weighted composition operators on hardy spaces let be analytic functions defined on d such that d d the operator given by f f is called a weighted composition operator in this paper we deal with the boundedness compactness weak compactness and complete continuity of weighted composition operators on hardy spaces hp 1 p in particular we prove that such an operator is compact on h1 if and only if it is weakly compact on this space this result depends on a technique which passes the weak compactness from an operator t to operators dominated in norm by t

global attractivity of positive periodic solution to periodic lotka volterra competition systems with pure delay abstract we consider a periodic lotka volterra competition system without instantaneous negative feedbacks i e pure delay systems x i t x i t r i t j 1 n a i j t x j t i j t i 1 2 n we establish some 3 2 type criteria for global attractivity of a positive periodic solution of the system which generalize the well known wright s 3 2 criteria for the autonomous delay logistic equation and thereby address the open problem proposed by both kuang y kuang global stability in delayed nonautonomous lotka volterra type systems without saturated equilibria differential integral equations 9 1996 557 567 and teng z teng nonautonomous lotka volterra systems with delays j differential equations 179 2002 538 561

stable periodic solution of a discrete periodic lotka volterra competition system abstract this paper discusses a discrete lotka volterra competition system we first obtain the persistence of the system assuming that the coefficients in the system are periodic we obtain the existence of a periodic solution moreover under some additional conditions this periodic solution is globally stable our results not only reduce to those for the scalar equation when there is no coupling but also improve and complement some in the literature

a complete parameterization of all positive rational extensions of a covariance sequence in this paper we formalize the observation that filtering and interpolation induce complementary or dual decompositions of the space of positive real rational functions of degree less than or equal to n from this basic result about the geometry of the space of positive real functions we are able to deduce two complementary sets of conclusions about positive rational extensions of a given partial covariance sequence on the one hand by viewing a certain fast filtering algorithm as a nonlinear dynamical system defined on this space we are able to develop estimates on the asymptotic behavior of the schur parameters 1918 of positive rational extensions on the other hand we are also able to provide a characterization of all positive rational extensions of a given partial covariance sequence indeed motivated by its application to signal processing speech processing and stochastic realization theory this characterization is in terms of a complete parameterization using familiar objects from systems theory and proves a conjecture made by georgiou 1983 1987 our basic result however also enables us to analyze the robustness of this parameterization with respect to variations in the problem data the methodology employed is a combination of complex analysis geometry linear systems and nonlinear dynamics

harmless delays for uniform persistence abstract this paper studies a two dimensional predator prey system with a finite number of discrete delays our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system the results are obtained by constructing suitable persistence functionals

two periodic solutions of neutral difference systems depending on two parameters in this paper we establish existence multiplicity and nonexistence of periodic solutions for a class of first order neutral difference systems our approach is based on a fixed point theorem in cones as well as some analysis techniques

the nevanlinna pick problem on the closed unit disk minimal norm rational solutions of low degree for the nevanlinna pick interpolation problem with n interpolation conditions interior and boundary we construct a family of rational solutions of degree at most n 1 we also establish necessary and sufficient conditions for the existence and the uniqueness of a solution with the minimally possible h norm and construct a family of minimal norm rational solutions of degree at most n 1 in the indeterminate case finally we supplement a result of ruscheweyh and jones showing that in case the interpolation nodes and the target values are all unimodular any rational solution of degree at most n 1 is necessarily a finite blaschke product

optimal boundary interpolation and one block optimal control problem with invariant zeros on the imaginary axis and infinity we formulate a matrix interpolation problem with existing interpolation points on the imaginary axis and infinity and existing equal left and right interpolation points using the concept of parametrisation of stabilising controllers then we solve the problem of obtaining all its solutions if interpolation points at infinity are absent we show that the introduced problem is equivalent to the existing one we apply this result to solve the problem of optimal interpolation with existent interpolation points on the imaginary axis and infinity we show by an example that the solution of optimal interpolation is directly applicable to the one block optimal control with existent invariant zeros on the imaginary axis and infinity it is seen from the example that not only the transfer matrix of the closed loop system is constrained on the extended imaginary axis but also its derivatives

almost periodic solutions of a discrete almost periodic logistic equation with delay abstract in this paper we consider an almost periodic discrete logistic equation with delay by constructing suitable lyapunov functional and almost periodic functional hull theory a sufficient condition is obtained for the existence of a unique almost periodic solution which is globally attractive an example together with its numerical simulation shows the feasibility of our main result

existence of positive periodic solutions of nonlinear discrete model exhibiting the allee effect in this paper we shall consider the discrete nonlinear delay population model with allee effectx n 1 x n exp a n b n x p n w c n x q n w where a n b n and c n are positive sequences of period w and p and q are positive integers by using the coincidence degree theorem as well as some priori estimates we will establish a sufficient condition for the existence of positive periodic solution x n

permanence for non autonomous food chain systems with delay in this paper we first establish a new general criterion for the permanence of kolmogorov type systems of nonautonomous functional differential equations then as applications of this criterion we study the permanence of a class of n species general nonautonomous food chain systems with delay and new sufficient condition are established

uniform persistence and periodic solutions for a discrete predator prey system with delays abstract in this paper we deal with a discrete predator prey system with delay we first give a sufficient condition for the uniform persistence of the system assuming that the coefficients in the system are periodic by generalizing the yoshizawa s theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays we obtain the existence of a periodic solution basing on the uniform persistence result

on permanence and global stability in a general gilpin ayala competition predator prey discrete system abstract in this paper we propose a discrete multispecies general gilpin ayala competition predator prey model by using new difference inequality and developing the analysis technique of chen and zhou y chen z zhou stable periodic solution of a discrete periodic lotka volterra competition system j math anal appl 277 2003 358 366 sufficient conditions are established for the permanence and the global stability an example shows the feasibility of our results

permanence criteria for general delayed discrete nonautonomous n species kolmogorov systems and its applications in this paper the permanence for the general nonautonomous n species discrete kolmogorov systems with delays is studied by using the method of multiple discrete lyapunov like functionals a quite general sufficient condition is established as application of this result new sufficient conditions are obtained to ensure the permanence of all species for the discrete nonautonomous pure delayed n species lotka volterra competitive systems and food chain systems particularly as special cases a series of new sufficient conditions on the permanence for the discrete nonautonomous pure delayed lotka volterra two species competitive systems predator prey systems and three species food chain systems and the discrete autonomous pure delayed lotka volterra competition systems and food chain systems are obtained

periodic solutions of a discrete time lotka volterra type food chain model with delays a periodic discrete time three trophic level lotka volterra type food chain model is investigated by using gaines and mawhin s continuation theorem of coincidence degree theory sufficient conditions are derived for the existence of positive periodic solutions of the model

permanence for a discrete time lotka volterra type food chain model with delays abstract considered is a delayed discrete time lotka volterra type food chain model sufficient conditions are established for the permanence and the feasibility of the obtained results are illustrated with an example

a convex optimization approach to the rational covariance extension problem in this paper we present a convex optimization problem for solving the rational covariance extension problem given a partial covariance sequence and the desired zeros of the modeling filter the poles are uniquely determined from the unique minimum of the corresponding optimization problem in this way we obtain an algorithm for solving the covariance extension problem as well as a constructive proof of georgiou s seminal existence result and his conjecture a stronger version of which we have resolved in byrnes et al ieee trans automat control ac 40 1995 pp 1841 1857

uniform persistence in functional differential equations abstract in this paper we investigate the question of uniform persistence for retarded functional differential equations by utilizing liapunov like functions razumikhin techniques and differential inequalities we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations difference equations and reaction diffusion equations we apply these criteria to some well known biological models with delay our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence moreover these conditions are equivalent to uniform persistence for the cases without delay as well

finite blaschke product interpolation on the closed unit disc abstract we show how to construct all finite blaschke product solutions and the minimal scaled blaschke product solution to the nevanlinna pick interpolation problem in the open unit disc by solving eigenvalue problems of the interpolation data based on a result of jones and ruscheweyh we note that there always exists a finite blaschke product of degree at most n 1 that maps n distinct points in the closed unit disc of which at least one is on the unit circle into n arbitrary points in the closed unit disc provided that the points inside the unit circle form a positive semi definite pick matrix of full rank finally we discuss a numerical limiting procedure

persistence and global stability in discrete models of lotka volterra type abstract in this paper we establish new sufficient conditions for global asymptotic stability of the positive equilibrium in the following discrete models of lotka volterra type n i p 1 n i p exp c i a i n i p j 1 n a i j n j p k i j p 0 1 i n n i p n i p 0 p 0 and n i 0 0 1 i n where each n i p for p 0 each c i a i and a i j are finite and a i 0 a i a i i 0 1 i n and k i j 0 1 i j n applying the former results y muroya persistence and global stability for discrete models of nonautonomous lotka volterra type j math anal appl 273 2002 492 511 on sufficient conditions for the persistence of nonautonomous discrete lotka volterra systems we first obtain conditions for the persistence of the above autonomous system and extending a similar technique to use a nonnegative lyapunov like function offered by y saito t hara and w ma y saito t hara w ma necessary and sufficient conditions for permanence and global stability of a lotka volterra system with two delays j math anal appl 236 1999 534 556 for n 2 to the above system for n 2 we establish new conditions for global asymptotic stability of the positive equilibrium in some special cases that k i j k j j 1 i j n and j 1 n a j i a j k 0 i k these conditions become a i j 1 n a j i 2 1 i n and improve the well known stability conditions a i j 1 n a j i 1 i n obtained by k gopalsamy k gopalsamy global asymptotic stability in volterra s population systems j math biol 19 1984 157 168

permanence and stability of equilibrium for a two prey one predator discrete model in this letter a predator prey system of two prey one predator discrete model is investigated it is proved that the system is permanence under some appropriate conditions by jacobian matrix method a sufficient and necessary condition is derived for the local asymptotic stability of a equilibrium of the system meanwhile we give a suitable example for supporting our theoretical result

a discrete periodic lotka volterra system with delays in this paper we investigate the following discrete periodic lotka volterra system with delays x n 1 x n expb n i 1qai n x n ti j 1mcj n y n li y n 1 y n expr n i 1qdi n x n ki j 1mej n y n si the sufficient and realistic conditions are obtained for the existence of positive periodic solutions and the permanence for the above system

the scalar nevanlinna pick interpolation problem with boundary conditions we show that if the nevanlinna pick interpolation problem is solvable by a function mapping into a compact subset of the unit disc then the problem remains solvable with the addition of any number of boundary interpolation conditions provided the boundary interpolation values have modulus less than unity we give new inductive proofs of the nevanlinna pick interpolation problem with any finite number of interpolation points in the interior and on the boundary of the domain of interpolation the right half plane or unit disc with function values and any finite number of derivatives specified our solutions are analytic on the closure of the domain of interpolation our proofs only require a minimum of matrix theory and operator theory we also give new straightforward algorithms for obtaining minimal h norm solutions finally some numerical examples are given

persistence and global stability for discrete models of nonautonomous lotka volterra type abstract consider the following discrete models of nonautonomous lotka volterra type n i p 1 n i p exp c i p a i p n i p j 1 n l 0 m a ij l p n j p k l 1 i n p 0 1 2 n i p n ip 0 p 0 and n i0 0 1 i n where each c i p a i p and a ij l p are bounded for p 0 and inf p 0 a i p 0 a ii 0 p 0 1 i n a ij l p 0 1 i j n 0 l m k 0 0 integers k l 0 1 l m in this paper to the above discrete system we apply the techniques offered by ahmad and lazer nonlinear anal 40 2000 37 49 and establish similar conditions of the persistence and global asymptotic stability of the system

interpolation with constraint on frequency region and systems control application abstract this paper elaborates on a bitangential interpolation problem with a norm constraint of the interpolant on a given frequency region and on its generalization and proves that it admits a solution a motivation from systems control for the problem is given and the solution is applied for construction of a stabilizing control for one block plants such that the closed loop transfer matrix is norm constrained on the frequency region illustrative numerical examples are given

essentially normal composition operators on h2 abstract we prove a simple criterion for essential normality of composition operators on the hardy space induced by maps in a reasonably large class s of analytic self maps of the unit disk by combining this criterion with boundary caratheodory fejer interpolation theory we exhibit a parametrization for all rational self maps of the unit disk which induce essentially normal composition operators

the interpolation problem with a degree constraint the author previously 1983 1987 showed that there is a correspondence between nonnegative hermitian trigonometric polynomials of degree spl les n and solutions to the standard nevanlinna pick caratheodory interpolation problem with n 1 constraints which are rational and also of degree spl les n it was conjectured that the correspondence under suitable normalization is bijective and thereby that it results in a complete parametrization of rational solutions of degree spl les n the conjecture was proven by byrnes et al 1995 along with a detailed study of this parametrization however byrnes et al used a slightly restrictive assumption that the trigonometric polynomials are positive and accordingly the corresponding solutions have positive real part the purpose of the present note is to extend the result to the case of nonnegative trigonometric polynomials as well we present the arguments in the context of the general nevanlinna pick caratheodory fejer interpolation

two periodic solutions of n dimensional neutral functional difference systems in this paper we establish existence multiplicity and nonexistence of periodic solutions for a class of first order n dimensional neutral functional difference systems our approach requires the krasnoselskii fixed point theorem in cones

nevanlinna pick meromorphic interpolation the degenerate case and minimal norm solutions abstract the nevanlinna pick interpolation problem is studied in the class s of meromorphic functions f with poles inside the unit disk d and with f l t 1 in the indeterminate case the parametrization of all solutions is given in terms of a family of linear fractional transformations with disjoint ranges a necessary and sufficient condition for the problem being determinate is given in terms of the pick matrix of the problem the result is then applied to obtain necessary and sufficient conditions for the existence of a meromorphic function with a given pole multiplicity which satisfies nevanlinna pick interpolation conditions and has the minimal possible l norm on the unit circle t

global stability of discrete population models with time delays and fluctuating environment the global stability of a discrete population model of volterra type is studied the model incorporates time delays and allows for a fluctuating environment by linearization of the model at positive solutions and construction of liapunov functionals sufficient conditions are obtained to ensure a positive solution of the model is stable and attracts all positive solutions

wrong side interpolation by positive real rational functions abstract using polynomial interpolation along with structural properties of the family of rational positive real functions we here show that a set of m nodes in the open left half of the complex plane can always be mapped to anywhere in the complex plane by rational positive real functions whose degree is at most m moreover we introduce an easy to find parametrization in r 2 m 3 of a large subset of these interpolating functions

permanence and global attractivity of the discrete gilpin ayala type population model in this paper we propose a discrete gilpin ayala competition model and a discrete gilpin ayala type multispecies competition predator model for general nonautonomous case sufficient conditions which ensure the permanence and the global stability of the system are obtained for periodic case sufficient conditions which ensure the existence of an unique globally stable positive periodic solution of the system are obtained an example together with its numeric simulations shows the feasibility of the main results

permanence in kolmogorov type systems of nonautonomous functional differential equations abstract in this paper we establish some general results on the permanence of the n species kolmogorov type nonautonomous functional differential system formula i 1 2 n these results are applied to the n species lotka volterra type systems with distributed delays that is when f i t x t are linear functions of x t our method consists of constructing n liapunov like functions which can be regarded as boundary functions of some compact region inside the positive cone in r n

products of composition and analytic toeplitz operators abstract we will consider the problem of which the products of composition and analytic toeplitz operators would be bounded or compact on the hardy space h 2 and the bergman space l a 2

permanence of a discrete n species food chain system with time delays in this paper a discrete n species food chain system with time delays is considered by applying the comparison theorem of difference equation sufficient conditions are obtained for the permanence of the system

a reformulation of augmented basic interpolation problem and an application to h control abstract in this paper we present a new formulation of the augmented basic interpolation problem abip with rational matrices in terms of the stability of four rational matrices so that the abip transforms into a purely linear algebraic problem actually the existing interpolation condition given by an integral is replaced by stability of a rational matrix the new condition is applied to the h optimal control of one block plants having imaginary axis invariant zeros a new parameter in the parametrization of h optimal controllers is revealed which is given in terms of the derivative of the closed loop system at the imaginary axis invariant zeros of the plant the h optimal control algorithm is illustrated by an example and compared to the existing algorithms

a necessary and sufficient condition for permanence of a lotka volterra discrete system with delays abstract in this paper we consider the permanence of the following lotka volterra discrete competition system with delays k1 k2 l1 and l2 x n 1 x n exp r1 1 x n k1 1y n k2 y n 1 y n exp r2 1 2x n l1 y n l2 we show the system is permanent for all nonnegative integers k1 k2 l1 and l2 if and only if 1

persistence and global stability in discrete models of pure delay nonautonomous lotka volterra type abstract consider the persistence and the global asymptotic stability of the following discrete model of pure delay nonautonomous lotka volterra type n i p 1 n i p exp c i p j 1 n l 0 m a ij l p n j p k l p 0 1 2 1 i n n i p n i p 0 p 0 and n i 0 0 1 i n where each ci p and aijl p are bounded for p 0 and inf p 0 l 0 m a ii l p 0 a ij l p 0 i j n 1 i n and k l 0 1 l m in this paper for the above discrete system of pure delay type by improving the former work j math anal appl 273 2002 492 511 which extended the averaged condition offered by s ahmad and a c lazer nonlinear anal 40 2000 37 49 we offer conditions of persistence and considering a lyapunov like discrete function to the above discrete system we establish sufficient conditions of global asymptotic stability