composition operators on noncommutative hardy spaces abstract in this paper we initiate the study of composition operators on the noncommutative hardy space h ball 2 which is the hilbert space of all free holomorphic functions of the form f x 1 x n k 0 k a x f n a 2 1 where the convergence is in the operator norm topology for all x 1 x n in the noncommutative operatorial ball b h n 1 and b h is the algebra of all bounded linear operators on a hilbert space h when the symbol is a free holomorphic self map of b h n 1 we show that the composition operator c f f f h ball 2 is bounded on h ball 2 several classical results about composition operators boundedness norm estimates spectral properties compactness similarity have free analogues in our noncommutative multivariable setting the most prominent feature of this paper is the interaction between the noncommutative analytic function theory in the unit ball of b h n the operator algebras generated by the left creation operators on the full fock space with n generators and the classical complex function theory in the unit ball of c n in a more general setting we establish basic properties concerning the composition operators acting on fock spaces associated with noncommutative varieties v p 0 h b h n 1 generated by sets p 0 of noncommutative polynomials in n indeterminates such that p 0 0 p p 0 in particular when p 0 consists of the commutators x i x j x j x i for i j 1 n we show that many of our results have commutative counterparts for composition operators on the symmetric fock space and consequently on spaces of analytic functions in the unit ball of c n

a hybrid approach based on pso and hadamard difference sets for the synthesis of square thinned arrays a hybrid approach for the synthesis of planar thinned antenna arrays is presented the proposed solution exploits and combines the most attractive features of a particle swarm algorithm and those of a combinatorial method based on the noncyclic difference sets of hadamard type numerical experiments validate the proposed solution showing improvements with respect to previous results

many to one stable matching geometry and fairness baiou and balinski characterized the stable admissions polytope using a system of linear inequalities the structure of feasible solutions to this system of inequalities fractional stable matchings is the focus of this paper the main result associates a geometric structure with each fractional stable matching this insight appears to be interesting in its own right and can be viewed as a generalization of the lattice structure for integral stable matchings to fractional stable matchings in addition to obtaining simple proofs of many known results the geometric structure is used to prove the following two results first it is shown that assigning each agent their median choice among all stable partners results in a stable matching which can be viewed as a fair compromise second sufficient conditions are identified under which stable matchings exist in a problem with externalities in particular in the stable matching problem with couples

stable matchings optimal assignments and linear programming vande vate 1989 described the polytope whose extreme points are the stable core matchings in the marriage problem rothblum 1989 simplified and extended this result this paper explores a corresponding linear program its dual and consequences of the fact that the dual solutions have an unusually direct relation to the primal solutions this close relationship allows us to provide simple proofs both of vande vate and rothblum s results and of other important results about the core of marriage markets these proofs help explain the structure shared by the marriage problem without sidepayments and the assignment game with sidepayments the paper further explores fractional matchings which may be interpreted as lotteries over possible matches or as time sharing arrangements we show that those fractional matchings in the stable marriage polytope form a lattice with respect to a partial ordering that involves stochastic dominance thus all expected utility functions corresponding to the same ordinal preferences will agree on the relevant comparisons finally we provide linear programming proofs of slightly stronger versions of known incentive compatibility results

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

characterization of stable matchings as extreme points of a polytope the purpose of this paper is to extend a modified version of a recent result of vande vate 1989 which characterizes stable matchings as the extreme points of a certain polytope our proofs are simpler and more transparent than those of vande vate

linear fractional maps of the unit ball a geometric study abstract we classify up to conjugation with automorphisms the linear fractional self maps of the unit ball of c n n 1 then we give some applications of these normal forms to the study of composition operators

blockers and antiblockers of stable matchings an implicit linear description of the stable matching polytope is provided in terms of the blocker and antiblocker sets of constraints of the matroid kernel polytope the explicit identification of both these sets is based on a partition of the stable pairs in which each agent participates here we expose the relation of such a partition to rotations we provide a time optimal algorithm for obtaining such a partition and establish some new related results most importantly that this partition is unique

the stable allocation or ordinal transportation problem the stable allocation problem generalizes the 0 1 stable matching problems one to one one to many and many to many to the allocation of real valued hours or quantities a strongly polynomial algorithm proves the existence of stable allocations the set of stable allocations is shown to be a distributive lattice in general but in the nondegenerate case it is a complete linear order indeed in the generic case when a problem is strongly nondegenerate there exists a single stable allocation a simple algorithm finds row optimal and column optimal stable allocations given any stable allocation when a problem is nondegenerate it finds all stable allocations

hypercyclic and cyclic vectors abstract let x denote an arbitrary separable banach space over the field of complex numbers and b x the banach algebra of all bounded linear operators on x we prove the following results 1 an element of the space x is hypercyclic supercyclic for all positive powers tn of an operator t in b x if it is hypercyclic supercyclic for t 2 under some condition on the spectrum of the adjoint of a cyclic operator the set of all cyclic vectors of the operator is dense this result extends to any cyclic commutative subset of b x 3 under a mild condition on the spectrum of a cyclic operator t the set of all separating vectors for the commutant t of t is dense this also extends to any cyclic commutative subset of b x 4 a slightly stronger version of a theorem of k f clancey and d d rogers on cyclic vectors finally we define and discuss hereditarily hypercyclic operators

classification of semigroups of linear fractional maps in the unit ball we give a complete classiflcation up to conjugation of continuous semigroups of linear fractional self maps of the unit ball

inner functions and cyclic composition operators on h2 bn abstract the present paper shows that the algebra c generated by c aut bn is cyclic on h2 bn and any nonconstant function f h2 bn is a cyclic vector of c in addition the hypercyclic and cyclic composition operators will be discussed

the role of the angle in supercyclic behavior abstract a bounded operator t acting on a hilbert space h is said to be supercyclic if there is a vector f h such that the projective orbit t n f n 0 and c is dense in h we use a new method based on a very simple geometric idea that allows us to decide whether an operator is supercyclic or not the method is applied to obtain the following result a composition operator acting on the hardy space whose inducing symbol is a parabolic linear fractional map of the disk onto a proper subdisk is not supercyclic this result finishes the characterization of the supercyclic behavior of composition operators induced by linear fractional maps and thus completes previous work of bourdon and shapiro

of stable marriages and graphs and strategy and polytopes this expository paper develops the principal known results and some new ones on the stable matchings of marriage games in the language of directed graphs this both unifies and simplifies the presentation and renders it more symmetric in addition it yields a new algorithm and a new proof for the existence of stable matchings new proofs for many known facts and some new results notably concerning players strategies and the properties of the stable matching polytope

hypercyclic operators are subspace hypercyclic abstract in this short note we prove that for a dense set a x x is a banach space there is a non trivial closed subspace m x such that a m is dense in m we use this result to answer a question posed in madore and martinez avendano 2011 9 in particular we show that every hypercyclic operator is subspace hypercyclic

parabolic composition operators on the ball abstract we give a classification up to automorphisms of parabolic linear fractional maps of the ball we then show that this classification is very convenient to study the geometric properties of these maps as well as the associated composition operators

hypercyclic tuples of operators and somewhere dense orbits in this paper we prove that there are hypercyclic n 1 tuples of diagonal matrices on cn and that there are no hypercyclic n tuples of diagonalizable matrices on cn we use the last result to show that there are no hypercyclic subnormal tuples in infinite dimensions we then show that on real hilbert spaces there are tuples with somewhere dense orbits that are not dense but we also give sufficient conditions on a tuple to insure that a somewhere dense orbit on a real or complex space must be dense

cyclic behavior of linear fractional composition operators in the unit ball of c n we characterize the cyclicity and hypercyclicity of composition operators induced by linear fractional self maps of b n on the hardy space h 2 b n based on the classification of linear fractional maps given by bisi and bracci c 2007 elsevier inc all rights reserved

a class of linear fractional maps of the ball and their composition operators abstract we study a class of linear fractional self maps of the ball which seems to be a good generalization of parabolic non automorphisms of the unit disk we give a normal form of these maps and use it to compute the spectrum of the composition operators induced by them we also show that these composition operators are never hypercyclic applications are given to the study of more general linear fractional transformations

self adjoint unitary and normal weighted composition operators in several variables abstract we study weighted composition operators on hilbert spaces of analytic functions on the unit ball with kernels of the form 1 z w for 0 we find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator we then obtain characterizations of self adjoint and unitary weighted composition operators normality of these operators is also investigated

linear structure of hypercyclic vectors abstract a vector x in a banach space b is called hypercyclic for a bounded linear operator t b b if the orbit t n x n 1 is dense in b our main result states that if t is a compact perturbation of an operator of norm 1 and satisfies an appropiate extra hypothesis then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t in particular the result applies to compact perturbations of the identity we also include applications to some weighted backward shifts and compact perturbations of the identity by weighted backward shifts this last result in combination with a recent one that states that every banach space admits an operator with a hypercyclic vector proves that in all banach space there is an operator t with an infinite dimensional closed subspace consisting except for zero of hypercyclic vectors the main result also applies to the differentiation operator and the translation operator t f z f z 1 on certain hilbert spaces consisting of entire functions

operators with the specification property abstract we study a version of the specification property for linear dynamics operators having the specification property are investigated and relationships with other well known dynamical notions such as mixing devaney chaos and frequent hypercyclicity are obtained

valiron s theorem in the unit ball and spectra of composition operators abstract we prove a version of valiron s conjugacy theorem for schur class mappings of the unit ball of c n as an application we obtain a formula for the spectral radius of composition operators on the ball with schur class symbols

the stable admissions polytope the stable admissions polytope the convex hull of the stable assignments of the university admissions problem is described by a set of linear inequalities it depends on a new characterization of stability and arguments that exploit and extend a graphical approach that has been fruitful in the analysis of the stable marriage problem

some characterizations for composition operators on the fock spaces abstract we study composition operators on the fock spaces f 2 c n for 0 problems considered including the essential norm normality spectra cyclicity and membership in the schatten classes we give perfect characterizations for these basic properties which are different with those composition operators on the hardy space and the weighted bergman spaces

erratum the stable allocation or ordinal transportation problem an incorrect version of this paper was printed in mathematics of operations research vol 27 no 3 august 2002 pp 485 503 the paper is reprinted correctly below the stable allocation problem generalizes the 0 1 stable matching problems one to one one to many and many to many to the allocation of real valued hours or quantities a strongly polynomial algorithm proves the existence of stable allocations the set of stable allocations is shown to be a distributive lattice in general but in the nondegenerate case it is a complete linear order indeed in the generic case when a problem is strongly nondegenerate there exists a single stable allocation a simple algorithm finds row optimal and column optimal stable allocations given any stable allocation when a problem is nondegenerate it finds all stable allocations

hyperbolic composition operators on the ball we give a classification up to automorphisms of hyperbolic linear fractional maps of the ball we then show that this classification is very convenient to study the geometric properties of these maps as well as the spectrum and the dynamics of the associated composition operators we conclude by showing how these properties can be tranfered to composition operators associated to hyperbolic self maps of the ball which are not linearfractional maps

synthesis of thinned planar circular and square arrays using density tapering two new hybrid density taper methods for designing thinned planar arrays are presented both methods make use of a model taper to allocate for a number of rings across the array aperture the amount of turned on elements per ring one method applies a modified version of the iterative fourier transform ift method to find the optimum turned on element distribution for each ring to get a prescribed low sidelobe level the second method gets suitable turned on element locations by distributing these elements in a uniform random way over each ring the purpose of the second method is to find the optimum model taper since it is computational faster than the first method using the model taper determined by the second method the first method finds then the optimum locations of the turned on element positions both new methods can deal with the synthesis of thinned planar arrays of any size any aperture shape and any degree of thinning a wide range of numerical examples covering very small up to extremely large arrays will demonstrate the effectiveness of the two proposed methods for both circular and square aperture shapes

large planar array thinning using iterative fft techniques a new approach for the synthesis of thinned periodic planar arrays featuring a minimum sidelobe level is presented the method is based on the iterative fourier technique to derive the array element excitations from the prescribed array factor using successive forward and backward fourier transforms array thinning is accomplished by setting the amplitudes of a predetermined number of largest element excitations to unity and the others to zero during each iteration cycle basically it is the same method successfully applied earlier to the thinning of periodic linear arrays the effectiveness of the iterative fourier technique for thinning periodic planar arrays will be demonstrated for a number of large arrays 1500 element positions with a circular aperture using various degree of thinning

simultaneous models for commuting holomorphic self maps of the ball abstract we prove that a finite family of commuting holomorphic self maps of the unit ball b q c q admits a simultaneous holomorphic conjugacy to a family of commuting automorphisms of a possibly lower dimensional ball and that such conjugacy satisfies a universal property as an application we describe when a hyperbolic and a parabolic holomorphic self map of b q can commute

norms and spectral radii of linear fractional composition operators on the ball abstract we give a new proof that every linear fractional map of the unit ball induces a bounded composition operator on the standard scale of hilbert function spaces on the ball and obtain new norm bounds analogous to the standard one variable estimates we also show that cowen s one variable spectral radius formula extends to these operators the key observation underlying these results is that every linear fractional map of the ball belongs to the schur agler class

non sequential weak supercyclicity and hypercyclicity abstract a bounded linear operator t acting on a banach space b is called weakly hypercyclic if there exists x b such that the orbit t n x n 0 1 is weakly dense in b and t is called weakly supercyclic if there is x b for which the projective orbit t n x c n 0 1 is weakly dense in b if weak density is replaced by weak sequential density then t is said to be weakly sequentially hypercyclic or supercyclic respectively it is shown that on a separable hilbert space there are weakly supercyclic operators which are not weakly sequentially supercyclic this is achieved by constructing a borel probability measure on the unit circle for which the fourier coefficients vanish at infinity and the multiplication operator m f z z f z acting on l 2 is weakly supercyclic it is not weakly sequentially supercyclic since the projective orbit under m of each element in l 2 is weakly sequentially closed this answers a question posed by bayart and matheron it is proved that the bilateral shift on l p z 1 p is weakly supercyclic if and only if 2 p and that any weakly supercyclic weighted bilateral shift on l p z for 1 p 2 is norm supercyclic it is also shown that any weakly hypercyclic weighted bilateral shift on l p z for 1 p 2 is norm hypercyclic which answers a question of chan and sanders

hypercyclic algebras for convolution and composition operators abstract we provide an alternative proof to those by shkarin and by bayart and matheron that the operator d of complex differentiation supports a hypercyclic algebra on the space of entire functions in particular we obtain hypercyclic algebras for many convolution operators not induced by polynomials such as cos d d e d or e d a i where 0 a 1 in contrast weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras