equivalence of hardy submodules generated by polynomials abstract in this paper we obtain a complete classification under unitary equivalence for hardy submodules on the polydisk which are generated by ideals of polynomials let i be an ideal of polynomials in n variables since i is generated by finitely many polynomials i has a greatest common divisor p so i can be uniquely written as i p l which is called the beurling form of i let i 1 p 1 l 1 i 2 p 2 l 2 we prove that i 1 and i 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n and p 1 l 1 p 1 l 2 consequently two principal submodules p 1 and p 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n furthermore we give a complete similarity classification for submodules generated by homogeneous ideals finally we point out that in the case of the hardy module on the unit ball i 1 and i 2 are unitarily equivalent if and only if they are equal if i 1 and i 2 are homogeneous ideals then i 1 and i 2 are quasi similar if and only if i 1 i 2

scattering and bound state green s functions on a plane via so 2 1 lie algebra we calculate the green s functions for the particle vortex system for two anyons on a plane with and without a harmonic regulator and in a uniform magnetic field these green s functions which describe scattering or bound states depending on the specific potential in each case are obtained exactly using an algebraic method related to the so 2 1 lie group from these green s functions we obtain the corresponding wave functions and for the bound states we also find the energy spectra

characteristic spaces and rigidity for analytic hilbert modules abstract it is well known that a polynomial in one variable is completely determined by its zeros counting multiplicities we generalize this result to an ideal of polynomials in several variables by introducing the characteristic spaces of the ideal one finds that the ideal is completely determined by its characteristic spaces on a characteristic set in particular a primary ideal is completely determined by its characteristic space at any zero point some straightforward applications of the above results yield the algebraic reduction theorem for analytic hilbert modules in several variables also we obtain some general rigidity results for analytic hilbert modules by using the techniques of af envelopes of analytic hilbert modules

path integral solution of two potentials related to the so 2 1 dynamical algebra two classes of generalized coulomb potentials related to the so 2 1 dynamical algebra are rigorously solved by path integration in terms of parabolic coordinates

c algebras of multiplication operators on bergman spaces soit un domaine borne dans c soit a 2 l espace de bergman de toutes les fonctions analytiques sur qui sont de carre integrable par rapport a la mesure volumetrique et soit c la c algebre engendree par les operateurs de multiplication par les fonctions coordonnee sur on etudie les proprietes de c

synchronization of hyperchaotic systems with delayed bidirectional coupling synchronization of three bidirectionally coupled hyperchaotic systems is studied using the ikeda model as the hyperchaotic unit the whole system is given by three delay differential equations with two distinct time lags sufficient condition for the global stability of the manifold of exact synchronization is found analytically local stability of the synchronization manifold is studied by numerical computation of the transverse lyapunov exponent and statistical properties of the orbits

on the dirichlet space for finitely connected regions this paper is devoted to the study of the dirichlet space dir g for finitely connected regions g we are particularly interested in the algebra of bounded multiplication operators on this space results in different directions are obtained one direction deals with the structure of closed subspaces invariant under all bounded multiplication operators in particular we show that each such subspace contains a bounded function for regions with circular boundaries we prove that a finite codimensional closed subspace invariant under multiplication by z must be invariant under all bounded multiplication operators and furthermore it is of the form p dir g where p is a polynomial with all its roots lying in g another direction is to study cyclic and noncyclic vectors for the algebra of all bounded multiplication operators typical results are if f e dir g and f is bounded away from zero then f is cyclic on the other hand if the zero set of the radial limit function of f on the boundary has positive logarithmic capacity then f is not cyclic also some other sufficient conditions for a function to be cyclic are given lastly we study transitive operator algebras containing all bounded multiplication operators we prove that they are dense in the algebra of all bounded operators in the strong operator topology

dynamical invariance algebra of the hartmann potential the accidental degeneracy occurring in the quantum mechanical treatment of the ring shaped potential v eta sigma 2r 1 1 2q eta 2 sigma 2 r sin theta 2 is explained by constructing an su 2 dynamical invariance algebra the schrodinger equation is solved in parabolic coordinates written in the framework of the kustaanheimo stiefel transformation and the hamilton jacobi equations are solved in ordinary parabolic coordinates all finite trajectories are found to be periodic

analytic hilbert spaces over the complex plane in this paper we study the structure of quasi invariant subspaces of analytic hilbert spaces over the complex plane we especially investigate when two quasi invariant subspaces are similar or unitarily equivalent for an analytic hilbert space over the complex plane

synchronization analysis of linearly coupled systems described by differential equations with a coupling delay when a transmission delay occurs in the interconnection of linearly coupled systems described by ordinary differential equations lcodes both synchronization and the final synchronized state will vary in this paper mathematical analysis is presented on the synchronization phenomena of lcodes with a single coupling delay criteria are derived for both local and global synchronization it is known that in addition to the dynamical behaviors of the underlying uncoupled system and the coupling configuration the coupling strength and the coupling delay also play key roles on the stability of synchronization both theoretical and numerical analysis indicate that under some conditions if the coupling strength is large enough the coupled system can be completely synchronized for any coupling delay on the other hand in some cases the coupled system can be synchronized if the coupling delay is small enough

separation of variables in path integrals and path integral solution of two potentials on the poincare upper half plane the author discusses how to separate variables in path integrals it is assumed that a one dimensional problem with potential v x has an exact solution with energy levels elambda and wavefunctions psi lambda in order to perform the separation of variables a time transformation is performed back and forth in the path integral which allows one to insert the path integral solution corresponding to the potential v x the author illustrates the method by discussing some specific potential problems on the poincare upper half plane

hidden symmetry algebra and overlap coefficients for two ring shaped potentials a new approach is proposed to general systems possessing su 1 1 su 1 1 dynamical symmetry on the base of this approach the quadratic hahn algebra qh 3 is shown to serve as a hidden symmetry in both quantum and classical pictures for two potentials generalizing the hartmann and the oscillator ring shaped potentials the overlap coefficients between wavefunctions in spherical and parabolic cylindrical coordinates are shown to coincide with clebsch gordan coefficients for su 1 1 algebra

general potentials described by so 2 1 dynamical algebra in parabolic coordinate systems the authors propose general three dimensional potentials in rotational and cylindrical parabolic coordinates which are generated by direct products of the so 2 1 dynamical group then they construct their green functions algebraically and find their spectra particular cases of these potentials which appear in the literature are also briefly discussed

invariant subspaces quasi invariant subspaces and hankel operators abstract in this paper using the theory of hilbert modules we study invariant subspaces of the bergman spaces on bounded symmetric domains and quasi invariant subspaces of the segal bargmann spaces we completely characterize small hankel operators with finite rank on these spaces

algebraic calculation of the green s function for the hartmann potential using the so 2 1 lie algebra and the baker campbell hausdorff formulas the green s function for the hartmann potential is constructed and its bound state energy spectrum is found also this green s function is constructed in a coherent state basis and the equivalence of the two descriptions is shown

algebraic treatment of super integrable potentials the so 2 1 lie algebra is applied to three classes of two and three dimensional smorodinsky winternitz super integrable potentials for which the path integral discussion has been recently presented in the literature we have constructed the green s functions for two important super integrable potentials in r2 among the super integrable potentials in r3 we have considered two examples one is maximally super integrable and another one minimally super integrable the discussion is made in various coordinate systems the energy spectrum and the suitably normalized wave functions of bound and continuous states are then deduced

finite codimensional invariant subspaces of bergman spaces abstract for a large class of bounded domains in c we describe thosefinite codimensional subspaces of the bergman space that are invariant undermultiplication by z using different techniques for certain domains in cn wedescribe those finite codimensional subspaces of the bergman space that areinvariant under multiplication by all the coordinate functions fix a positive integer n and let v denote lebesgue volume measure on cn sothat if n 1 then v is just area measure let q c c be a domain which asusual means that 0 is a nonempty open connected subset of c for an analyticfunction from 0 to c and 1 p oo the norm n p is defined by wfh r jn f pdv the bergman space l q is defined to be the set of analytic functions from fi toc such that n p oo our goal in this paper is to describe the closed finite codimensional subspaces oflpa 0 that are invariant under multiplication by the coordinate functions zi

the core operator and congruent submodules abstract the hardy spaces h 2 d 2 can be conveniently viewed as a module over the polynomial ring c z 1 z 2 submodules of h 2 d 2 have connections with many areas of study in operator theory a large amount of research has been carried out striving to understand the structure of submodules under certain equivalence relations unitary equivalence is a well known equivalence relation in set of submodules however the rigidity phenomenon discovered in douglas et al algebraic reduction and rigidity for hilbert modules amer j math 117 1 1995 75 92 and some other related papers suggests that unitary equivalence being extremely sensitive to perturbations of zero sets lacks the flexibility one might need for a classification of submodules in this paper we suggest an alternative equivalence relation namely congruence the idea is motivated by a symmetry and stability property that the core operator possesses the congruence relation effectively classifies the submodules with a finite rank core operator near the end of the paper we point out an essential connection of the core operator with operator model theory

invariant subspaces with finite codimension in bergman spaces let omega be a domain in the complex plane denote by l p roman a omega 1 le p infty the bergman space over omega the author presents a description of finite codimensional space e subset l p roman a omega such that ze subset e under some conditions on omega an analogous result is due to n s axler en and n p bourdon en same journal bf306 1988 no 2 805 817 mr0933319 89f 46051 for an arbitrary bounded domain in c there are described those finite codimensional subspaces of the bergman space that are invariant under multiplication by z

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

solvable potentials generated by sl 2 r canonical transformations are used to build realisations of sl 2 r in terms of the basic quantum mechanical operators q and p the results are used to construct solvable potentials in the framework of one dimensional quantum mechanics

global mu synchronization of linearly coupled unbounded time varying delayed neural networks with unbounded delayed coupling in this brief we study the global synchronization of linearly coupled neural networks with delayed couplings where the intrinsic systems are recurrently connected neural networks with unbounded time varying delays and the couplings include instant couplings and unbounded delayed couplings the concept of mu synchronization is introduced some sufficient conditions are derived for the global mu synchronization for the underlined coupled systems

a new ring shaped potential and its dynamical invariance algebra a new ring shaped potential obtained by replacing the coulomb part of the hartmann potential by a harmonic oscillator term is investigated the schrodinger equation is solved in spherical circular cylindrical prolate and oblate spheroidal coordinates as in the case of the hartmann potential the accidental degeneracies occurring in the spectrum are shown to be due to an su 2 dynamical invariance algebra this establishes a close connection between both ring shaped potentials

operator theory and algebraic geometry on presente des resultats en theorie des operateurs multivariable dont les demonstrations se relient a des techniques issues de la geometrie algebrique

single variable realisation of the su 1 1 spectrum generating algebra and discrete eigenvalue spectra of a class of potentials a wide range of operators can be expressed in terms of the generators of the su 1 1 algebra the spectral properties of which are well known we attempt to find a realisation of the algebra in its most general form and thus evolve a unified approach to the problem of finding the spectra of hamiltonians amenable to the technique rather than taking each case separately we extend the analysis to obtain the spectra of potentials whose coordinate dependence is implicit