commutators and related operators on harmonic bergman space of rn 1 abstract we study commutators and related operators on harmonic bergman space the l 2 r n 1 closure of the null space of laplacian by decomposing l 2 r n 1 into the sum of null spaces of powers of laplacian and using the theory of paracommutators studied in jp we characterize harmonic symbols for which the associated commutators are bounded or compact operators associated to the div curl theorem in clms in the theory of compensated compactness are also characterized

a characterization of bloch space and besov space on the unit disk of the complex plane a characterization for the membership of bloch space and analytic besov space is expressed extending known results

toeplitz and hankel operators on bergman spaces in this paper we consider toeplitz and hankel operators on the bergman spaces of the unit ball and the polydisk in c n whose symbols are bounded measurable functions we giv e necessary and sufficient conditions on the symbols for these operators to be compact we study the fredholm theory of topelitz operators for which the corresponding hankel operator is compact for these toeplitz operators the essential spectrum is computed and shown to be connected we also consider symbols that extend to continuous functions on the maximal ideal space of h for these symbols we describe when the toeplitz or hankel operators are compact

on the membership of hankel operators in a class of lorentz ideals abstract recall that the lorentz ideal c p is the collection of operators a satisfying the condition a p j 1 j p 1 p s j a consider hankel operators h f h 2 s l 2 s d h 2 s where h 2 s is the hardy space on the unit sphere s in c n in this paper we characterize the membership h f c p 2 n p

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

a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

the bergman space the bloch space and commutators of multiplication operators soit d le disque unite ouvert dans le plan complexe c soit h d l ensemble des fonctions analytiques bornees sur d on caracterise les fonctions feh d telles que t f t f tft f est un operateur compact ou t f est l operateur multiplication t f l a 2 l a 2 defini par t f g fg

limit operators compactness and essential spectra on bounded symmetric domains abstract this paper is a follow up to a recent article about the essential spectrum of toeplitz operators acting on the bergman space over the unit ball as mentioned in the said article some of the arguments can be carried over to the case of bounded symmetric domains and some cannot the aim of this paper is to close the gaps to obtain comparable results for general bounded symmetric domains in particular we show that a toeplitz operator on the bergman space a p is fredholm if and only if all of its limit operators are invertible even more generally we show that this is in fact true for all band dominated operators an algebra that contains the toeplitz algebra moreover we characterize compactness and explain how the berezin transform comes into play in particular we show that a bounded linear operator is compact if and only if it is band dominated and its berezin transform vanishes at the boundary for p 2 band dominated can be replaced by contained in the toeplitz algebra

a boundedness criterion for singular integral operators of convolution type on the fock space abstract we show that for an entire function belonging to the fock space f 2 c n on the complex euclidean space c n the integral operator s f z c n f w e z w z w d w z c n is bounded on f 2 c n if and only if there exists a function m l r n such that z r n m x e 2 x i 2 z 2 d x z c n here d w n e w 2 d w is the gaussian measure on c n with this characterization we are able to obtain some fundamental results of the operator s including the normality the c algebraic properties the spectrum and its compactness moreover we obtain the reducing subspaces of s in particular in the case n 1 we give a complete solution to an open problem proposed by k zhu for the fock space f 2 c on the complex plane c zhu 2015 30

on algebras generated by toeplitz operators and their representations abstract we study banach and c algebras generated by toeplitz operators acting on weighted bergman spaces a 2 b 2 over the complex unit ball b 2 c 2 our key point is an orthogonal decomposition of a 2 b 2 into a countable sum of infinite dimensional spaces each one of which can be identified with a differently weighted bergman space a 2 d over the complex unit disk d moreover all elements of the above algebras leave each of the summands in the above decomposition invariant and their restriction to each level acts as a compact perturbation of a toeplitz operator on a 2 d the symbols of the generating toeplitz operators are chosen to be suitable extensions to b 2 of families s of bounded functions on d symbol classes s that generate important classical commutative and non commutative toeplitz algebras in l a 2 d are of particular interest in this paper we discuss various examples in the case of s c d and s c d l 0 1 we characterize all irreducible representations of the resulting toeplitz operator c algebras their calkin algebras are described and index formulas are provided

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

non extensive behavior of a stock market index at microscopic time scales abstract this paper presents an empirical investigation of the intraday brazilian stock market price fluctuations considering q gaussian distributions that emerge from a non extensive statistical mechanics our results show that when price returns are measured over intervals less than one hour the empirical distributions are well fitted by q gaussians with exponential damped tails scaling behavior is also observed for these microscopic time intervals we find that the time evolution of the return distributions is according to a super diffusive q gaussian stationary process within a nonlinear fokker planck equation this regime breaks down due to the exponential fall off of the tails which in turn governs the transient dynamics to the long term macroscopic gaussian regime this exponentially damped non extensive modeling provides a new framework to investigate the dynamics of other stock markets intraday price fluctuations

products of hankel and toeplitz operators on the bergman space we consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products tftg are bounded on the bergman space we prove results analogous to those obtained by the second author 17 for such toeplitz products on the hardy space we furthermore obtain similar results for hankel products hfh g where f and g are square integrable on the unit disk and for the mixed haplitz products hftg and tgh f where f and g are square integrable on the unit disk and g is analytic

approximation in weighted bergman spaces and hankel operators on strongly pseudoconvex domains suppose d is a bounded strongly pseudoconvex domain in mathbb c n with smooth boundary and let rho be its defining function for 1 p infty and alpha 1 we show that the weighted bergman projection p alpha is bounded on l p d rho alpha dv with non isotropic estimates for overline partial and stein s theorem on non tangential maximal operators we prove that bounded holomorphic functions are dense in the weighted bergman space a p d rho alpha dv and hence hankel operators can be well defined on these spaces for all 1 p q infty we characterize bounded resp compact hankel operators from p th weighted bergman space to q th weighted lebesgue space with possibly different weights as a consequence we generalize the main results in pau et al indiana univ math j 65 1639 1673 2016 and resolve a question posed in lv and zhu integr equ oper theory 2019

gleason parts and cop let h denote the banach algebra of bounded analytic functions on the open unit disc d and let m h denote the maximal ideal space of h one of the results in this paper shows that if two gleason parts in m h have distinct closures then there exists an h function which is identically zero on one part and nonzero on the other from this one obtains a corona theorem for certain subalgebras of h let cop denote the algebra of bounded analytic functions that are in the little bloch space it is shown here that there exists a cop function h and an inner function i such that i divides h in h1 but the result is not in cop

bmo in the bergman metric on bounded symmetric domains for bounded symmetric domains in cn a notion of bounded mean oscillation in terms of the bergman metric is introduced it is shown that for in l2 dv is in bmo if and only if the densely defined operator m p m p pm on l2 dv is bounded here m is multiplication by and p is the bergman projection with range the bergman subspace h2 dv la2 dv of holomorphic functions in l2 dv an analogous characterization of compactness for m p is provided by functions of vanishing mean oscillation at the boundary of

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

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

toeplitz operators and quantum mechanics abstract toeplitz operators on the segal bargmann spaces of gaussian measure square integrable entire functions on complex n space c n are studied the c algebra generated by the weyl form of the canonical commutation relations consists precisely of the uniform limits of almost periodic toeplitz operators the question of which toeplitz operators admit a symbol calculus modulo the compact operators is raised and sufficient conditions are given for such a calculus these conditions involve a notion of slow oscillation at infinity

central limit behavior of deterministic dynamical systems we investigate the probability density of rescaled sums of iterates of deterministic dynamical systems a problem relevant for many complex physical systems consisting of dependent random variables a central limit theorem clt is valid only if the dynamical system under consideration is sufficiently mixing for the fully developed logistic map and a cubic map we analytically calculate the leading order corrections to the clt if only a finite number of iterates is added and rescaled and find excellent agreement with numerical experiments at the critical point of period doubling accumulation a clt is not valid anymore due to strong temporal correlations between the iterates nevertheless we provide numerical evidence that in this case the probability density converges to a q gaussian thus leading to a power law generalization of the clt the above behavior is universal and independent of the order of the maximum of the map considered i e relevant for large classes of critical dynamical systems

hankel operators and toeplitz operators on the bergman space abstract we consider in this paper the question of when the semi commutator t fg t f t g on the bergman space with bounded harmonic symbols is compact several conditions equivalent to compactness of t fg t f t g are given as a consequence we prove a conjecture of axler that for bounded analytic functions f and g on the unit disk t fg t g t f is compact iff either f or g is constant on each gleason part p m except d

toeplltz operators and the berezin transform on h2 abstract for t a bounded linear operator on the hardy space h2 its berezin transform is the function t on the unit disc defined by t tk k where k z 1 2 1 2 1 z is the normalized reproducing szego kernel when t t gf is a toeplitz operator it turns out that the nontangential boundary values of t gf coincide with gf almost everywhere this allows us to construct extensions and or generalizations of the classical symbol calculus for toeplitz operators to larger operator algebras briefly discussed is also the relation between our results and the recent results of berger coburn and zhu for toeplitz and hankel operators on the bergman space

compensated compactness paracommutators and hardy spaces abstract letb1 r n r n1 r m1 b2 r n r n2 r m2andq r m2 r m1be bilinear forms which are related as follows if and satisfyb1 0 andb2 0 for some 0 then q 0 supposep 1 q 1 1 coifman lions meyer and semmes proved that ifu lp r n andv lq r n and the first order systemsb1 d u 0 b2 d v 0 hold thenu qvbelongs to the hardy spaceh1 r n provided that both i p q 2 and ii the ranks of the linear mapsbj r nj r m1are constant we apply the theory of paracommutators to show that this result remains valid when only one of the hypotheses i ii is postulated the removal of the constant rank condition whenp q 2 involves the use of a deep result of lojasiewicz from singularity theory

function theory on cartan domains and the berezin toeplitz symbol calculus cn with dv z normalized lebesgue measure on 9 we let l l2 q dv be the usual space of lebesgue square integrable complex valued functions on 9 by h2 h2 q dv we denote the bergman subspace of l2 consisting of holomorphic functions the orthogonal projection operator from l2 onto h2 is denoted by p forf in l q the space of essentially bounded measurable functions on 9 we will consider the multiplication operator

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

closer look at time averages of the logistic map at the edge of chaos the probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown see u tirnakli c beck and c tsallis phys rev e 75 040106 r 2007 to be numerically consistent with a q gaussian the distribution which under appropriate constraints maximizes the nonadditive entropy sq the basis of nonextensive statistical mechanics this analysis was based on a study of the tails of the distribution we now check the entire distribution in particular its central part this is important in view of a recent q generalization of the central limit theorem which states that for certain classes of strongly correlated random variables the rescaled sum approaches a q gaussian limit distribution we numerically investigate for the logistic map with a parameter in a small vicinity of the critical point under which conditions there is convergence to a q gaussian both in the central region and in the tail region and find a scaling law involving the feigenbaum constant our results are consistent with a large number of already available analytical and numerical evidences that the edge of chaos is well described in terms of the entropy sq and its associated concepts

a reproducing kernel thesis for operators on bergman type function spaces abstract in this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on bergman type spaces in particular the results in this paper apply to the weighted bergman space on the unit ball the unit polydisc and more generally to weighted fock spaces

bergman commutators and norm ideals let p be the orthogonal projection from l2 b dv onto the bergman space la2 b dv of the unit ball in cn in this paper we characterize the membership of commutators of the form mf p in the norm ideal c where the symmetric gauge function is allowed to be arbitrary

generalizations of the forelli rudin estimates we give elementary proofs of the forelli rudin estimates and generalizations of these estimates as an application we obtain lp boundedness results for classes of integral operators that include bergman projections and hankel operators

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

the dixmier trace of hankel operators on the bergman space abstract we give a formula for the dixmier trace of big hankel operators on the bergman space of the disk or of finitely connected domains for harmonic symbols we find the regularity required of the symbol for the formula to hold

paracommutators boundedness and schatten von neumann properties definition d une classe d operateurs denommes paracommutateurs operant sur les fonctions de l 2 r d par analogie avec la para multiplication de bony et les commutateurs des operateurs de calderon zygmund etablissement de la borne et des proprietes de schatten von neumann

norm estimates for iterated commutators on the bergman spaces of the unit ball introduction we study the iterated commutators of the bergman projection and the multiplication by measurable functions called the symbols unlike the commutators the iterated commutators are no longer depending linearly on their symbols therefore most of the techniques used successfully in studying the first order commutators fail to work effectively for the nth order iterated commutators these operators are also very different from their analogs on l2 rm which has been studied by l peng t qian in pq using the s jason and j peeter s technique established in jp and r rochberg s semmes in rs where deeper tools of harmonic analysis in r are employed in this paper by using the bergman geometry properties of holomorphic functions and related analyses we characterize the conjugate holomorphic symbols for which the corresponding iterated commutators are bounded compact or in the schatten p class some lp estimates are also included in our discussion let 1m be the open unit ball of cm and dv z be the volume measure on blm

relationships and scaling laws among correlation fractality lyapunov divergence and q gaussian distributions abstract we numerically introduce the relationships among correlation fractality lyapunov divergence and q gaussian distributions the scaling arguments between the range of the q gaussian and correlation fractality lyapunov divergence are obtained for periodic windows i e periods 2 3 and 5 of the logistic map as chaos threshold is approached firstly we show that the range of the q gaussian g tends to infinity as the measure of the deviation from the correlation dimension d c o r r 0 5 at the chaos threshold this deviation will be denoted by l approaches to zero moreover we verify that a scaling law of type 1 g l is evident with the critical exponent 0 23 0 01 similarly as chaos threshold is approached the quantity l scales as l a a c where the exponent is 0 84 0 01 secondly we also show that the range of the q gaussian exhibits a scaling law with the correlation length 1 g lyapunov divergence 1 g and the distance to the critical box counting fractal dimension 1 g d d c with the same exponent 0 43 finally we numerically verify that these three quantities d d c scale with the distance to the critical control parameter of the map i e a a c in accordance with the universal huberman rudnick scaling law with the same exponent 0 448 0 003 all these findings can be considered as a new evidence supporting that the central limit behaviour at the chaos threshold is given by a q gaussian

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

compactness of hankel operators and analytic discs in the boundary of pseudoconvex domains abstract using several complex variables techniques we investigate the interplay between the geometry of the boundary and compactness of hankel operators let be a function smooth up to the boundary on a smooth bounded pseudoconvex domain c n we show that if is convex or the levi form of the boundary of is of rank at least n 2 then compactness of the hankel operator h implies that is holomorphic along analytic discs in the boundary furthermore when is convex in c 2 we show that the condition on is necessary and sufficient for compactness of h

bounded symbols and reproducing kernel thesis for truncated toeplitz operators compressions of toeplitz operators to coinvariant subspaces of h2 are called truncated toeplitz operators we study two questions related to these operators the first raised by sarason is whether boundedness of the operator implies the existence of a bounded symbol the second is the reproducing kernel thesis we show that in general the answer to the first question is negative and we exhibit some classes of spaces for which the answers to both questions are positive

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

bmo on strongly pseudoconvex domains hankel operators duality and overline partial estimates we study the condition that characterizes the symbols of bounded hankel operators on the bergman space of a strongly pseudoconvex domain and show that it is equivalent to bmo plus analytic here we mean the bergman metric bmo of berger coburn and zhu in the course of the proof we obtain new 0 estimates that may be of independent interest some applications include a decomposition of bmo similar to the classical li l and two characterizations of the dual of vmo which is also a predual of bmo in addition we obtain some partial results on the boundedness of hankel operators in l1 norm

clifford analysis and commutators on the besov spaces abstract we study commutators between multiplication by a function called the symbol and riesz transformations on the besov spaces we characterize symbols by potential capacity for which the associated commutators are bounded clifford analysis plays a key role in our approach

central limit behavior in the kuramoto model at the edge of chaos abstract we study the relationship between chaotic behavior and the central limit theorem clt in the kuramoto model we calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that when chaos is sufficiently strong the pdfs of the sums tend to a gaussian consistently with the standard clt on the other hand when the system is at the edge of chaos i e in a regime with vanishing lyapunov exponents robust q gaussian like limit distributions naturally emerge consistently with recently proved generalizations of the clt

boundedness for iterated commutators on the mixed norm spaces abstract this paper studies the iterated commutators on mixed norm spaces l 2 characterizing the conjugate holomorphic symbols for which the corresponding iterated commutators are bounded by using the bergman geometry properties of holomorphic functions and related analysis

limit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustness abstract in this paper we numerically investigate the distribution of the sums of the iterates of the logistic map and the relationships among the important properties of the nonlinear dynamics in the vicinity of the chaos threshold by adding two kinds of contributions with different densities the first one is the well known white noise whereas the second is a newly defined one named as quartic term which makes contributions from the own structure of the map as the chaos threshold is approached the iterates of the standard logistic map i e noise free have strong correlations and the standard central limit theorem is not valid anymore in a recent work tirnakli 2009 it has been shown that the limit distribution seems to converge to q gaussian distribution which maximizes the nonadditive entropy s q 1 i p i q q 1 under appropriate conditions in this work we investigate the effect of these contributions i e white noise and quartic term on the limit distribution and on the range of the obtained q gaussian distribution as a result of these findings under the existence of white noise and also the quartic term we analyse the validity of the scaling relations among correlation fractality the lyapunov divergence and q gaussian distributions which have recently been observed in afsar 2014 the results obtained here strengthen the argument that the central limit behaviour is given by a q gaussian as the chaos threshold is approached and indicate that the scaling relations obtained for the standard logistic map among the range of the q gaussian the correlation dimension the correlation length the lyapunov exponent fractality and the distance from the chaos threshold are robust under the existence of white noise and the quartic term

compact and weakly compact composition operators from the bloch space into mobius invariant spaces we obtain exhaustive results and treat in a unified way the question of boundedness compactness and weak compactness of composition operators from the bloch space into any space from a large family of conformally invariant spaces that includes the classical spaces like bmoa q and analytic besov spaces bp in particular by combining techniques from both complex and functional analysis we prove that in this setting weak compactness is equivalent to compactness for the operators into the corresponding small spaces we also characterize the boundedness and show that it is equivalent to compactness

central limit theorem and deformed exponentials the central limit theorem clt can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines notably in statistical thermodynamics we show that there exists a natural extension of the clt from exponentials to so called deformed exponentials also denoted as q gaussians our proposal applies exactly in the usual conditions in which the classical clt is used

on q gaussians and exchangeability the q gaussian distributions introduced by tsallis are discussed from the point of view of variance mixtures of normals and exchangeability for each there is a q gaussian distribution that maximizes the tsallis entropy under suitable constraints this paper shows that q gaussian random variables can be represented as variance mixtures of normals when q 1 these variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables thereby providing a possible model that has been extensively studied in probability theory the formulation provided has the additional advantage of yielding for each q a process which is naturally the q analog of the brownian motion explicit mixing distributions for q gaussians should facilitate applications to areas such as option pricing the model might provide insight into the study of superstatistics

physical meaning of the time correlation length obtained in a computer simulation a comparison is made of three statistical methods of determining the autocorrelation coefficients and correlation length in a time data series obtained by a computer simulation three points of state were chosen where the fluctuations and correlations play different roles in the liquid in the solid near melting and in the melting zone taking account of the physical meaning of the results it is found that there is always a limiting value of the lag at which the series must be cut off

tsallis non extensive statistical mechanics in the ionospheric detrended total electron content during quiet and storm periods abstract in this paper the tsallis non extensive q statistics in ionospheric dynamics was investigated using the total electron content tec obtained from two global positioning system gps receiver stations this investigation was carried out considering the geomagnetically quiet and storm periods the micro density variation of the ionospheric total electron content was extracted from the tec data by method of detrending the detrended total electron content which represent the variation in the internal dynamics of the system was further analyzed using for non extensive statistical mechanics using the q gaussian methods our results reveals that for all the analyzed data sets the tsallis gaussian probability distribution q gaussian with value q 1 were obtained it was observed that there is no distinct difference in pattern between the values of q q u i e t and q s t o r m however the values of q varies with geophysical conditions and possibly with local dynamics for the two stations also observed are the asymmetric pattern of the q gaussian and a highly significant level of correlation for the q index values obtained for the storm periods compared to the quiet periods between the two gps receiver stations where the tec was measured the factors responsible for this variation can be mostly attributed to the varying mechanisms resulting in the self reorganization of the system dynamics during the storm periods the result shows the existence of long range correlation for both quiet and storm periods for the two stations

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

localization carleson measure and bmo toeplitz operators on the bergman space abstract in this paper we prove that a toeplitz operator with complex borel measure symbol whose total variation is carleson is weakly localized on the bergman space we define strongly localized and sufficiently localized operators on the bergman space and show that they are also weakly localized finally we show that bounded toeplitz operators with b m o 1 symbols are strongly and therefore also weakly localized and that the bergman space toeplitz algebra has yet another characterization as the c algebra generated by this class of operators

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

the semantics of incomplete databases as an expression of preferences abstract we address the problem of incomplete information in deductive databases from a semantic point of view we want to treat the problem in a homogeneous way using a formalism which can handle different types of incompleteness we argue that it is convenient to define an incomplete database as a double entity an underlying incomplete database together with selection criteria formally some preference relation on the set of models of the underlying database intended to reduce the incompleteness such an idea has been already exploited in the perfect model semantics of negation as failure in the stratified databases we propose another notion of preference which induces a stronger selection of models and captures an intuitive process of making choices in disjunctive databases we study both the declarative and the operational semantics for this notion of preference

hankel operators induced by radial bekolle bonami weights on bergman spaces we study big hankel operators h f nu a p omega rightarrow l q nu generated by radial bekolle bonami weights nu when 1 p le q infty here the radial weight omega is assumed to satisfy a two sided doubling condition and a p omega denotes the corresponding weighted bergman space a characterization for simultaneous boundedness of h f nu and h overline f nu is provided in terms of a general weighted mean oscillation compared to the case of standard weights that was recently obtained by pau et al indiana univ math j 65 5 1639 1673 2016 the respective spaces depend on the weights omega and nu in an essentially stronger sense this makes our analysis deviate from the blueprint of this more classical setting as a consequence of our main result we also study the case of anti analytic symbols

a local inequality for hankel operators on the sphere and its application abstract let h 2 s be the hardy space on the unit sphere s in c n we establish a local inequality for hankel operators h f 1 p m f h 2 s as an application of this local inequality we characterize the membership of h f in the lorentz like ideal c p 2 n p

saturation nonmonotonic reasoning and the closed world assumption abstract to deal with the problem of implicit negative information in databases it is necessary to use a nonmonotonic form of reasoning the form of reasoning described in this paper uses an ordering relation on interpretations of the type i is inferior to j if every elementary fact true in i is true in j in simple cases this rule may be defined by a set p of formulas implies a formula q if every minimal model of p satisfies q in more general cases this definition leads to paradox if p is consistent and has no minimal model p must not imply q and its negation we have 1 1 carefully formulated the definition of a special type of implication called sub implication to avoid this type of paradox 2 2 proved that if p is a set of clauses then p has a minimal model and more generally that every model of a set of clauses is minored by one of its minimal models 3 3 developed in this last case subject to certain conditions such as the use of a particular set of clauses called groundable clauses or g clauses a decidable algorithm to compute whether p implies q q being practically any formula

toeplitz operators on the segal bargmann space in this paper we give a complete characterization of those functions on 2n dimensional euclidean space for which the berezin toeplitz quantizations admit a symbol calculus modulo the compact operators the functions in question are characterized by a condition of small oscillation at infinity

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

on the relationship between circumscription and negation as failure abstract the aim of this paper is to investigate two powerful methods of handling negative information in logic based knowledge representation systems the logical minimization in the form of circumscription and the negation as failure rule formalized by various closures or completions of original theories we suggest a new more powerful form of the negation as failure rule and describe an important class of theories for which this form of negation as failure is equivalent to particular forms of circumscription these results establish a close relationship between the two important formalizations of nonmonotonic reasoning and provide a syntactic characterization of the corresponding circumscriptive theories this allows us to apply existing methods of deduction using various negation as failure rules to answering queries in a broad class of circumscriptive theories

an algorithm to compute circumscription abstract mccarthy s theory of circumscription appears to be the most powerful among various formalizations of nonmonotonic reasoning designed to handle incomplete and negative information in knowledge representation systems in this paper we describe a query answering algorithm for circumscriptive theories the closed world assumption cwa and its generalizations the generalized closed world assumption gcwa and the extended closed world assumption ecwa can be considered as special forms of circumscription consequently our algorithm also applies to answering queries in theories using the closed world assumption and its generalizations similarly since prioritized circumscription is equivalent to a conjunction of parallel circumscriptions our algorithm can be used to answer queries in theories circumscribed by prioritized circumscription

minimum solution of k 1 and middle hankel operators abstract we formulate the solution of the equation k 1 f f with minimum l 2 norm and characterize the symbol functions so that the corresponding middle hankel operators are bounded compact and belong to the schatten p class p 1 this generalizes the earlier results by peng rochberg wu the approach is inspired by a recent work of luecking

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators

nonlinear statistical coupling abstract by considering a nonlinear combination of the probabilities of a system a physical interpretation of tsallis statistics as representing the nonlinear coupling or decoupling of statistical states is proposed the escort probability is interpreted as the coupled probability with q 1 q defined as the degree of nonlinear coupling between the statistical states positive values of q have coupled statistical states a larger entropy metric and a maximum coupled entropy distribution of compact support coupled gaussians negative values of q have decoupled statistical states and for 2 q 0 a maximum coupled entropy distribution of heavy tail coupled gaussians the conjugate transformation between the heavy tail and compact support domains is shown to be q 2 q 2 q for coupled gaussian distributions this conjugate relationship has been used to extend the generalized fourier transform to the compact support domain and to define a scale invariant correlation structure with heavy tail limit distribution in the present paper we show that the conjugate is a mapping between the source of nonlinearity in non stationary stochastic processes and the nonlinear coupling which defines the coupled gaussian limit distribution the effects of additive and multiplicative noise are shown to be separable into the coupled variance and the coupling parameter q providing further evidence of the importance of the generalized moments