hyponormal operators with finite rank self commutators and quadrature domains this paper studies some classes of pure hyponormal operators with finite rank self commutators satisfying the condition that their spectra are unions of a finite collection of the closures of quadrature domains

subnormal and quasinormal toeplitz operators with matrix valued rational symbols abstract in this paper we deal with the subnormality and the quasinormality of toeplitz operators with matrix valued rational symbols in particular in view of halmos s problem 5 we focus on the question which subnormal toeplitz operators are normal or analytic we first prove let l m n be a matrix valued rational function having a matrix pole i e there exists d for which ker h z h c n 2 where h denotes the hankel operator with symbol if i t is hyponormal ii ker t t is invariant for t then t is normal hence in particular if t is subnormal then t is normal next we show that every pure quasinormal toeplitz operator with a matrix valued rational symbol is unitarily equivalent to an analytic toeplitz operator

boundedness of riesz transforms for elliptic operators on abstract wiener spaces let e h be an abstract wiener space and let dv vd where d denotes the malliavin derivative and v is a closed and densely defined operator from h into another hilbert space h given a bounded operator b on h coercive on the range r v we consider the operators a v bv in h and a vv b in h as well as the realisations of the operators l dv bdv and l dvdv b in lp e and lp e h respectively where 1 p our main result asserts that the following four assertions are equivalent 1 d l d dv with lf p dvf p for f d l 2 l admits a bounded h functional calculus on r dv 3 d a d v with ah vh for h d a 4 a admits a bounded h functional calculus on r v moreover if these conditions are satisfied then d l d dv2 d da the equivalence 1 4 is a non symmetric generalisation of the classical meyer inequalities of malliavin calculus where h h v i b 12i a one sided version of 1 4 giving lp boundedness of the riesz transform dv l in terms of a square function estimate is also obtained as an application let a generate an analytic c0 contraction semigroup on a hilbert space h and let l be the lp realisation of the generator of its second quantisation our results imply that two sided bounds for the riesz transform of l are equivalent with the kato square root property for a the boundedness of the riesz transform is used to obtain an lp domain characterisation for the operator l

remarks on nonlinear stochastic partial differential equations an application of the splitting up method the objective of this article is to apply the splitting up method to the existence theorem for nonlinear stochastic partial differential equations with use of this method an approximating sequence is constructed by the compactness argument a convergent subsequence can be extracted and this fact provides the solution

adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems we introduce a numerical approximation method for estimating an unknown parameter of a primary chaotic system which is partially observed through a scalar time series specifically we show that the recursive minimization of a suitably designed cost function that involves the dynamic state of a fully observed secondary system and the observed time series can lead to the identical synchronization of the two systems and the accurate estimation of the unknown parameter the salient feature of the proposed technique is that the only external input to the secondary system is the unknown parameter which needs to be adjusted we present numerical examples for the lorenz system which show how our algorithm can be considerably faster than some previously proposed methods

on a class of jointly hyponormal toeplitz operators we characterize when a pair of toeplitz operators t t t is jointly hyponormal under various assumptions for example is analytic or is a trigonometric polynomial or is analytic a typical characterization states that t t t is jointly hyponormal if and only if an algebraic relation of and holds and the single toeplitz operator t is hyponormal where is a combination of and more general results for an n tuple of toeplitz operators are also obtained

approximation of the zakai equation by the splitting up method the objective of this article is to apply an operator splitting method to the time integration of zakai equation using this approach one can decompose the numerical integration into a stochastic step and a deterministic one both of them much simpler to handle than the original problem a strong convergence theorem is given in the spirit of existing results for deterministic problems

convergence rates of the splitting scheme for parabolic linear stochastic cauchy problems we study the splitting scheme associated with the linear stochastic cauchy problem du t au t dt dw t t in 0 t u 0 x here a is the generator of an analytic c 0 semigroup s s t t geqslant0 on a banach space e and w w t t geqslant0 is a brownian motion with values in a fractional domain space e beta associated with a we prove that if alpha beta gamma theta geqslant0 are such that gamma theta 1 and alpha beta theta gamma frac 1 2 then the approximate solutions u n converge to the solution u in the space c gamma 0 t e alpha both in l p means and almost surely with rate 1 n theta

hyponormal toeplitz operators and extremal problems of hardy spaces the symbols of hyponormal toeplitz operators are completely described and those are also studied being related with the extremal problems of hardy spaces moreover we discuss halmos s question about a subnormal toeplitz operator when the self commutator is finite rank

stochastic evolution equations in umd banach spaces we discuss existence uniqueness and space time holder regular ity for solutions of the parabolic stochastic evolution equation du t au t f t u t dt b t u t dwh t t 2 0 t0 u 0 u0 where a generates an analytic c0 semigroup on a umd banach space e and wh is a cylindrical brownian motion with values in a hilbert space h we prove that if the mappings f 0 t e e and b 0 t e l h e satisfy suitable lipschitz conditions and u0 is f0 measurable and bounded then this problem has a unique mild solution which has trajectories in c 0 t d a provided 0 and 0 satisfy 1 2 vari ous extensions of this result are given and the results are applied to parabolic stochastic partial dierential equations

estimating model parameters by chaos synchronization using chaos synchronization and a proposed iterative method of parameter adaptation we precisely estimate the model parameters of chaotic systems and synchronize two chaotic systems with originally mismatching model parameters this parameter adaptation method can be applied to a spatiotemporal chaotic system with a one way coupled map lattice as a biomedical application this method is capable of estimating the asymmetric tension parameter of a vocal fold model

complete description of determinantal representations of smooth irreducible curves abstract determinantal representations of algebraic curves are interesting in themselves and their classification is equivalent to the simultaneous classification of triples of matrices we present a complete description of determinantal representations of smooth irreducible curves over any algebraically closed field we used the notion of the class of divisors of the vector bundle corresponding to a determinantal representation we prove that two determinantal representations of a smooth curve f are equivalent if and only if the classes of divisors of the corresponding vector bundles coincide we give a precise characterization of those classes of divisors that arise from vector bundles corresponding to determinantal representations of f then we obtain a parametrization of determinantal representations of f up to equivalence by the points of the jacobian variety of f not on some exceptional subvariety in particular it follows that any smooth curve of order 3 or greater possesses an infinite number of nonequivalent determinantal representations we also specialize our results to symmetrical and self adjoint representations

parameter evaluation from time sequences using chaos synchronization unknown parameters in nonlinear equations are estimated from chaotic time sequences using chaos synchronization the method is based on a random optimization method the parameters are randomly searched for in a sequential manner as the degree of the chaos synchronization is increased the method is applied for the parameter evaluation in the lorenz equation and the lang kobayashi model for the chaotic semiconductor laser

real separated algebraic curves quadrature domains ahlfors type functions and operator theory abstract the aim of this paper is to inter relate several algebraic and analytic objects such as real type algebraic curves quadrature domains functions on them and rational matrix functions with special properties and some objects from operator theory such as vector toeplitz operators and subnormal operators our tools come from operator theory but some of our results have purely algebraic formulation we make use of xia s theory of subnormal operators and of the previous results by the author in this direction we also correct in section 5 some inaccuracies in the works of d v yakubovich subnormal operators of finite type i xia s model and real algebraic curves in c 2 rev mat iberoamericana 14 1998 95 115 d v yakubovich subnormal operators of finite type ii structure theorems rev mat iberoamericana 14 1998 623 681 by the author

a gap between hyponormality and subnormality for block toeplitz operators this paper concerns a gap between hyponormality and subnormality for block toeplitz operators we show that there is no gap between 2 hyponormality and subnormality for a certain class of trigonometric block toeplitz operators e g its co analytic outer coefficient is invertible in addition we consider the extremal cases for the hyponormality of trigonometric block toeplitz operators in this case hyponormality and normality coincide

use of synchronization and adaptive control in parameter estimation from a time series a technique is introduced for estimating unknown parameters when a time series of only one variable from a multivariate nonlinear dynamical system is given the technique employs a combination of two different control methods linear feedback for synchronizing system variables and adaptive control and is based on dynamic minimization of synchronization error the technique is shown to work even when the unknown parameters appear in the evolution equations of the variables other than the one for which the time series is given the technique not only establishes that explicit detailed information about all system variables and parameters is contained in a scalar time series but also gives a way to extract it out under suitable conditions illustrations are presented for lorenz and rossler systems and a nonlinear dynamical system in plasma physics also it is found that the technique is reasonably stable against noise in the given time series and the estimated value of a parameter fluctuates around the correct value with the error of estimation growing linearly with the noise strength for small noise

dynamic algorithm for parameter estimation and its applications we consider a dynamic method based on synchronization and adaptive control to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series we present an important extension of the method when the time series of a scalar function of the variables of the underlying dynamical system is given we find that it is possible to obtain synchronization as well as parameter estimation using such a time series we then consider a general quadratic flow in three dimensions and discuss the applicability of our method of parameter estimation in this case in practical situations one expects only a finite time series of a system variable to be known we show that the finite time series can be repeatedly used to estimate unknown parameters with an accuracy that improves and then saturates to a constant value with repeated use of the time series finally we suggest an important application of the parameter estimation method we propose that the method can be used to confirm the correctness of a trial function modeling an external unknown perturbation to a known system we show that our method produces exact synchronization with the given time series only when the trial function has a form identical to that of the perturbation

pathwise holder convergence of the implicit linear euler scheme for semi linear spdes with multiplicative noise in this article we prove pathwise holder convergence with optimal rates of the implicit euler scheme for the abstract stochastic cauchy problem begin aligned left begin aligned du t au t dt f t u t dt g t u t dw h t quad t in 0 t u 0 x 0 end aligned right end aligned here a is the generator of an analytic c 0 semigroup on a umd banach space x w h is a cylindrical brownian motion in a hilbert space h and the functions f 0 t times x rightarrow x theta f and g 0 t times x rightarrow fancyscript l h x theta g satisfy appropriate local lipschitz conditions the results are applied to a class of second order parabolic spdes driven by multiplicative space time white noise

a mild ito formula for spdes this article introduces a new somehow mild ito type formula for the solution process of a stochastic partial differential equation of evolutionary type

synchronization based estimation of all parameters of chaotic systems from time series by a simple combination of adaptive scheme and linear feedback with the updated feedback strength for a large class of chaotic systems it is proved rigorously by using the invariance principle of differential equations that all unknown model parameters can be estimated dynamically this approach supplies a systematic and analytical procedure for estimating parameters from time series and it is simple to implement in practice in addition this method is quite robust against the effect of noise and able to respond rapidly to changes in operating parameters of the experimental system lorenz and r ossler hyperchaos systems are used to illustrate the validity of this technique

on a recursive method for the estimation of unknown parameters of partially observed chaotic systems we investigate a recently proposed method for on line parameter estimation and synchronization in chaotic systems this novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series it works by periodically updating the parameter of interest in a secondary system with the same functional form as the primary one but no explicit coupling between their dynamic variables in order to minimize a suitably defined cost function in this paper we review the basics of the method and investigate its robustness and new extensions in particular we study the performance of the novel technique in the presence of noise either observational i e an additive contamination of the observed time series or dynamical i e a random perturbation of the system dynamics and when there is a mismatch between the primary and secondary systems numerical results including comparisons with other techniques are presented finally we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations

statistical methods of parameter estimation for deterministically chaotic time series we discuss the possibility of applying some standard statistical methods the least square method the maximum likelihood method and the method of statistical moments for estimation of parameters to deterministically chaotic low dimensional dynamic system the logistic map containing an observational noise a segmentation fitting maximum likelihood ml method is suggested to estimate the structural parameter of the logistic map along with the initial value x 1 considered as an additional unknown parameter the segmentation fitting method called piece wise ml is similar in spirit but simpler and has smaller bias than the multiple shooting previously proposed comparisons with different previously proposed techniques on simulated numerical examples give favorable results at least for the investigated combinations of sample size n and noise level besides unlike some suggested techniques our method does not require the a priori knowledge of the noise variance we also clarify the nature of the inherent difficulties in the statistical analysis of deterministically chaotic time series and the status of previously proposed bayesian approaches we note the trade off between the need of using a large number of data points in the ml analysis to decrease the bias to guarantee consistency of the estimation and the unstable nature of dynamical trajectories with exponentially fast loss of memory of the initial condition the method of statistical moments for the estimation of the parameter of the logistic map is discussed this method seems to be the unique method whose consistency for deterministically chaotic time series is proved so far theoretically not only numerically

normal singular cauchy integral operators with operator valued symbols abstract in this paper we characterize a class of normal isometric coisometric unitary hyponormal singular cauchy integral operators with operator valued or matrix valued symbols on vector valued or c n valued l 2 spaces

subnormal toeplitz operators and the kernels of their self commutators abstract in this note we give a connection between subnormal toeplitz operators and the kernels of their self commutators this is closely related to p r halmos s problem 5 is every subnormal toeplitz operator either normal or analytic our main theorem is as follows if l is such that and are of bounded type that is they are quotients of two analytic functions on the open unit disk and if the kernel of the self commutator of t is invariant for t then t is either normal or analytic

hyponormality of toeplitz operators with polynomial symbols a bounded linear operator a on a hilbert space h with inner product is said to be hyponormal if its selfcommutator a a a a aa induces a positive semidefinite quadratic form on h via 7 a a for h let h t denote the hardy space of the unit circle t d in the complex plane recall that given l t the toeplitz operator with symbol is the operator t on h t defined by t f p f where f h t and p denotes the projection that maps l t onto h t the hyponormality of toeplitz operators has been studied by c cowen 1 2 p fan 4 c gu 8 t ito and t wong 9 t nakazi and k takahashi 11 d yu 13 k zhu 14 r curto d farenick the second and the third named authors 3 5 6 10 and others an elegant theorem of c cowen 2 characterizes the hyponormality of a toeplitz operator t on h t by properties of the symbol l t k zhu 14 reformulated cowen s criterion and then showed that the hyponormality of t with polynomial symbols can be decided by a method based on the classical interpolation theorem of i schur 12 also farenick and the third named author 5 characterized the hyponormality of t in terms of the fourier coefficients of the trigonometric polynomial in the cases that the outer coefficients of have the same modulus but the case of arbitrary trigonometric polynomials though solved in principle by cowen s theorem or zhu s theorem is in practice very complicated on the other hand nakazi and takahashi 11 corollary 5 showed that if z n n m anz n is a trigonometric polynomial with m n and if for every zero of z such that 1 the number 1 is a zero of z in the open unit disk d of multiplicity greater than or equal to the multiplicity of then t is hyponormal but the converse is not true in general to see this consider the following trigonometric polynomial z z 2 z 2 z 1 z 15 z 13 then z 2 15z 2 19 15z 55 15 53 15z z using an argument of p fan 4 theorem 1 for every trigonometric polynomial of the form z 2 n 2 anz

hyponormality of toeplitz operators with rational symbols in this article we introduce a notion of division for rational functions and then give a criterion for hyponormality of open image in new window f g are rational functions in the cases where g divides f furthermore we show that we may assume without loss of generality that g divides f when we consider the hyponormality of open image in new window

which subnormal toeplitz operators are either normal or analytic abstract we study subnormal toeplitz operators on the vector valued hardy space of the unit circle along with an appropriate reformulation of p r halmos s problem 5 which subnormal block toeplitz operators are either normal or analytic we extend and prove abrahamse s theorem to the case of matrix valued symbols that is we show that every subnormal block toeplitz operator with bounded type symbol i e a quotient of two bounded analytic functions whose analytic and co analytic parts have the left coprime factorization is normal or analytic we also prove that the left coprime factorization condition is essential finally we examine a well known conjecture of whether every subnormal toeplitz operator with finite rank self commutator is normal or analytic

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

order of convergence of splitting schemes for both deterministic and stochastic nonlinear schrodinger equations we first prove the second order convergence of the strang type splitting scheme for the nonlinear schrodinger equation the proof does not require commutator estimates but crucially relies on an integral representation of the scheme it reveals the connection between strang type splitting and the midpoint rule we then show that the integral representation idea can also be used to study the stochastic nonlinear schrodinger equation with multiplicative noise of stratonovich type even though the nonlinear term there is not globally lipschitz we prove the first order convergence of a splitting scheme of it both schemes preserve the mass they are very efficient because they use explicit formulas to solve the subproblems containing the nonlinear or the nonlinear plus stochastic terms

a generalization of cowen s characterization of hyponormal toeplitz operators abstract in this paper we extend an elegant result of c c cowen proc amer math soc 103 1988 809 812 on the hyponormality of toeplitz operators to a class of generalized toeplitz operators in order to do this by a commutant lifting approach we study the operator equation h a h b t c where h a h b are generalized hankel operators and t c is an analytic toeplitz operator related results about the range inclusion of hankel and toeplitz operators are also obtained

convergence of numerical schemes for the solution of parabolic stochastic partial differential equations we consider the numerical solution of the stochastic partial differential equation u t 2 u x 2 u w x t where w is space time white noise using finite differences for this equation gyongy has obtained an estimate of the rate of convergence for a simple scheme based on integrals of w over a rectangular grid we investigate the extent to which this order of convergence can be improved and find that better approximations are possible for the case of additive noise u 1 if we wish to estimate space averages of the solution rather than pointwise estimates or if we are permitted to generate other functionals of the noise but for multiplicative noise u u we show that no such improvements are possible

parameter adaptive identical synchronization disclosing lorenz chaotic masking a parameter adaptive rule that globally synchronizes oscillatory lorenz chaotic systems with initially different parameter values is reported in principle the adaptive rule requires access to the three state variables of the drive system but it has been readapted to work with the exclusive knowledge of only one variable a potential message carrier the rule is very robust and can be used to trace parameter modulation conveying hidden messages the driven system is defined according to a drive driven type of coupling that guarantees synchronization if parameters are identical from any arbitrary initial state the parameters of the driven system are dynamically adapted to reach convergence to the drive parameter values at this point synchronization mismatch or parameter tracing is used to unmask any potential hidden message

stochastic integration in umd banach spaces in this paper we construct a theory of stochastic integration of processes with values in l h e where h is a separable hilbert space and e is a umd banach space i e a space in which martingale differences are unconditional the integrator is an h cylindrical brownian motion our approach is based on a two sided l p decoupling inequality for umd spaces due to garling which is combined with the theory of stochastic integration of l h e valued functions introduced recently by two of the authors we obtain various characterizations of the stochastic integral and prove versions of the ito isometry the burkholder davis gundy inequalities and the representation theorem for brownian martingales

parameter estimation in spatially extended systems the karhunen loeve and galerkin multiple shooting approach parameter estimation for spatiotemporal dynamics for coupled map lattices and continuous time domain systems is shown using a combination of multiple shooting karhunen loeve decomposition and galerkin s projection methodologies the resulting advantages in estimating parameters have been studied and discussed for chaotic and turbulent dynamics using small amounts of data from subsystems availability of only scalar and noisy time series data effects of space time parameter variations and in the presence of multiple time scales

hyponormality and subnormality of block toeplitz operators abstract in this paper we are concerned with hyponormality and subnormality of block toeplitz operators acting on the vector valued hardy space h c n 2 of the unit circle first we establish a tractable and explicit criterion on the hyponormality of block toeplitz operators having bounded type symbols via the triangularization theorem for compressions of the shift operator second we consider the gap between hyponormality and subnormality for block toeplitz operators this is closely related to halmos s problem 5 is every subnormal toeplitz operator either normal or analytic we show that if is a matrix valued rational function whose co analytic part has a coprime factorization then every hyponormal toeplitz operator t whose square is also hyponormal must be either normal or analytic third using the subnormal theory of block toeplitz operators we give an answer to the following toeplitz completion problem find the unspecified toeplitz entries of the partial block toeplitz matrix a u u so that a becomes subnormal where u is the unilateral shift on h 2

a study of solitonic combinations based on the theory of commuting non self adjoint operators abstract an intimate connection between two mathematical concepts the theory of solitons on the one hand and the theory of commuting non self adjoint operators on the other hand is established the link is provided by the marchenko method for solving nonlinear partial differential equations in general and the korteweg de vries equation in particular the solution of this equation is cast in a special form in terms of solitonic combinations such that the role played by a pair of commuting non self adjoint operators is evident and lends itself to generalization solitonic combinations are closely related to collective motions of spatiotemporal systems whose theory is reviewed here and extended to the physical space of four dimensions one time and three space a novel interpretation of the physical concept of quasiparticle is presented

synchronization based approach for estimating all model parameters of chaotic systems the problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved the variational calculus based method is robust in the presence of noise enables online estimation of the parameters and is also able to rapidly track changes in operating parameters of the experimental system the method is demonstrated using the lorenz rossler chaos and hyperchaos models its possible application in decoding communications using chaos is discussed

hyponormality of trigonometric toeplitz operators in this paper we establish a tractable and explicit criterion for the hyponormality of arbitrary trigonometric toeplitz operators i e toeplitz operators t with trigonometric polynomial symbols our criterion involves the zeros of an analytic polynomial f induced by the fourier coefficients of moreover the rank of the selfcommutator of t is computed from the number of zeros of f in the open unit disk d and in c d counting multiplicity

on the splitting up method and stochastic partial differential equations we consider two stochastic partial differential equations du varepsilon t l ru varepsilon t f r t dv varepsilon t r m k u varepsilon t g k t circ dy t k qquad hspace 5pt varepsilon 0 1 driven by the same multidimensional martingale y yk and by different increasing processes vr0 vr1 r 1 2 d1 where lr and mk are second and first order partial differential operators and stands for the stratonovich differential we estimate the moments of the supremum in t of the sobolev norms of u1 t u0 t in terms of the supremum of the differences break vr0t vr1t hence we obtain moment estimates for the error of a multistage splitting up method for stochastic pdes in particular for the equation of the unnormalized conditional density in nonlinear filtering

kernels of hankel operators and hyponormality of toeplitz operators we give a formula for mathrm ker h overline theta 1 ast h overline theta 2 and describe when mathrm ker h overline theta 1 ast h overline theta 2 mathrm ker h overline theta 2 we explore the hyponormality of toeplitz operators whose symbols are of circulant type and some more general types in addition we discuss formulas for and estimates of the rank of the self commutator of a hyponormal toeplitz operator