limits of hypercyclic and supercyclic operators abstract an operator t on a complex separable infinite dimensional hilbert space h is hypercyclic if there is a vector y in h such that the orbit y ty t2y is dense in h it is shown that if t is hypercyclic then t does not have any eigenvalue and that the union of the spectrum of t and the unit circle is a connected set this result is used to obtain a spectral characterization of the norm closure of the class hc h of all hypercyclic operators acting on h as well as a formula for the distance from a given operator to hc h analogous results are obtained for the closely related class sc h of all supercyclic operators this paper includes some information about the structure of the set of all hypercyclic supercyclic vectors of a given hypercyclic supercyclic resp operator t

almost perfect polyphase sequences with small phase alphabet new classes of polyphase sequences with small phase alphabets of size k are presented these almost perfect sequences of length n have a vanishing periodic autocorrelation function spl theta spl tau for all spl tau spl ne 0 mod n k the sequences are derived from q ary m sequences by a k valued character operation

mean ergodic composition operators on banach spaces of holomorphic functions abstract given a symbol i e a holomorphic endomorphism of the unit disc we consider the composition operator c f f defined on the banach spaces of holomorphic functions a d and h d we obtain different conditions on the symbol which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces these conditions are related to the asymptotic behavior of the iterates of the symbol finally we deal with some particular case in the setting of weighted banach spaces of holomorphic functions

binary and quadriphase sequences with optimal autocorrelation properties a survey time discrete signals with good autocorrelation properties are used in various applications in communications engineering from an implementation point of view usually sequences with a small phase alphabet and a maximal energy efficiency i e a uniform envelope are most favorable for this reason known methods as well as several new construction techniques of binary and quadriphase sequences with optimal or best known autocorrelation properties are discussed in this correspondence in many cases the achievable correlation properties can be improved significantly if a single zero element per sequence is accepted these almost binary and almost quadriphase sequences are considered as well the optimality criteria used include the maximum absolute sidelobe and the merit factor of the periodic and the odd periodic autocorrelation function respectively for sequence lengths of up to 44 in the binary case and up to 32 in the quadriphase case the best known parameters obtained by computer search are compared with the constructed results

on universal subsets of banach spaces we prove that to most of the known hypercyclic operators a on separable banach spaces there exist compact compact convex compact connected subsets k of e such that each compact compact convex compact connected subset of e can be approximated with respect to hausdorff s distance by a n k for suitable n in mathbb n

hypercyclic weighted shifts an operator t acting on a hilbert space is hypercyclic if for some vector x in the space the orbit tnx n 0 is dense in this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic as a consequence we show within the class of weighted shifts that multi hypercyclic shifts and direct sums of fixed hypercyclic shifts are both hypercyclic for general hypercyclic operators the corresponding questions were posed by d a herrero and they still remain open using a different technique we prove that i t is hypercycic whenever t is a unilateral backward weighted shift thus answering in more generality a question recently posed by k c chan and j h shapiro

integrability of lie brackets in this paper we present the solution to a longstanding problem of differential geometry lie s third theorem for lie algebroids we show that the integrability problem is controlled by two computable obstructions as applications we derive explain and improve the known integrability results we establish integrability by local lie groupoids we clarify the smoothness of the poisson sigma model for poisson manifolds and we describe other geometrical applications

existence and nonexistence of almost perfect autocorrelation sequences shows that almost perfect autocorrelation sequences are the same as certain cyclic divisible difference sets the authors apply known theorems on divisible difference sets to simplify and strengthen results by j wolfmann 1992 in particular they answer two questions which were posed by wolfman

ds cdma signature sequences based on pr qmf banks in this paper we propose two classes of multivalued signature sequences for direct sequence code division multiple access ds cdma systems the proposed classes are obtained from the coefficients of the subbands of perfect reconstruction quadrature mirror filterbanks pr qmf the first and second classes are derived from the tree and lattice structure pr qmf banks respectively and they both have perfect correlation properties for synchronous ds cdma systems the second class in addition has generally better correlation properties than other well known sequences in asynchronous ds cdma systems some numerical results for the performance of the asynchronous ds cdma systems with several sequences including the second class of sequences are obtained

semi fredholm theory hypercyclic and supercyclic subspaces a vector x in a banach space cal b is called hypercyclic for a bounded linear operator t cal b rightarrow cal b if the orbit t n x n geq 1 is dense in cal b we prove that if t is hereditarily hypercyclic and its essential spectrum meets the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is also true even if t is not hereditarily hypercyclic in this way we improve and extend to banach spaces a recent result for hilbert spaces we also investigate the corresponding problem for supercyclic operators in this case we obtain a description of the norm closure of the class of all supercyclic operators that have an infinite dimensional closed subspace of hypercyclic vectors moreover for certain kinds of supercyclic operators we can characterize when they have an infinite dimensional closed subspace of supercyclic vectors 1991 mathematics subject classification 47b38 47b99

hypercyclic operators that commute with the bergman backward shift the backward shift b on the bergman space of the unit disc is known to be hypercyclic meaning it has a dense orbit here we ask which operators that commute with b inherit its hypercyclicity we show that the problem reduces to the study of operators of the form 9p b where so is a holomorphic self map of the unit disc that multiplies the dirichlet space into itself and that the question of hypercyclicity for such an operator depends on how freely 9p z is allowed to approach the unit circle as lz s 1

hereditarily hypercyclic operators abstract we show that a continuous linear operator t on a frechet space satisfies the so called hypercyclicity criterion if and only if it is hereditarily hypercyclic and if and only if the direct sum t t is hypercyclic in particular hypercyclic operators with either a dense generalized kernel or a dense set of periodic points i e chaotic in the sense of r l devaney 1989 an introduction to chaotic dynamical systems addison wesley reading ma must satisfy the criterion finally we provide a characterization of those weighted shifts t that are hereditarily hyper cyclic with respect to a given sequence n k of positive integers as well as conditions under which t and t n k k 1 share the same set of hypercyclic vectors

almost perfect quadriphase sequences a new class of quadriphase sequences of length n p sup j 1 spl equiv 2 mod 4 p odd prime j 1 2 is presented these almost perfect sequences have a periodic autocorrelation function spl theta spl tau which vanishes for all spl tau spl ne 0mod n 2

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

cyclicity of bicyclic operators and completeness of translates we study cyclicity of operators on a separable banach space which admit a bicyclic vector such that the norms of its images under the iterates of the operator satisfy certain growth conditions a simple consequence of our main result is that a bicyclic unitary operator on a banach space with separable dual is cyclic our results also imply that if s a n n in mathbb z longmapsto a n 1 n in mathbb z is the shift operator acting on the weighted space of sequences ell omega 2 mathbb z if the weight satisfies some regularity conditions and n 1 for nonnegative n then s is cyclic if rm lim n rightarrow infty rm log omega n sqrt n 0 on the other hand one can see that s is not cyclic if the series sum n geq 1 rm log omega n n 2 diverges we show that the question of herrero whether either s or s is cyclic on ell omega 2 mathbb z admits a positive answer when the series sum n in mathbb z rm log s n n 2 1 is convergent we also prove completeness results for translates in certain banach spaces of functions on mathbb r

existence of hypercyclic operators on topological vector spaces the present paper introduces a very simple but very useful notion of the so called quasi extension ofl1 operators and proves that a large class of topological vector spaces admit continuous hypercyclic operators in particular it answers in the affirmative a question of s rolewicz posed in 1969 whether or not every infinite dimensional separable banach space admits a continuous hypercyclic operator

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

lie algebroid structures on double vector bundles and representation theory of lie algebroids abstract a vb algebroid is essentially defined as a lie algebroid object in the category of vector bundles there is a one to one correspondence between vb algebroids and certain flat lie algebroid superconnections up to a natural notion of equivalence in this setting we are able to construct characteristic classes which in special cases reproduce characteristic classes constructed by crainic and fernandes we give a complete classification of regular vb algebroids and in the process we obtain another characteristic class of lie algebroids that does not appear in the ordinary representation theory of lie algebroids

representations up to homotopy of lie algebroids we introduce and study the notion of representation up to homotopy of a lie algebroid paying special attention to examples we use representations up to homotopy to define the adjoint representation of a lie algebroid and show that the resulting cohomology controls the deformations of the structure the weil algebra of a lie algebroid is defined and shown to coincide with kalkman s brst model for equivariant cohomology in the case of group actions the relation of this algebra with the integration of poisson and dirac structures is explained in arias abad crainic ann inst fourier

hypercyclic operators on non normable frechet spaces abstract every infinite dimensional separable non normable frechet space admits a continuous hypercyclic operator a large class of separable countable inductive limits of banach spaces with the same property is given but an example of a separable complete inductive limit of banach spaces which admits no hypercyclic operator is provided it is also proved that no compact operator on a locally convex space is hypercyclic

lie algebroid fibrations abstract a degree 1 non negative graded super manifold equipped with a degree 1 vector field q satisfying q q 1 namely a so called nq 1 manifold is in plain differential geometry language a lie algebroid we introduce a notion of fibration for such super manifolds that essentially involves a complete ehresmann connection as it is the case for lie algebras such fibrations turn out not to be just locally trivial products we also define homotopy groups and prove the expected long exact sequence associated to a fibration in particular crainic and fernandes s obstruction to the integrability of lie algebroids is interpreted as the image of a transgression map in this long exact sequence

a dynamical characterization of sub arakelian subsets abstract we are going to characterize those sets which can be covered by an arakelian set in terms of dynamical properties of entire functions via similarities moreover if we consider the set of universal entire functions via similarities that are bounded on such a sub arakelian set then it is shown that its algebraic size is as large as possible as a consequence we prove that the set of universal entire functions bounded on every straight line is algebraically large

large zero autocorrelation zones of golay sequences and their applications golay sequences have been studied for more than five decades since golay first discovered those sequences however the periodic autocorrelation of a single golay sequence is unknown in this paper for h 2 being an arbitrary even integer we show there exist three different constructions of h ary golay sequences with a zero autocorrelation zone zacz of length approximately an half a quarter or one eighth of their period those new discoveries on golay sequences can be explored during synchronization and detection at the receiver end and thus improve the performance of the communication system we present the application of binary golay sequences with zacz for intersymbol interference isi channel estimation compared with m sequences golay sequence aided channel estimation has perfect autocorrelations within the zone compared with frank zadoff chu sequences golay sequence aided channel estimation requires much lower hardware and computational complexity we also discuss the performance of golay sequence aided channel estimation in terms of its error variance finally simulations are conducted to show the performance of our proposed scheme against m sequences and fzc sequences in terms of symbol error rate the simulations also confirm with our theoretical results

large vector spaces generated by bounded universal functions abstract we provide a general framework to construct large vector spaces generated by bounded universal functions we provide necessary and sufficient conditions on a sequence of automorphisms n of a domain in c n for there to exist a norm closed infinite dimensional vector space v generated by functions in b f h f 1 such that v is locally uniformly dense in h v is linearly isometric with l 1 and every f v with f 1 is universal for the composition operators c n f f n by which we mean the set f n n 1 is locally uniformly dense in b in the case when is a bounded symmetric domain in c n we provide sufficient conditions on a sequence of holomorphic self maps n of for there to exist a vector space v generated by a locally uniformly dense set of inner functions such that v has each of the properties mentioned above

a nonlinear age and maturity structured model of population dynamics i basic theory a nonlinear model of age and maturity structured population dynamics is analyzed the population is structured by age and maturity of the individuals and the nonlinearity in the equations corresponds to density dependent limitation of population growth the existence and asymptotic behavior of solutions are studied

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

optimal growth of entire functions frequently hypercyclic for the differentiation operator we solve a problem posed by bonilla and grosse erdmann 2007 7 by constructing an entire function f which is frequently hypercyclic with respect to the differentiation operator and satisfies mf r cerr 1 4 where c 0 may be chosen arbitrarily small this growth rate is sharp we also obtain optimal results for minimal growth in terms of average lp norms among other tools the proof uses the rudin shapiro polynomials and heat kernel estimates

on the ground states of the bernasconi model the ground states of the bernasconi model are binary sequences of length n with low autocorrelations we introduce the notion of perfect sequences binary sequences with one valued off peak correlations of minimum amount if they exist they are ground states using results from the mathematical theory of cyclic difference sets we specify all values of n for which perfect sequences exist and how to construct them for other values of n we investigate almost perfect sequences i e sequences with two valued off peak correlations of minimum amount numerical and analytical results support the conjecture that almost perfect sequences exist for all values of n but that they are not always ground states we present a construction for low energy configurations that works if n is the product of two odd primes

vector bundles over lie groupoids and algebroids abstract we study vb groupoids and vb algebroids which are vector bundles in the realm of lie groupoids and lie algebroids through a suitable reformulation of their definitions we elucidate the lie theory relating these objects i e their relation via differentiation and integration we also show how to extend our techniques to describe the more general lie theory underlying double lie algebroids and la groupoids

on a class of almost perfect sequences abstract periodic 1 sequences all but one of whose out of phase autocorrelation coefficients are zero are studied by 9 using the equivalence of these almost perfect sequences to certain classes of cyclic divisible difference sets as noted by 7 we investigate the case 2 in the terminology of 9 sequences of periods 8 12 and 28 are given and several nonexistence results are obtained our results suggest that it is unlikely to have such sequences for periods greater than 28

representations up to homotopy and bott s spectral sequence for lie groupoids abstract in this paper we study the notion of representation up to homotopy of a lie groupoid and the resulting derived category and show that the adjoint representation is well defined as a representation up to homotopy as an application we extend bott s spectral sequence converging to the cohomology of classifying spaces of lie groups to the case of lie groupoids we explain the relation of this construction with the models of cartan and getzler for equivariant cohomology our work is closely related to and inspired by behrend s 3 bott s 4 and getzler s 9

almost perfect autocorrelation sequences almost perfect autocorrelation sequences are defined as complex periodic sequences such that all the out of phase autocorrelation coefficients are zero except one the study is restricted to 1 1 sequences in this case such sequences exist only if the period n is a multiple of 4 after setting up theoretical results several sequences are constructed for every period n multiple of 4 in the range 8

operators with dense invariant cyclic vector manifolds abstract we study a class of banach space operators patterned after the weighted backward shifts on hilbert space and show that any non scalar operator in the commutant of one of these generalized backward shifts has a dense invariant linear manifold whose non zero members are cyclic vectors under appropriate extra hypotheses on the commuting operator stronger forms of cyclicity are possible the most extreme being hypercyclicity density of an orbit motivated by these results we examine the cyclic behavior of two seemingly unrelated classes of operators adjoint multiplications on hilbert spaces of holomorphic functions and differential operators on the frechet space of entire functions we show that each of these operators other than the scalar multiples of the identity possesses a dense invariant linear submanifold each of whose non zero elements is hypercyclic finally we explore some connections with dynamics many of the hypercyclic operators discussed here are in at least one of the commonly accepted senses of the word chaotic

universal entire functions for affine endomorphisms of c n abstract in this paper the affine endomorphisms of c n which support compositionally universal entire functions are completely characterized

how to get universal inner functions we characterize a property that is useful for constructing large spaces of universal functions in a wide variety of settings in particular we show that given any sequence of automorphisms of the ball that admits a universal function f in h infty b n there exists a closed infinite dimensional subspace generated by inner functions that is isometric to ell 1 we put our results in the context of bounded symmetric domains

strong ergodic properties of a first order partial differential equation on etudie l equation differentielle d ordre 1 u t c x u x f x u pour t x 0 0 1 avec la condition initiale u 0 x v x pour x 0 1 on demontre l existence d une mesure invariante exacte ayant certaines proprietes supplementaires

spectral theory and hypercyclic subspaces a vector x in a hilbert space h is called hypercyclic for a bounded operator t h h if the orbit tnx n 1 is dense in h our main result states that if t satisfies the hypercyclicity criterion and the essential spectrum intersects the closed unit disk then there is an infinite dimensional closed subspace consisting except for zero entirely of hypercyclic vectors for t the converse is true even if t is a hypercyclic operator which does not satisfy the hypercyclicity criterion as a consequence other characterizations are obtained for an operator t to have an infinite dimensional closed subspace of hypercyclic vectors these results apply to most of the hypercyclic operators that have appeared in the literature in particular they apply to bilateral and backward weighted shifts perturbations of the identity by backward weighted shifts multiplication operators and composition operators the main result also applies to the differentiation operator and the translation operator t f z f z 1 defined on certain hilbert spaces consisting of entire functions we also obtain a spectral characterization of the norm closure of the class of hypercyclic operators which have an infinite dimensional closed subspace of hypercyclic vectors

on a universality property of certain integral operators in this paper we establish a universality property of fourier and hankel convolution operators and dunkl transforms

binary alexis sequences with perfect correlation binary alexis 1986 sequences are useful signals for fast start up equalization channel estimation synchronization or ranging the aperiodic autocorrelation functions of alexis sequences vanish in a broad window region when correlated using additional binary preamble and postamble sequences originally alexis sequences were found by computer search two methods are presented by which such sequences can be constructed for any length n p sup a and n 2 p sup a 1 where p is an odd prime and a 1 2 3

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