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

toeplitz operators on doubling fock spaces abstract we study toeplitz operator theory on the doubling fock spaces which are fock spaces whose exponential weight is associated to a subharmonic function with doubling riesz measure namely we characterize the boundedness compactness and membership in the schatten class of toeplitz operators on doubling fock spaces whose symbol is a positive radon measure

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

operators on spaces of analytic functions belonging to l 1 abstract let h be a separable hilbert space and k be the ideal of compact operators on h a t k is said to be in l 1 if n t o log n for n 2 or equivalently supn 2 1 log n n1 n t l 1 specifically we will show that the function space characterizing the symbols of these operators is a nonseparable banach space which lies strictly between b1 d and all the other holomorphic besov spaces bp d p 1

on the derivative nonlinear schro dinger equation abstract in this paper we discuss the cauchy problem for the derivative nonlinear schrodinger equation i t 2i x 2 0 0 x x where 0 under an explicit smallness condition of the initial data we prove the unique global existence of solutions to this problem in the usual sobolev spaces in the weighted sobolev spaces and in the schwartz class we describe the smoothing effect in detail furthermore for the data decaying exponentially at infinity we prove that the above equation has unique local solutions which are analytic in the space direction

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

integration operators between hardy spaces on the unit ball of cn abstract we completely describe the boundedness of the volterra type operator j g between hardy spaces in the unit ball of c n the proof of the one dimensional case used tools such as the strong factorization for hardy spaces that are not available in higher dimensions and therefore other techniques must be used in particular a generalized version of the description of hardy spaces in terms of the area function is needed

characterizations of certain classes of hankel operators on the bergman spaces of the unit disk let f be an integrable function on the unit disk the hankel operator hf is densely defined on the bergman space ap by hfg fg p fg where g is a bounded analytic function and p is the bergman projection orthogonal projection from l2 to a2 extended to l1 via its integral formula in this paper the functions f for which hf extends to a bounded operator from ap to lp are characterized 1 p also characterized are the functions f for which hf extends to a compact or schatten class operator on a2 the proofs can be extended to handle any smoothly bounded domain in c in place of the unit disk

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

on boundedness and compactness of toeplitz operators in weighted h spaces abstract we characterize the boundedness and compactness of toeplitz operators t a with radial symbols a in weighted h spaces h v on the open unit disc of the complex plane the weights v are also assumed radial and to satisfy the condition b introduced by the second named author the main technique uses taylor coefficient multipliers and the results are first proved for them we formulate a related sufficient condition for the boundedness and compactness of toeplitz operators in reflexive weighted bergman spaces on the disc we also construct a bounded harmonic symbol f such that t f is not bounded in h v for any v satisfying mild assumptions as a corollary the bergman projection is never bounded with respect to the corresponding weighted sup norms however we also show that for normal weights v all toeplitz operators with a trigonometric polynomial as the symbol are bounded on h v

well posedness and smoothing effect of schrodinger poisson equation in this work we take under consideration the cauchy problem for the schrodinger poisson type equation i tu x2u v u u f u 2 u where f represents a local nonlinear interaction we take into account both attractive and repulsive models and v is taken as a suitable solution of the poisson equation v 1 2 x c u 2 c cc is the doping profile or impurities we show that this problem is locally well posed in the weighted sobolev spaces hs hs r 1 x2 1 2 2 with s 1 which means the local existence uniqueness and continuity of the solution with respect to the initial data moreover under suitable assumptions on the local interaction we show the existence of global solutions finally we establish that for s 1 local in time and space smoothing effects are present in the solution more precisely in this problem there is locally a gain of half a derivative

toeplitz operators defined by sesquilinear forms fock space case the classical theory of toeplitz operators in spaces of analytic functions deals usually with symbols that are bounded measurable functions on the domain in question a further extension of the theory was made for symbols being unbounded functions measures and compactly supported distributions all of them subject to some restrictions in the context of a reproducing kernel hilbert space we propose a certain framework for a maximally possible extension of the notion of toeplitz operators for a maximally wide class of highly singular symbols using the language of sesquilinear forms we describe a certain common pattern for a variety of analytically defined forms which besides the covering of all previously considered cases permits us to introduce a further substantial extension of a class of admissible symbols that generate bounded toeplitz operators although our approach is unified for all reproducing kernel hilbert spaces for concrete operator consideration in this paper we restrict ourselves to toeplitz operators acting on the standard fock or segal bargmann space

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

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

a generalized hilbert matrix acting on hardy spaces abstract if is a positive borel measure on the interval 0 1 the hankel matrix h n k n k 0 with entries n k 0 1 t n k d t induces formally the operator h f z n 0 k 0 n k a k z n on the space of all analytic functions f z k 0 a k z k in the unit disc d in this paper we describe those measures for which h is a bounded compact operator from h p into h q 0 p q we also characterize the measures for which h lies in the schatten class s p h 2 1 p

asymptotic behavior of eigenvalues of toeplitz operators on the weighted analytic spaces abstract in this paper we consider toeplitz operators on a class of analytic function spaces including standard bergman spaces on the unit disc and bargman fock spaces we give a complete characterization of those compact operators whose eigenvalues have a prescribed slow decay to zero

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

hankel operators on the bergman space of bounded symmetric domains let q be a bounded symmetric domain in cin with normalized volume measure dv let p be the orthogonal projection from l 2 q d v onto the bergman space la q of holomorphic functions in l 2 q d v let a p be the orthogonal projection from l 2 q dv onto the closed subspace of antiholomorphic functions in l 2 2 d v the little hankel operator hf with symbol f is the operator from l2 q into l2 q d v defined by hfg p fg we characterize the boundedness compactness and membership in the schatten classes of the hankel operators hf in terms of a certain integral transform of the symbol f these characterizations are further studied in the special cases of the open unit ball and the poly disc in cn

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

analyticity and global existence of small solutions to some nonlinear schrodinger equations in this paper we will study the nonlinear schrodinger equations begin gathered i partial t u tfrac 1 2 delta u left u right 2 u t x in mathbb r times mathbb r x n hfill u 0 x phi x x in mathbb r x n hfill end gathered it is shown that the solutions of exist and are analytic in space variables fort 0 if x h2n 1 2 xn decay exponentially as x andn 2

strong correlations between text quality and complex networks features abstract concepts of complex networks have been used to obtain metrics that were correlated to text quality established by scores assigned by human judges texts produced by high school students in portuguese were represented as scale free networks word adjacency model from which typical network features such as the in outdegree clustering coefficient and shortest path were obtained another metric was derived from the dynamics of the network growth based on the variation of the number of connected components the scores assigned by the human judges according to three text quality criteria coherence and cohesion adherence to standard writing conventions and theme adequacy development were correlated with the network measurements text quality for all three criteria was found to decrease with increasing average values of outdegrees clustering coefficient and deviation from the dynamics of network growth among the criteria employed cohesion and coherence showed the strongest correlation which probably indicates that the network measurements are able to capture how the text is developed in terms of the concepts represented by the nodes in the networks though based on a particular set of texts and specific language the results presented here point to potential applications in other instances of text analysis

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

analytic solutions to nonelliptic nonlinear schrodinger equations abstract we prove local existence of analytic solutions for nonlinear schrodinger type equations the class we consider includes a number of equations derived from the physical context of water waves

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

a metric to search for relevant words abstract we propose a new metric to evaluate and rank the relevance of words in a text the method uses the density fluctuations of a word to compute an index that measures its degree of clustering highly significant words tend to form clusters while common words are essentially uniformly spread in a text if a word is not rare the metric is stable when we move any individual occurrence of this word in the text furthermore we prove that the metric always increases when words are moved to form larger clusters or when several independent documents are merged using the holy bible as an example we show that our approach reduces the significance of common words when compared to a recently proposed statistical metric

schatten class toeplitz operators on generalized fock spaces abstract in this paper we characterize the schatten p class membership of toeplitz operators with positive measure symbols acting on generalized fock spaces for the full range 0 p

characterizations for besov spaces and applications part i the main theorem of this paper gives a characterization for holomorphic besov space bp d over a large class of bounded domains d in cn which states that there is a bounded linear operator vd bp d lp d d so that pvd i on bp d where p is the bergman projection and d z k z z dv is the biholomorphic invariant measure with k z z being bergman kernel function for d moreover some application for characterizing schatter von neumann p class small hankel operation is given as a direct consequence of this theorem

embedding theorems and integration operators on bergman spaces with rapidly decreasing weights we completely describe those positive borel measures in the unit disc d such that the bergman space ap w lq 0 0 and some double exponential type weights as an application of that result we characterize the boundedness and the compactness of tg ap w aq w 0 p q w w where tg is the integration operator tgf z 0zf g d the particular choice of the weight w r answers an open question posed by a aleman and a siskakis we also describe those analytic functions in d for which tg belongs to the schatten p class of a2 w 0 p

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

toeplitz operators on the space of analytic functions with logarithmic growth abstract continuous and compact toeplitz operators for positive symbols are characterized on the space h v of analytic functions with logarithmic growth on the open unit disc of the complex plane the characterizations are in terms of the behaviour of the berezin transform of the symbol the space h v was introduced and studied by taskinen the bergman projection is continuous on this space in a natural way which permits to define toeplitz operators sufficient conditions for general symbols are also presented

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

forward and reverse carleson inequalities for functions in bergman spaces and their derivatives is satisfied in the process a simple proof of certain inequalities on derivatives of functions in hp is obtained section 3 as well as some information on interpolation sequences for lp section 5 inequalities like 1 1 have already been used to provide information on bergman toeplitz operators l1 and are useful for obtaining representations of functions in lp section 4 theorem 4 6 the inequality which reverses the roles of a and m in 1 1 is relatively easy even if an appropriate weighting factor is included with m theorem a below it was obtained by oleinik and pavlov op and independently when p q 1 by stegenga s and with c 0 hastings ha the results of oleinik and pavlov which are more general than theorem a were extended somewhat by oleinik in 0 cima and wogen cw using stegenga s methods proved the analogue of theorem a in several variables the methods of l3 more or less supercede all these results

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

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

well posedness of the initial value problem for the korteweg de vries equation 1 1 itu axu u1xu o x t e r u x 0 uo x the kdv equation which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves 21 has been considered in different contexts namely in its relation with the inverse scattering method in plasma physics and in algebraic geometry see 24 and references therein our purpose is to study local and global well posedness of the ivp 1 1 in classical sobolev spaces hs r we shall say that the ivp 1 1 is locally resp globally well posed in the function space x if it induces a dynamical system on x by generating a continuous local resp global flow it was established in the works of bona and smith 3 bona and scott 2 saut and temam 30 and kato 1 5 that the ivp 1 1 is locally resp globally well posed in hs with s 3 2 resp s 2 roughly speaking global well posedness in hs depends on the available local theory and on the conservation laws satisfied by solutions of 1 1 namely

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

thesaurus as a complex network abstract a thesaurus is one out of many possible representations of term or word connectivity the terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph the directionality of the links retains all the thesaurus information and allows the measurement of several quantities this has lead to a new term classification according to the characteristics of the nodes for example nodes with no links in no links out etc using an electronic available thesaurus we have obtained the incoming and outgoing link distributions while the incoming link distribution follows a stretched exponential function the lower bound for the outgoing link distribution has the same envelope of the scientific paper citation distribution proposed by tsallis and albuquerque eur phys j b 13 2000 777 however a better fit is obtained by simpler function which is the solution of ricatti s differential equation we conjecture that this differential equation is the continuous limit of a stochastic growth model of the thesaurus network we also propose a new manner to arrange a thesaurus using the inversion method