global integral criteria for composition operators abstract let d denote the dirichlet type space of functions analytic on the unit disk u and q the conformal invariant version of this space any analytic self map of u induces a composition operator c acting on d respectively q by c f f where f d respectively f q the aim of this paper is to characterize boundedness and compactness of such operators in terms of global area integrals of

analytic solutions of the fisher equation the authors analyse the fisher equation via the expanded painleve analysis approach they obtain its singular property auto backlund transformation and analytic solutions including some interesting heteroclinic and homoclinic solutions

compact composition operators on weighted hilbert spaces of analytic functions we characterize the compactness of composition operators acting on a large family of hilbert spaces of analytic functions which lie between bergman and dirichlet spaces our characterization is given in terms of generalized nevanlinna counting functions

composition operators on hardy spaces on lavrentiev domains in this note composition operators on bergman spaces of a simply connected domain are studied characterizing boundedness and compactness of such operators whenever the domain is lavrentiev

invariant solutions of certain nonlinear evolution type equations with small parameters the fisher equation which arises in the study of reaction diffusion waves in biology does not display a high level of symmetry properties consequently only travelling wave solutions are obtainable using the method of invariants this has a direct bearing on studying perturbed forms of the equation which may arise from considering e g damping or dissipative factors we show here how one can get around this limitation by appending some unknown function to the perturbation and obtain interesting practical results using invariants the ideas have significant consequences for equations which do not admit large class of symmetry properties the method used in this analysis is then extended to other classes of evolution type equations that involve perturbations for e g the kdv type equations

bispectrum estimation a parametric approach higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality estimation of the bispectrum which is a third order spectrum has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non gaussianness of processes existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations the paper proposes a parametric approach to bispectrum estimation based on a non gaussian white noise driven autoregressive ar model the ar parameter estimates are obtained by solving the third order recursion equations which may be toeplitz in form but not symmetric it is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids the method provides significantly better resolution

trace class criteria for toeplitz and composition operators on small bergman spaces abstract we characterize the schatten class toeplitz operators induced by a positive borel measure on the unit disc and the reproducing kernel of the bergman space a 2 where is a radial weight satisfying the doubling property r 1 s d s c 1 r 2 1 s d s by using this we describe the schatten class composition operators we also discuss basic properties of composition operators acting from a p to a v q

composition operators on noncommutative hardy spaces abstract in this paper we initiate the study of composition operators on the noncommutative hardy space h ball 2 which is the hilbert space of all free holomorphic functions of the form f x 1 x n k 0 k a x f n a 2 1 where the convergence is in the operator norm topology for all x 1 x n in the noncommutative operatorial ball b h n 1 and b h is the algebra of all bounded linear operators on a hilbert space h when the symbol is a free holomorphic self map of b h n 1 we show that the composition operator c f f f h ball 2 is bounded on h ball 2 several classical results about composition operators boundedness norm estimates spectral properties compactness similarity have free analogues in our noncommutative multivariable setting the most prominent feature of this paper is the interaction between the noncommutative analytic function theory in the unit ball of b h n the operator algebras generated by the left creation operators on the full fock space with n generators and the classical complex function theory in the unit ball of c n in a more general setting we establish basic properties concerning the composition operators acting on fock spaces associated with noncommutative varieties v p 0 h b h n 1 generated by sets p 0 of noncommutative polynomials in n indeterminates such that p 0 0 p p 0 in particular when p 0 consists of the commutators x i x j x j x i for i j 1 n we show that many of our results have commutative counterparts for composition operators on the symmetric fock space and consequently on spaces of analytic functions in the unit ball of c n

compactness of resolvent operators generated by a class of composition semigroups on hp consider a semigroup of composition operators t tf f circ phi t t geq 0 acting on the standard hardy space h p 1 leq p infty of the unit disk d assuming that the phi t have a common fixed point at 0 a unique univalent function h can be found such that h phi t z e ct h z z in d t geq 0 where c is a constant which is related to the infinitesimal generator a of t t in this paper the compactness of the resolvent operator r lambda a is studied using the function h it is shown that r lambda a is compact if and only if h lies in h q for each q infty in the cases where r lambda a is not compact it is shown that the spectrum of r lambda a contains a nontrivial disk a condition under which compactness of r lambda a implies compactness of the operators in t t is also obtained the methods used are function theoretic in particular the notion of a spiral like function plays a key role less

nonlinear evolution type equations and their exact solutions using inverse variational methods we present the role of invariants in obtaining exact solutions of differential equations firstly conserved vectors of a partial differential equation p d e allow us to obtain reduced forms of the p d e for which some of the lie point symmetries in vector field form are easily concluded and therefore provide a mechanism for further reduction secondly invariants of reduced forms of a p d e are obtainable from a variational principle even though the p d e itself does not admit a lagrangian in this latter case the reductions carry all the usual advantages regarding noether symmetries and double reductions the examples we consider are nonlinear evolution type equations such as the korteweg devries equation but a detailed analysis is made on the fisher equation which describes reaction diffusion waves in biology inter alia other diffusion type equations lend themselves well to the method we describe e g the fitzhugh nagumo equation which is briefly discussed some aspects of painleve properties are also suggested

hausdorff measures capacities and compact composition operators it is shown that there exist analytic self maps of the unit disc inducing compact composition operators on the hardy space 1 p such that the hausdorff dimension of the set is one sharpening a classical result due to schwartz moreover the same holds in the weighted dirichlet spaces with 0 1 as a consequence we deduce that there exist symbols inducing compact composition operators on such that the capacity of e is positive which is no longer true for those just inducing hilbert schmidt composition operators on

completely continuous composition operators a composition operator tbf f o b is completely continuous on h1 if and only if lbl 1 a e if the adjoint operator tb is completely continuous on vmoa then tb is completely continuous on h1 examples are given to show that the converse fails in general two results are given concerning the relationship between the complete continuity of an operator and of its adjoint in the presence of certain separability conditions on the underlying banach space

compact composition operators on h 2 and hardy orlicz spaces abstract we compare the compactness of composition operators on h 2 and on orlicz hardy spaces h we show that for every 1 p there exists an orlicz function such that h p e h h p for every e 0 and a composition operator c which is compact on h p and on h p e but not on h we also show that for every orlicz function which does not satisfy condition 2 there is a composition operator c which is compact on h 2 but not on h and that when grows fast enough there is a function such that c is in all schatten classes s p for p 0 but is not compact on h

difference of weighted composition operators abstract we obtain complete characterizations in terms of carleson measures for bounded compact differences of weighted composition operators acting on the standard weighted bergman spaces over the unit disk unlike the known results we allow the weight functions to be non holomorphic and unbounded as a consequence we obtain a compactness characterization for differences of unweighted composition operators acting on the hardy spaces in terms of carleson measures and as a nontrivial application of this we show that compact differences of composition operators with univalent symbols on the hardy spaces are exactly the same as those on the weighted bergman spaces as another application we show that an earlier characterization due to acharyya and wu for compact differences of weighted composition operators with bounded holomorphic weights does not extend to the case of non holomorphic weights we also include some explicit examples related to our results

adjoints of composition operators on hardy spaces of the half plane abstract building on techniques used in the case of the disc we use a variety of methods to develop formulae for the adjoints of composition operators on hardy spaces of the upper half plane in doing so we prove a slight extension of a known necessary condition for the boundedness of such operators and use it to provide a complete classification of the bounded composition operators with rational symbol we then consider some specific examples comparing our formulae with each other and with other easily deduced formulae for simple cases

composition operators with univalent symbol in schatten classes abstract we study composition operators induced by a sub domain of the unit disc whose boundary intersects the unit circle at 1 and which has in a neighborhood of 1 a polar equation 1 r see fig 1 we obtain an explicit characterization for the membership in schatten p classes in terms of

compact differences of composition operators abstract a characterization of compact difference is given for composition operators acting on the standard weighted bergman spaces and necessary conditions are given on a larger scale of weighted dirichlet spaces conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts the additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component

measures induced by analytic functions and a problem of walter rudin let h denote the set of bounded analytic functions in the unit disk u zec izi l and let ho denote those p e h for which p 0 0 every p e h has a nontangential limit at almost every point of u and the resulting function on du is measurable for this and other basic facts about h and related function spaces discussed in this paper see e g d g we denote the boundary function of p also by p and define the induced measure of p by the formula

a new numerical scheme for the fisher equation in the context of the one dimensional fisher equation 1937 the authors study a new numerical scheme for reaction diffusion equations proposed by oono and puri 1987 they find that this scheme enables a reasonable simulation of the fisher equation at high values of the time increment where conventional schemes are not applicable for lower values of the time increment the new scheme compares favourably with conventional schemes

conservation laws of high order nonlinear pdes and the variational conservation laws in the class with mixed derivatives the construction of conserved vectors using noether s theorem via a knowledge of a lagrangian or via the recently developed concept of partial lagrangians is well known the formulas to determine these for higher order flows are somewhat cumbersome but peculiar and become more so as the order increases we carry out these for a class of high order partial differential equations from mathematical physics and then consider some specific ones with mixed derivatives in the latter set of examples our main focus is that the resultant conserved flows display some previously unknown interesting divergence properties owing to the presence of the mixed derivatives overall we consider a large class of equations of interest and construct some new conservation laws

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

nearly weakly orthonormal sequences singular value estimates and calderon zygmund operators abstract the direct way to estimate the singular values of a compact operator is to decompose it as a sum of orthogonal rank one pieces however such decompositions can generally not be found in practice we give a variation of the decomposition using nearly weakly orthonormal nwo sequences the nwo decomposition is easier to do in examples but is still strong enough to give good singular value estimates we illustrate this by giving sharp trace ideal estimates for the double layer potential and for the first and higher commutators of multiplication operators and calderon zygmund operators in particular nwo sequences seem well suited for dealing with operators which depend nonlinearly on their symbol we also show that the class of operators which admit nwo expansions is well behaved under composition under conjugation by weights and under conjugation by changes of variable

compact composition operators on bergman orlicz spaces we construct an analytic self map of the unit disk and an orlicz functionfor which the composition operator of symbol is compact on the hardy orlicz space h but not on the bergman orlicz space b for that we first prove a carleson embedding theorem and then characterize the compact ness of composition operators on bergman orlicz spaces in terms of carleson function of order 2 we show that this carleson function is equivalent to the nevanlinna counting function of order 2 mathematics subject classification primary 47b33 secondary 30d50 30d55 46e15

on compactness of the difference of composition operators abstract let and be analytic self maps of the unit disc and denote by c and c the induced composition operators the compactness and weak compactness of the difference t c c are studied on h p spaces of the unit disc and l p spaces of the unit circle it is shown that the compactness of t on h p is independent of p 1 the compactness of t on l 1 and m the space of complex measures is characterized and examples of and are constructed such that t is compact on h 1 but non compact on l 1 other given results deal with l weakly compact counterparts of the previous results and a conjecture of j e shapiro

an application of atomic decomposition in bergman spaces to the study of differences of composition operators abstract in this paper we characterize bounded differences of composition operators from standard weighted bergman spaces a p into lebesgue spaces l q when 1 and p q in the process we also find an interesting connection between the difference operator and certain weighted composition operators answering a question raised in saukko 2011 18 by combining the results of this paper with those of saukko 2011 18 we obtain a complete characterization of bounded and compact differences between standard weighted bergman spaces

carleson embeddings and some classes of operators on weighted bergman spaces we prove carleson type embedding theorems for weighted bergman spaces with bekolle weights we use this to study properties of toeplitz type operators integration operators and composition operators acting on such spaces in particular we investigate the membership of these operators to schatten class ideals

spectral theory for algebraic combinations of toeplitz and composition operators abstract we determine the essential spectra of algebraic combinations of toeplitz operators with continuous symbol and composition operators induced by a class of linear fractional non automorphisms of the unit disk the operators in question act on the hardy space h 2 on the unit disk our method is to realize the c algebra that they generate as an extension of the compact operators by a concrete c algebra whose invertible elements are easily characterized

toeplitzness of products of composition operators and their adjoints we examine the toeplitzness of products of composition operators and their adjoints we show among other things that c c is strongly asymptotically toeplitz for all analytic self maps of the unit disk and that c c is toeplitz if and only if is the identity or a rotation also we see that c c can exhibit varying degrees of asymptotic toeplitzness

subnormality and composition operators on h2 if is a non constant analytic function defined on the unit disk d such that d d the composition operator c is the operator on the hardy space h2 of the unit disk defined by c f f in this paper we investigate the relationship between properties of the symbol and the subnormality of the operators c and c the main theorem shows under a regularity hypothesis that c is subnormal if and only if is in a restricted class of linear fractional transformations the two previously known special cases the affine transformations associated with the cesaro operator and the automorphisms are included as the extreme examples the proof of the main theorem consists of verifying a moment condition and yields in addition the construction of a measure that exhibits cgj as multiplication by an analytic function on p2 and the identification of the minimal normal extension as a weighted sum of shifts

difference of composition operators between different hardy spaces abstract some estimates for the norm and essential norm of the difference of two composition operators between different hardy spaces are given in this paper

contact points and schatten composition operators we study composition operators on hardy and dirichlet spaces belonging to schatten classes we give some new examples and analyse the size of contact set of the symbol of such operators

trace ideal criteria for embeddings and composition operators on model spaces abstract let k be a model space generated by an inner function we study the schatten class membership of composition operators c k h 2 d with a holomorphic function d d and more generally of embeddings i k l 2 with a positive measure in d in the case of one component inner functions we show that the problem can be reduced to the study of natural extensions of i and c to the hardy smirnov space e 2 d in some domain d d in particular we obtain a characterization of schatten membership of c in terms of nevanlinna counting function by example this characterization does not hold true for general

composition operators belonging to operator ideals abstract with each composition operator c f f acting between classical bergman spaces ap and aq 1 p q a if and only if the diagonal operator d lp lq given by ak ak k belongs to a conversely we show that for any max 2 q 2 p 0 and r there exists a composition operator c ap aq whose associated sequence is equivalent to k log k k 2 this provides an effective tool to separate quasi banach ideals by means of composition operators the results can be generalized to standard weighted bergman spaces and beyond

boundary correspondence of nevanlinna counting functions for self maps of the unit disc let be a holomorphic self map of the unit disc d for every a d there is a measure on d sometimes called aleksandrov measure defined by the poisson representation re z z f p z d its singular part measures in a natural way the affinity of for the boundary value a the affinity for values w inside d is provided by the nevanlinna counting function n w of we introduce a natural measure valued refinement m w of n w and establish that the measures d are obtained as boundary values of the refined nevanlinna counting function m more precisely we prove that is the weak limit of m w whenever w converges to a non tangentially outside a small exceptional set e we obtain a sharp estimate for the size of e in the sense of capacity

linear relations in the calkin algebra for composition operators we consider this and related questions when is a finite linear combination of composition operators acting on the hardy space or the standard weighted bergman spaces on the unit disk a compact operator

compact composition operators on besov spaces we give a carleson measure characterization of the compact composition operators on besov spaces we use this characterization to show that every compact composition operator on a besov space is compact on the bloch space finally we give conditions that guarantee that the converse holds

essential norm of composition operators between weighted hardy spaces abstract an asymptotic formula for the essential norm of composition operators acting between two weighted hardy spaces h w 1 and h w 2 where w1 and w2 are two admissible weight functions is given the boundedness of the operators is also characterized

composition operators acting on weighted dirichlet spaces abstract we study composition operators acting on weighted dirichlet spaces we obtain estimates for the essential norm describe the membership in schatten von neumann ideals and characterize the composition operators with closed range

arma bispectrum approach to nonminimum phase system identification an identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase fir finite impulse response system the method is based on parametric modeling of the third moments of the output sequence and uses causal and anticausal autoregressive moving average arma models the magnitude and phase response of the system are expressed in terms of the ar parameters of the arma models in particular the ar part of the causal arma model captures the minimum phase component of the system and the ar part of the anticausal arma captures the maximum phase component both sets of parameters are obtained by solving overdetermined linear systems of equations a model order selection criterion based on third order moments is proposed the arma bispectrum approach is compared to more conventional approaches for magnitude and phase reconstruction it is demonstrated that the proposed identification procedure exhibits improved modeling performance the method does not require knowledge of the non gaussian noise distribution

composition operators on the normal weight zygmund spaces in high dimensions abstract let be a normal function on 0 1 suppose that is a holomorphic self map on the unit ball b of c n in this paper the authors give a new kind of equivalent norm of the normal weight zygmund space z b on the basis of recent work the authors further study boundedness criteria of composition operators c on z b and the essential norm of c for all normal weights when 0 1 0 r d t t d r or 0 1 d r r the authors further give a brief compactness criteria of c on z b or b

norms of linear fractional composition operators we obtain a representation for the norm of the composition operator c on the hardy space h 2 whenever is a linear fractional mapping of the form z b cz d the representation shows that for such mappings the norm of c always exceeds the essential norm of c moreover it shows that a formula obtained by cowen for the norms of composition operators induced by mappings of the form z sz t has no natural generalization that would yield the norms of all linear fractional composition operators for rational numbers s and t cowen s formula yields an algebraic number as the norm we show e g that the norm of c 1 2 z is a transcendental number our principal results are based on a process that allows us to associate with each non compact linear fractional composition operator c for which c c e an equation whose maximum real solution is c 2 our work answers a number of questions in the literature for example we settle an issue raised by cowen and maccluer concerning co hyponormality of a certain family of composition operators

in koenigs footsteps diagonalization of composition operators abstract let d d be a holomorphic map with a fixed point d such that 0 1 we show that the spectrum of the composition operator c on the frechet space hol d is 0 n n 0 1 and its essential spectrum is reduced to 0 this contrasts the situation where a restriction of c to banach spaces such as h 2 d is considered our proofs are based on explicit formulae for the spectral projections associated with the point spectrum found by koenigs finally as a byproduct we obtain information on the spectrum for bounded composition operators induced by a schroder symbol on arbitrary banach spaces of holomorphic functions

mean growth of koenigs eigenfunctions in 1884 g koenigs solved schroeder s functional equation f o a af in the following context is a given holomorphic function mapping the open unit disk u into itself and fixing a point a e u f is holomorphic on u and a is a complex scalar koenigs showed that if 0 equation for p has a unique holomorphic solution cr satisfying a co p a a and o 0 1 moreover he showed that the only other solutions are the obvious ones given by constant multiples of powers of a we call a the koenigs eigenfunction of motivated by fundamental issues in operator theory and function theory we seek to understand the growth of integral means of koenigs eigenfunctions for 0 of to belong to the hardy space hp and show that the condition is necessary when is analytic on the closed disk for many mappings the condition may be expressed as a relationship between p a and derivatives of at points on ou that are fixed by some iterate of our work depends upon a formula we establish for the essential spectral radius of any composition operator on the hardy space hp department of mathematics washington and lee university lexington virginia 24450 e mail address pbourdonfwlu edu department of mathematics michigan state university east lansing michigan 48824 e mail address shapirofmath msu edu this content downloaded from 157 55 39 211 on sat 25 jun 2016 06 33 26 utc all use subject to http about jstor org terms

trace ideal criteria for toeplitz operators for a complex measure on the open unit disk u define an operator t on a hilbert space h of analytic functions with reproducing kernel k z w by u for a certain scale of hilbert spaces h 1 which includes the hardy space h2 and weighted bergman spaces a2 conditions are obtained which imply t belongs to a schatten ideal sp if is a positive measure then these conditions are necessary and sufficient application to composition operators and restriction operators are indicated

weighted differentiation composition operators from mixed norm spaces to weighted type spaces motivated by the recent paper x zhu products of differentiation composition and multiplication from bergman type spaces to bers spaces integral transform spec funct 18 3 2007 223 231 we study the boundedness and compactness of the weighted differentiation composition operator d f u n f z u z f n f z where u is a holomorphic function on the unit disk d f is a holomorphic self map of d and email protected n 0 from the mixed norm space h p q f where p q 0 and f is normal to the weighted type space h m or the little weighted type space h m 0 for the case of the weighted bergman space a a p p 1 some bounds for the essential norm of the operator are also given

essential norm estimates for composition operators on bmoa abstract we provide two function theoretic estimates for the essential norm of a composition operator c acting on the space bmoa one in terms of the n th power n of the symbol and one which involves the nevanlinna counting function we also show that if the symbol is univalent then the essential norm of c is comparable to its essential norm on the bloch space

the koebe semigroup and a class of averaging operators on hp d we study on the hardy space h p the operators t f given by formule where f z is analytic on the unit disc d and has re f z 0 each such operator is closely related to a strongly continuous semigroup of weighted composition operators by studying first an extremal such semigroup the koebe semigroup we are able to obtain the upper bound t f p 2p re 1 f 0 im 1 f 0 for the norm we also show that t f is compact on h p if and only if the measure in the herglotz representation of 1 f is continuous

small bergman orlicz and hardy orlicz spaces and their composition operators we show that the weighted bergman orlicz space a alpha psi coincides with some weighted banach space of holomorphic functions if and only if the orlicz function psi satisfies the so called delta 2 condition in addition we prove that this condition characterizes those a alpha psi on which every composition operator is bounded or order bounded into the orlicz space l alpha psi this provides us with estimates of the norm and the essential norm of composition operators on such spaces we also prove that when psi satisfies the delta 2 condition a composition operator is compact on a alpha psi if and only if it is order bounded into the so called morse transue space m alpha psi our results stand in the unit ball of mathbb c n

on the connected component of compact composition operators on the hardy space we show that there exist non compact composition operators in the connected component of the compact ones on the classical hardy space h2 this answers a question posed by shapiro and sundberg in 1990 we also establish an improved version of a theorem of maccluer giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols as a main tool we use aleksandrov clark measures

composition operators from bloch type spaces to hardy and besov spaces boundedness and compactness of composition operators from bloch type spaces to hardy spaces and analytic besov spaces are characterized by function theoretic properties of their inducing maps for the case of the bloch space the characterizations involve the hyperbolic versions of hardy and besov classes the conditions for the hyperbolic besov classes are then interpreted geometrically when the symbols are univalent and strict inclusion between different hyperbolic besov classes is shown by an example

travelling wave and similarity solutions to nonlinear evolution type equations through inverse variational and symmetry methods abstract shallow water equations are usually modelled by nonlinear kdv type equations of which various generalisations now exist for example there are vector versions of the modified kdv equation and shallow water equations with nonlinear internal waves we discuss the reduction and solutions of these and other large classes of such type of equations using inverse variational and symmetry methods

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

solitary wave solutions to some classes of nonlinear evolution type equations using inverse variational methods abstract invariants of reduced forms of a p d e are obtainable from a variational principle even though the p d e itself does not admit a lagrangian the reductions carry all the advantages regarding noether symmetries and double reductions via first integrals or conserved quantities the examples we consider are nonlinear evolution type equations like the general form of the fizhugh nagumo and kdv burgers equations some aspects of painleve properties of the reduced equations are also obtained

on shapiroʼs compactness criterion for composition operators abstract we give an elementary and direct proof of the identity lim sup w 1 n w 1 w lim sup a 1 1 a 2 1 1 a h 2 2 for any analytic self map of z z 1 where n denotes the nevanlinna counting function of we further show that one can find analytic self maps of z z 1 where the composition operator c on the hardy space h 2 is compact such that n h 2 tends to zero at an arbitrarily slow rate as n even in the case that is univalent among these are new examples where c is compact on h 2 but not in any of the schatten classes

nevanlinna counting function and carleson function of analytic maps we show that the maximal nevanlinna counting function and the carleson function of analytic self maps of the unit disk are equivalent up to constants

closed range composition operators on hilbert function spaces abstract we show that a carleson measure satisfies the reverse carleson condition if and only if its berezin symbol is bounded below on the unit disk d we provide new necessary and sufficient conditions for the composition operator to have closed range on the bergman space the pull back measure of area measure on d plays an important role we also give a new proof in the case of the hardy space and conjecture a condition in the case of the dirichlet space

compact composition operators on the dirichlet space and capacity of sets of contact points we prove several results about composition operators on the dirichlet space d for every compact set k d of logarithmic capacity capk 0 there exists a schur function both in the disk algebra a d and in d such that the composition operator c is in all schatten classes sp d p 0 and for which k eit eit 1 eit eit 1 for every bounded composition operator c on d and every d the logarithmic capacity of eit eit is 0 every compact composition operator c on d is compact on b 2 and on h 2 in particular c is in every schatten class sp p 0 both on h2 and on b2 there exists a schur function such that c is compact on h 2 but which is not even bounded on d there exists a schur function such that c is compact on d but in no schatten class sp d

absolutely summing carleson embeddings on hardy spaces we consider the carleson embeddings of the classical hardy spaces on the disk into a l p space where is a carleson measure on the unit disk this includes the case of composition operators we characterize such operators which are r summing on h p where p 1 and r 1 this completely extends the former results on the subject and solves a problem open since the early seventies

toeplitz operators on harmonically weighted bergman spaces and applications to composition operators on dirichlet spaces abstract in this paper we consider toeplitz operators acting on bergman spaces associated with harmonic weights we give a complete description of those operators which belong to p schatten classes we also obtain an upper estimate for the reproducing kernel of these spaces applications to composition operators on dirichlet spaces are given

strongly disordered chain of impedances theoretical analysis and numerical results the authors study the input impedance of a chain of random resistors chosen according to a broad distribution i e decaying as a power law for large arguments as a function of frequency the modulus of the input impedance varies as a power law while its phase has a well defined value a simple theoretical analysis based on estimations of sums of random variables yields the value of the exponents which are in perfect agreement with numerical simulations even when logarithmic corrections come into play the analysis can be extended further to investigate the sample to sample fluctuations of the impedance again agreement with simulations is very good

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

some examples of compact composition operators on h2 abstract we construct in an essentially explicit way various composition operators on h 2 and study their compactness or their membership in the schatten classes we construct non compact composition operators on h 2 whose symbols have the same modulus on the boundary of d as symbols whose composition operators are in various schatten classes s p with p 2 compact composition operators which are in no schatten class but whose symbols have the same modulus on the boundary of d as symbols whose associated composition operators are in s p for every p 2

on higher order autospectra by maximum entropy method by r o plaisted and h g pena geophysics 48 1409 1410 october 1983 as stated in the short note by r o plaisted and h g pena they derived what they believed to be a maximum entropy mem representation for bispectra and they claimed that their result can be generalized to an nth order mem auto spectrum the purpose of this discussion is to point out the faults in the derivation and show that the claim of mem is not correct furthermore the parametric representation of the bispectrum that the authors actually attempted to derive is not new but can be found elsewhere huber et al 1971 plaisted and pena stated that the random variables et in their equation 1 can be assumed generally to be normally distributed with zero mean and variance e2 this is a serious mistake with this assumption the third order moment sequence of the xt process given by their equation 3 vanishes i e k l 0 for all k l and therefore the bispectrum of xt is identical to zero the random variables et in their equation 1 and hence xt have to be non gaussian for the b

composition operators between bergman and hardy spaces we study composition operators between weighted bergman spaces certain growth conditions for generalized nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact particular choices for the weights yield results on composition operators between the classical unweighted bergman and hardy spaces

on norms of composition operators acting on bergman spaces for arbitrary composition operators acting on a general bergman space we improve the known lower bound for the norm and also generalize a related recent theorem of d g pokorny and j e shapiro next we obtain a geometric formula for the norms of composition operators with linear fractional symbols thus extending a result of c cowen and p hurst and revealing the meaning of their computation finally we obtain a lower bound for essential norm of an arbitrary composition operator related to the well known criterion of b maccluer and j h shapiro as a corollary norms and essential norms are obtained for certain univalently induced noncompact composition operators in terms of the minimum of the angular derivative of the symbol

products of multiplication composition and differentiation operators on weighted bergman spaces abstract let be a holomorphic function on the open unit disk d and a holomorphic self map of d let c m and d denote the composition multiplication and differentiation operator respectively we consider linear operators induced by products of these operators on weighted bergman spaces on d the boundedness is established by using carleson type measures