optimal domain for the hardy operator abstract we study the optimal domain for the hardy operator considered with values in a rearrangement invariant space in particular this domain can be represented as the space of integrable functions with respect to a vector measure defined on a ring a precise description is given for the case of the minimal lorentz spaces

quasipolynomial generalization of lotka volterra mappings in recent years it has been shown that lotka volterra mappings constitute a valuable tool from both the theoretical and the applied points of view with developments in very diverse fields such as physics population dynamics chemistry and economy the purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism originally conceived for the analysis of ordinary differential equations can be extended into the mapping domain the extension of the formalism into the discrete time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case it will be demonstrated that lotka volterra mappings play a central role in the quasipolynomial formalism for the discrete time case moreover the extension of the formalism into the discrete time domain allows a significant generalization of lotka volterra mappings as well as a whole transfer of algebraic methods into the discrete time context the result is a novel and more general conceptual framework for the understanding of lotka volterra mappings as well as a new range of possibilities that become open not only for the theoretical analysis of lotka volterra mappings and their generalizations but also for the development of new applications

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

multifractal characterization of complete genomes this paper develops a theory for characterization of dna sequences based on their measure representation the measures are shown to be random cascades generated by an infinitely divisible distribution this probability distribution is uniquely determined by the exponent function in the multifractal theory of random cascades curve fitting to a large number of complete genomes of bacteria indicates that the gamma density function provides an excellent fit to the exponent function and hence to the probability distribution of the complete genomes

correlation property of length sequences based on global structure of the complete genome this paper considers three kinds of length sequences of the complete genome detrended fluctuation analysis spectral analysis and the mean distance spanned within time l are used to discuss the correlation property of these sequences the values of the exponents from these methods of these three kinds of length sequences of bacteria indicate that the long range correlations exist in most of these sequences the correlations have a rich variety of behaviors including the presence of anti correlations furthermore using the exponent gamma it is found that these correlations are all linear gamma 1 0 0 03 it is also found that these sequences exhibit l f noise in some interval of frequency f l the length of this interval of frequency depends on the length of the sequence the shape of the periodogram in f l exhibits some periodicity the period seems to depend on the length and the complexity of the length sequence

cesaro averaging operators we define a family of cesaro operators re 0 and consider the question of their boundedness on h p spaces we also consider discrete versions of these operators acting on sequence spaces

recognition of an organism from fragments of its complete genome this paper considers the problem of matching a fragment to an organism using its complete genome our method is based on the probability measure representation of a genome we first demonstrate that these probability measures can be modeled as recurrent iterated function systems rifs consisting of four contractive similarities our hypothesis is that the multifractal characteristics of the probability measure of a complete genome as captured by the rifs is preserved in its reasonably long fragments we compute the rifs of fragments of various lengths and random starting points and compare with that of the original sequence for recognition using the euclidean distance a demonstration on five randomly selected organisms supports the above hypothesis

solid hulls of quasi banach spaces of analytic functions and interpolation abstract we study solid hulls of abstract hardy spaces of analytic functions on the unit disk interpolation of sublinear operators is used to description of solid hulls of quasi banach spaces generated by interpolation methods associated to classical hardy spaces h p for 0 p 1 we specialize our results to solid hulls of hardy orlicz and hardy lorentz spaces and we are able to characterize multipliers from hardy lorentz spaces to any solid sequence space we give for example a complete description of multipliers with the domain in hardy lorentz zygmund spaces

growth conditions compact perturbations and operator subdecomposability with applications to generalized cesaro operators abstract we adapt recent results of albrecht and ricker to obtain conditions under which growth constraints on the left resolvent of a banach space operator are preserved under suitable perturbations as an application we establish bishop s property for certain generalized cesaro operators on the classical hardy spaces h p 1 p our methods also apply to unilateral weighted shifts whose weight sequence converges sufficiently rapidly as well as to perturbations of restrictions of a class of generalized scalar operators

cesaro averaging operators on hardy spaces it is shown that the cesaro averaging operator 1 satisfies an inequality which immediately implies that it is bounded on certain hardy spaces including h p 0 p h p 0 p 2 for 0 the operator which is conjugate to on h 2 is also shown to be bounded on h p for 1 p p and 0

points d evaluation pour les operateurs cycliques ayant la propriete de bishop β abstract let t be a linear bounded cyclic operator in a separable complex hilbert space h let b t and ba t denote respectively the set of bounded point evaluation and the set of analytic point evaluation of t we show that if t has the bishop property then ba t b t ap t where ap t is the approximate spectrum of t in the particular case when t is an operator of multiplication by z in a hardy space this was proved by trent pacific j math 80 1979 279 on the other hand using the generalized and the local spectral theory we obtain sufficient conditions on ba t under which the spectrum of t and the local spectrum of t at any y 0 in h coincide at the end results involving the spectral picture of quasi similar cyclic operators are given

some phase transitions in coupled map lattices we study finite coupled map lattices of size d 2 with individual maps 0 1 0 1 and constant diffuse coupling for x 2x mod 1 we give sufficient conditions that the coupled system has a continuum of ergodic components in the case d 2 we determine the number of ergodic components for all coupling strengths if is a mixing tent map close to the transition from mixing to a periodic interval with period 2 the uncoupled system is mixing whereas numerical studies suggest that coupling with a suitable strength breaks up the phase space into domains which are interchanged with period 2 in case d 2 we prove this rigorously

an additive formula for samuel multiplicities on hilbert spaces of analytic functions abstract we establish a short exact sequence to relate the germ model of invariant subspaces of a hilbert space of vector valued analytic functions and the sheaf model of the corresponding coinvariant subspaces as a consequence we obtain an additive formula for samuel multiplicities as an application we give a different proof for a formula relating the fibre dimension and the samuel multiplicity which is first proved in fang 2005 11 the feature of the new proof is that the analytic arguments in fang 2005 11 are now subsumed by algebraic machinery

open embeddings and pseudoflat epimorphisms abstract we characterize open embeddings of stein spaces and of c manifolds in terms of certain flatness type conditions on the respective homomorphisms of function algebras

solid extensions of the cesaro operator on the hardy space h2 d abstract we introduce and study the largest banach space of analytic functions on the unit disc which is solid for the coefficient wise order and to which the classical cesaro operator c h 2 h 2 can be continuously extended while still maintaining its values in h 2 properties of this banach space h c e s 2 as well as a characterization of individual analytic functions which belong to h c e s 2 are presented in addition both the multiplier space of h c e s 2 and the spectrum of c h c e s 2 h c e s 2 are determined

diffusion coefficients of two dimensional viral dna walks dna sequences are represented as two dimensional walkers based on groups of mapping rules for the nucleotides in the dna sequences digital sequences from irrational and random numbers in base 4 are generated and their diffusion properties are then compared with those of 21 nucleotide sequences of animal and plant viruses by defining the diffusion coefficient as a function of the number of steps taken in a walk we show that the coefficients for the viral dna sequences generally have maximum values considerably larger than those for the random number sequences of same lengths moreover using the walker diagrams generated by different mapping groups we can study the dominance of any of the nucleotide pairs ag or ct ac or gt or at or cg in a dna sequence other possible studies of this approach are mentioned

the cesaro space of dirichlet series and its multiplier algebra abstract we consider the space h c e s p of all dirichlet series whose coefficients belong to the cesaro sequence space c e s p consisting of all complex sequences whose absolute cesaro means are in l p for 1 p it is a banach space of analytic functions for which we study the maximal domain of analyticity and the boundedness of point evaluations we identify the algebra of analytic multipliers on h c e s p as the wiener algebra of dirichlet series shifted to the vertical half plane c 1 q s c s 1 q where 1 p 1 q 1

crises and hysteresis in coupled logistic maps a new type of crisis is found in coupled logistic maps in this crisis several chaotic attractors undergo cyclic collisions with their basin boundaries and merge into a bigger one whose chaotic dynamical behavior exhibits cyclic transitions among its components with a well defined overall period

compact composition operators on the bloch space necessary and sufficient conditions are given for a composition operator cof f o q to be compact on the bloch space w and on the little bloch space o weakly compact composition operators on o are shown to be compact if q e o is a conformal mapping of the unit disk d into itself whose image q d approaches the unit circle t only in a finite number of nontangential cusps then co is compact on 7o on the other hand if there is a point of t n q d at which q d does not have a cusp then co is not compact

cesaro operators on hardy spaces in the unit ball this article establishes the boundedness of the generalized cesaro operator on holomorphic hardy spaces in the unit ball the approach consists in writing the generalized cesaro operator as a composition of certain integral operators

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

computational explorations into the dynamics of rings of coupled oscillators this paper deals with the response of homogeneous and inhomogeneous rings of coupled oscillators where each individual oscillator when uncoupled from the others is chaotic it is shown that coupling can bring about a wide variety of global responses and that there is a significant range of coupling values when the response of the ring is periodic despite the fact that each oscillator is chaotic in fact numerous periodic solutions can be found depending on the initial conditions the response of a coupled set of homogeneous and non homogeneous rings is also investigated showing that the behavior of such coupled compartmental models can be quite counterintuitive and sensitive to the parameters that describe the extent and nature of coupling

symmetry breaking bifurcation for coupled chaotic attractors the authors consider transitions from synchronous to asynchronous chaotic motion in two identical dissipatively coupled one dimensional mappings they show that the probability density of the asymmetric component satisfies a scaling law the exponent in this scaling law varies continuously with the distance from the bifurcation point and is determined by the spectrum of local lyapunov exponents of the uncoupled map finally they show that the topology of the invariant set is rather unusual though the attractor for supercritical coupling is a line it is surrounded by a strange invariant set which is dense in a two dimensional neighbourhood of the attractor

compactness properties of sobolev imbeddings for rearrangement invariant norms compactness properties of sobolev imbeddings are studied within the context of rearrangement invariant norms attention is focused on the extremal situation namely when the imbedding is considered as defined on its optimal sobolev domain with the range space fixed the techniques are based on recent results which reduce the question of boundedness of the imbedding to boundedness of an associated kernel operator of just one variable

statistical properties of one dimensional binary sequences with power law power spectrum abstract by the fourier filtering method we generate one dimensional binary sequences from coarse grained continuous sequences with preset exponents 0 using the spectrum analysis we find that the corresponding binary sequences have pure 1 f power spectrum and spectrum exponents 0 0 2 0 where f is the frequency we evaluate numerically the relation between and 0 using the autocorrelation function analysis the detrended fluctuation analysis the duration time analysis and the entropy analysis we investigate extensively the statistical properties of such binary sequences we find that the statistical properties are basically different for 1 and 1 and binary sequences become more and more ordered as increases

the dirac operator of a commuting d tuple abstract given a commuting d tuple t t1 td of otherwise arbitrary operators on a hilbert space there is an associated dirac operator dt significant attributes of the d tuple are best expressed in terms of dt including the taylor spectrum and the notion of fredholmness in fact all properties of t derive from its dirac operator we introduce a general notion of dirac operator in dimension d 1 2 that is appropriate for multivariable operator theory we show that every abstract dirac operator is associated with a commuting d tuple and that two dirac operators are isomorphic iff their associated operator d tuples are unitarily equivalent by relating the curvature invariant introduced in a previous paper to the index of a dirac operator we establish a stability result for the curvature invariant for pure d contractions of finite rank it is shown that for the subcategory of all such t that are a fredholm and and b graded the curvature invariant k t is stable under compact perturbations we do not know if this stability persists when t is fredholm but ungraded although there is concrete evidence that it does

small random perturbations of dynamical systems and the definition of attractors the strange attractors plotted by computers and seen in physical experiments do not necessarily have an open basin of attraction in view of this we study a new definition of attractors based on ideas of conley we argue that the attractors observed in the presence of small random perturbations correspond to this new definition

fiber dimension for invariant subspaces abstract in this paper we study the fiber dimension of invariant subspaces for a large class of operators we define a class of invariant subspaces called cf subspaces which are related to the codimension one property we obtain several characterizations of cf subspaces including one in terms of samuel multiplicity other new findings include 1 a lattice additive formula and its applications section 4 2 a new concept of absorbance which describes a rough containment relation for invariant subspaces section 5 3 the existence of a unique smallest cf subspace containing an arbitrary invariant subspace and preserving the fiber dimension section 6

unitary invariants for hilbert modules of finite rank we associate a sheaf model to a class of hilbert modules satisfying a natural finiteness condition it is obtained as the dual to a linear system of hermitian vector spaces in the sense of grothendieck a refined notion of curvature is derived from this construction leading to a new unitary invariant for the hilbert module a division problem with bounds originating in douady s privilege is related to this framework a series of concrete computations illustrate the abstract concepts of the paper

estimates for hilbertian koszul homology abstract the objective of this paper is to give new kind of estimates for hilbertian koszul homology inspired by commutative algebra in multivariable fredholm theory

dynamics of coupled nonlinear maps and its application to ecological modeling this paper investigates the behavior of coupled nonlinear dynamical systems we take two such dynamical systems or units couple them together and study the effect of coupling on the dynamics we demonstrate that coupling two chaotic units can indeed stabilize both of them several results describing the global dynamics of the coupled nonlinear system are established using them we show that by and large the presence of coupling appears to increase the orderliness of the coupled system s response producing periodicity synchronicity and quasi symmetry using exponential maps which are commonly used to simulate population dynamics we establish the applicability of our results to population dynamics

statistical properties of dna sequences revisited the role of inverse bilateral symmetry in bacterial chromosomes abstract herein it is shown that in order to study the statistical properties of dna sequences in bacterial chromosomes it suffices to consider only one half of the chromosome because they are similar to its corresponding complementary sequence in the other half this is due to the inverse bilateral symmetry of bacterial chromosomes contrary to the classical result that dna coding regions of bacterial genomes are purely uncorrelated random sequences here it is shown via a renormalization group approach that dna random fluctuations of single bases are modulated by log periodic variations distance series of triplets display long range correlations in each half of the intact chromosome and in protein coding sequences or both long range correlations and log periodic modulations along the whole chromosome hence scaling analyses of distance series of dna sequences have to consider the functional units of bacterial chromosomes

resolvent estimates and decomposable extensions of generalized cesaro operators we determine the spectrum of generalized cesaro operators with essentially rational symbols acting on various spaces of analytic functions including hardy spaces weighted bergman and dirichlet spaces then we show that in all cases these operators are subdecomposable c 2009 elsevier inc all rights reserved

measure representation and multifractal analysis of complete genomes this paper introduces the notion of measure representation of dna sequences spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes the main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria from the measure representations and the values of the dq spectra and related cq curves it is concluded that these complete genomes are not random sequences in fact spectral analyses performed indicate that these measure representations considered as time series exhibit strong long range correlation here the long range correlation is for the k strings with dictionary ordering and it is different from the base pair correlations introduced by other people for substrings with length k58 the dq spectra of all organisms studied are multifractal like and sufficiently smooth for the cq curves to be meaningful with the decreasing value of k the multifractality lessens the cq curves of all bacteria resemble a classical phase transition at a critical point but the analogous phase transitions of chromosomes of nonbacteria organisms are different apart from chromosome 1 of c elegans they exhibit the shape of double peaked specific heat function a classification of genomes of bacteria by assigning to each sequence a point in two dimensional space d21 d1 and in three dimensional space d21 d1 d22 was given bacteria that are close phylogenetically are almost close in the spaces d21 d1 and d21 d1 d22

multifractal characterisation of length sequences of coding and noncoding segments in a complete genome the coding and noncoding length sequences constructed from a complete genome are characterised by multifractal analysis the dimension spectrum dq and its derivative the analogous specific heat cq are calculated for the coding and noncoding length sequences of bacteria where q is the moment order of the partition sum of the sequences from the shape of the dq and cq curves it is seen that there exists a clear difference between the coding noncoding length sequences of all organisms considered and a completely random sequence the complexity of noncoding length sequences is higher than that of coding length sequences for bacteria almost all dq curves for coding length sequences are flat so their multifractality is small whereas almost all dq curves for noncoding length sequences are multifractal like it is seen that the analogous specific heats of noncoding length sequences of bacteria have a rich variety of behaviour which is much more complex than that of coding length sequences we propose to characterise the bacteria according to the types of the cq curves of their noncoding length sequences this new type of classification allows a better understanding of the relationship among bacteria at the global gene level instead of nucleotide sequence level

the fredholm index of a pair of commuting operators ii this paper concerns fredholm theory in several variables and its applications to hilbert spaces of analytic functions one feature is the introduction of ideas from commutative algebra to operator theory specifically we introduce a method to calculate the fredholm index of a pair of commuting operators to achieve this we define and study the hilbert space analogs of samuel multiplicities in commutative algebra then the theory is applied to the symmetric fock space in particular our results imply a satisfactory answer to arveson s program on developing a fredholm theory for pure d contractions when d 2 including both the fredholmness problem and the calculation of indices we also show that arveson s curvature invariant is in fact always equal to the samuel multiplicity for an arbitrary pure d contraction with finite defect rank it follows that the curvature is a similarity invariant

on the spectrum of the cesaro operator on spaces of analytic functions this paper concerns the cesaro operator acting on various spaces of analytic functions on the unit disc the remarkable fact that this operator is subnormal when acting on the hardy space h2 has lead to extensive studies of its spectral picture on other spaces of this type we present some of the methods that have been used to obtain information about the spectrum of the cesaro operator acting on hardy and bergman spaces and give a unified approach to these problems which also yields new results in this direction in particular we prove that the cesaro operator is subdecomposable on h1 and on the standard weighted bergman spaces 0

statistics of dna sequences a low frequency analysis we study statistical properties of dna chains of thirteen microbial complete genomes we find that the power spectrum of several of the sequences studied flattens off in the low frequency limit this implies the correlation length in those sequences is much smaller than the entire dna chain consequently in contradiction with previous studies we show that the fractal behavior of dna chains does not always prevail through the entire dna molecule

a class of integral operators on spaces of analytic functions abstract we determine the spectrum and essential spectrum as well as resolvent estimates for a class of integral operators t f z z 1 1 z 0 z f 1 1 d acting on either the analytic besov spaces or other banach spaces of analytic functions on the unit disc including the classical hardy and weighted bergman spaces as well as certain dirichlet spaces and generalized bloch spaces our results unify and extend recent work by aleman and persson 2 the current authors 4 and albrecht and miller 1

the classes of local spectral theory in this paper we consider several classes of operators on a complex hilbert space which appear in local spectral theory a complete description in terms of properties of various parts of the spectrum is obtained for the operators in the closure and for the operators in the interior of each of these classes

spectral properties of cesaro like operators on weighted bergman spaces abstract we determine spectral pictures and resolvent estimates for a class of integral operators on the weighted bergman spaces l a p d m for p 1 1 and show in particular these operators are subdecomposable moreover in the case that p 2 we show that some of these operators are subnormal some are normaloid and some are subscalar

carleson measures multipliers and integration operators for spaces of dirichlet type for 0 1 we let d p denote the space of those functions f which are analytic in the unit disc d z c z 1 and satisfy d 1 z 2 f z p dx dy in this paper we characterize the positive borel measures in d such that d p l q d 0 p q we also characterize the pointwise multipliers from d p to d q 0 p q i fp 2 p in particular we prove that if

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

perturbation of spectra of operator matrices and local spectral theory abstract for a l x b l y and c l y x we denote by m c the operator defined on x y by a c 0 b in this article we study defect set d a b m c for different spectra including the spectrum the essential spectrum weyl spectrum and the approximate point spectrum we then apply the obtained results to the stability of such spectra d and the classes of operators c for which stability holds of m c using local spectral theory