best classical algorithms known to date

control by interconnection of mixed port hamiltonian systems in this note the regulation problem for mixed finite and infinite dimensional port hamiltonian systems m ph systems is discussed a m ph system results from the power conserving interconnection of finite and infinite dimensional systems in port hamiltonian form in particular the system given by the interconnection of two finite dimensional systems one of which is the controller by means of an infinite dimensional connection is studied the proposed control methodology is a generalization to the infinite dimensional case of a well established passivity based control technique for finite dimensional port hamiltonian systems the control by interconnection and energy shaping according to which the open loop energy function is shaped so that a minimum in the desired configuration is introduced this procedure is possible once the state variable of the controller is related to the state variable of the plant by constraining the state of the closed loop system on a structural invariant defined by a set of casimir functions in this way the energy function of the controller which is freely assignable becomes a function of the configuration of the plant and then it can be easily shaped in order to solve the regulation problem

poisson transforms on some c algebras generated by isometries abstract a noncommutative poisson transform associated to a certain class of sequences of operators on hilbert spaces with property p is defined on some universal c algebras resp nonselfadjoint algebras generated by isometries its properties are described and used to study these universal algebras and their representations as consequences we obtain a functional calculus isometric resp unitary dilations and commutant lifting theorem for the class of sequences of operators with property p our geometrical approach leads also to new and elementary proofs as well as extensions of some classical results

the spatial product of arveson systems is intrinsic abstract we prove that the spatial product of two spatial arveson systems is independent of the choice of the reference units this also answers the same question for the minimal dilation of the powers sum of two spatial cp semigroups it is independent up to cocycle conjugacy

discrete product systems and their c algebras continuous product systems or product systems over r were recently introduced by arveson to develope an index theory for continuous semigroups of endomorphisms of b h in this paper we continue his work by studying discrete product systems or product systems over g where g is a countable dense subgroup of r we give examples of discrete product systems and compute their automorphism groups to each discrete product system e over g we associate a separable c algebra oe g whose non degenerate representations correspond bijectively to representations of e this family of c algebras may be regarded as analogues of cuntz algebras or car algebras in some degenerate cases these c algebras are the generalized toeplitz algebras we show that oe g is simple and study its gauge automorphisms quasi free automorphisms and fock state