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

differences of weighted composition operators from bloch space to h on the unit ball abstract in this paper we study the boundness and compactness of differences of weighted composition operators from the bloch space b to the space h of bounded analytic functions on the open unit ball of c n moreover we estimate the norm and the essential norm of differences of composition operators from b to h

a new multiplicative consistency based method for decision making with triangular fuzzy reciprocal preference relations abstract triangular fuzzy reciprocal preference relations tfrprs are good choices to denote the decision makers fuzzy preferences consistency analysis is a very important topic to preference relations that can avoid the illogical ranking order however all previous multiplicative consistency concepts for tfrprs cannot well address this type of preference relations to address this issue this paper introduces a new multiplicative consistency concept for tfrprs which can be seen as a natural extension of tanino s multiplicative consistency concept for reciprocal preference relations based on the new consistency concept 0 1 mixed programming models for judging the multiplicative consistency of tfrprs are constructed and an approach for deriving multiplicative consistent tfrprs is provided considering the incomplete case programming models to determine missing values are constructed subsequently a multiplicative consistency based method for decision making with tfrprs is presented that can address the inconsistent and incomplete cases meanwhile illustrative examples are provided to show the concrete application of the proposed procedure and comparison analysis is also made

additive functionals of several time reversible markov processes i 1 additive functionals of markov processes have been studied by many authors we refer to 1 and 5 for the early history and to 161 i1719 61 181 f or more recent developments the most complete results for the case of a time reversible process are due to fukushima lo in this paper we study additive functionals of several independent time reversible markov processes the results are useful in particular for investigating a certain class of gaussian random fields which includes the free field of euclidean quantum field theory and the so called brownian sheet 9 our approach is different from that of fukushima even in the case of one markov process his results do not imply ours in the introduction first additive functionals of brownian motions are discussed on an intuitive level then the general concept of standard timereversible markov processes is outlined and the rigorous definition of additive functionals is given on this base the principal results of the paper are formulated we mention also some open problems

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

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

markov processes as a tool in field theory abstract in a recent paper brydges frohlich and spencer have successfully applied markov chains to classical spin systems using probabilistic methods in a more systematic way we improve some of their results the methods can be extended to fields with continuous parameter such as p fields

hilbert schmidt differences of composition operators on the bergman space in the setting of the weighted bergman space over the unit disk we characterize hilbert schmidt differences of two composition operators in terms of integrability condition involving pseudohyperbolic distance between the inducing functions we also show that a linear combination of two composition operators can be hilbert schmidt except for trivial cases only when it is essentially a difference we apply our results to study the topological structure of the space of all composition operators under the hilbert schmidt norm topology we first characterize components and then provide some sufficient conditions for isolation or for non isolation

necessary condition for compactness of a difference of composition operators on the dirichlet space abstract let be a self map of the unit disk and let c denote the composition operator acting on the standard dirichlet space d a necessary condition for compactness of a difference of two bounded composition operators acting on d is given as an application a characterization of disk automorphisms and for which the commutator c c is compact is given

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

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

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

gaussian and non gaussian random fields associated with markov processes to every markov process with a symmetric transition density there correspond two random fields over the state space a gaussian field the free field and the occupation field t which describes amount of time the particle spends at each state a relation between these two random fields is established which is useful both for the field theory and theory of markov processes

consistency analysis of triangular fuzzy reciprocal preference relations abstract in order to simulate the uncertainty associated with impression or vagueness a decision maker may give her his judgments by means of triangular fuzzy reciprocal preference relations in the process of decision making the study of their consistency becomes a very important aspect to avoid a misleading solution based on the reciprocity property this paper proposes a new definition of consistent triangular fuzzy reciprocal preference relations the new definition is different from that reduced by consistent fuzzy reciprocal preference relations proposed by buckley 1985 the properties of consistent triangular fuzzy reciprocal preference relations in the light of the new definition are studied in detail in addition the shortcomings of the proof procedure of the proposition given by wang and chen 2008 are pointed out and the proposition is reproved by using the new definition of consistent triangular fuzzy reciprocal preference relations finally using the n 1 restricted comparison ratios a method for obtaining consistent triangular fuzzy reciprocal preference relations is proposed and an algorithm is shown to make a consistent decision ranking numerical results are further calculated to illustrate the new definition and the obtained algorithm

compact linear combination of composition operators on bergman spaces abstract motivated by the question of shapiro and sundberg raised in 1990 study on linear combinations of composition operators has been a topic of growing interest in this paper we completely characterize the compactness of any finite linear combination of composition operators with general symbols on the weighted bergman spaces in two classical terms one is a function theoretic characterization of julia caratheodory type and the other is a measure theoretic characterization of carleson type our approach is completely different from what has been known so far

proprietes d intersection des marches aleatoires i convergence vers le temps local d intersection we study intersection properties of multi dimensional random walks letx andy be two independent random walks with values in d d 3 satisfying suitable moment assumptions and letin denote the number of common points to the paths ofx andy up to timen the sequence in suitably normalized is shown to converge in distribution towards the intersection local time of two independent brownian motions results are applied to the proof of a central limit theorem for the range of a two dimensional recurrent random walk thus answering a question raised by n c jain and w e pruitt

harmonic analysis of additive levy processes let x1 xn denote n independent d dimensional levy processes and consider the n parameter random field mathfrak x t x 1 t 1 cdots x n t n first we demonstrate that for all nonrandom borel sets f subseteq bf r d the minkowski sum mathfrak x bf r n oplus f of the range mathfrak x bf r n of mathfrak x with f can have positive d dimensional lebesgue measure if and only if a certain capacity of f is positive this improves our earlier joint effort with yuquan zhong by removing a certain condition of symmetry in khoshnevisan et al ann probab 31 2 1097 1141 2003 moreover we show that under mild regularity conditions our necessary and sufficient condition can be recast in terms of one potential densities this rests on developing results in classical non probabilistic harmonic analysis that might be of independent interest as was shown in khoshnevisan et al ann probab 31 2 1097 1141 2003 the potential theory of the type studied here has a large number of consequences in the theory of levy processes presently we highlight a few new consequences

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

compact linear combinations of composition operators induced by linear fractional maps it has been known that the difference of two composition operators induced by linear fractional self maps of a ball cannot be nontrivially compact on either the hardy space or any standard weighted bergman space in this paper we extend this result in two significant directions the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension

self intersection local times occupation fields and stochastic integrals where functions 6 converge to 6 as jo it turns out that b d co for every open set d which intersects with the diagonal t t2 however varadhan v has shown that b d u log s converges to a finite limit as e jo if d 0 s t u rosen r2 has found an expression for the limit in terms 1 of ito s stochastic integrals the integrals 0 1 and their renormalizations have been studied also in y 1 l 1 l2 and for the brownian motion in lr3 in rl r3 w y23 0 2 in this paper we investigate more general self intersection local times

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

fuzzy least squares priority method in the analytic hierarchy process the least squares priority method is an effective priority method in the analytic hierarchy process but it is not appropriate under fuzziness this paper is concerned with the question of estimation of weights of factors by least squares from a fuzzy judgment matrix first the expression form of least squares under fuzziness is given then the associated system of equation is developed after some properties of the system are investigated the explicit solution is derived finally it is shown that the solution of the system is the solution of the fuzzy least squares in this paper an example is also given to illustrate the procedure

weighted composition operators between hilbert spaces of analytic functions in the operator norm and hilbert schmidt norm topologies abstract we here investigate the topological structure of the space of weighted composition operators boundedly acting between two hilbert spaces of analytic functions on the open unit disk satisfying some natural hypotheses we will consider the operator norm topology and the hilbert schmidt norm topology respectively these results will be involved in the investigation for the explicit cases of the classical hardy hilbert space the weighted bergman spaces and the dirichlet space furthermore we will estimate the hilbert schmidt norms of difference of two composition operators acting from the dirichlet space to the hardy and the weighted bergman spaces

polynomials of the occupation field and related random fields abstract to every symmetric markov process there correspond two random fields over the state space a gaussian free field x and the occupation field t x which describes the amount of time spent by a particle at each state for the brownian motion in d 2 dimensions both fields are generalized using a relation between t x and the field x x 2 2 established in a previous publication polynomials of the fields t and are investigated in particular polynomials of t characterize self intersections of the process

on fuzzy rank ordering in polyoptimization the application of polyoptimization in decision making gives the user a certain number of efficient points in general obtained by numerical methods for a final and reasonable solution for instance in projecting in chemical engineering this set must be reduced this can be done using additional information in the present paper we use statements on the pairwise comparison of importance between the several objective functions to facilitate reasonable decision making under consideration of given aspects such as distance measures regarding individual extrema at this we desire from the decision maker user only fuzzy information on the pairwise rank ordering between the objectives which often appears more reasonable than so called crisp quantitive statements especially for practical problems it is shown how to take advantage of zadeh s theory of fuzzy sets 1965 for our aims a numerical example is also investigated

differences of generalized composition operators on the bloch space abstract the boundedness and compactness of the differences of two generalized composition operators on the bloch space in the unit disk are investigated in this paper

joint carleson measure and the difference of composition operators on aαp bn we introduce a concept of joint carleson measure and characterize when the difference of two composition operators on a p bn the weighted bergman space over the unit ball bn in cn is bounded or compact we apply this joint carleson measure characterization to composition operators with smooth symbols and construct an interesting example which shows that the boundedness or the compactness depends on p when n 2 this is in sharp contrast with the single composition operator case where the boundedness or the compactness is independent of p 0 moreover the compact difference on the weighted bergman spaces over the unit disc is known to be independent of p 0 and the compact difference on a p bn is known to be independent of p 0 if each composition operator is bounded on a p bn for some 1 2

difference of composition operators between standard weighted bergman spaces we obtain estimates for the norm and essential norm of the difference of two composition operators between certain bergman spaces in particular a necessary and sufficient condition for boundedness and compactness of the operator is established finally we give a sufficient condition for boundedness and compactness of the difference operator between hardy spaces

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

which linear fractional composition operators are essentially normal abstract we characterize the essentially normal composition operators induced on the hardy space h2 by linear fractional maps they are either compact normal or the nontrivial case induced by parabolic nonautomorphisms these parabolic maps induce the first known examples of nontrivially essentially normal composition operators in addition we characterize those linear fractionally induced composition operators on h2 that are essentially self adjoint and present a number of results for composition operators induced by maps that are not linear fractional

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

compact double differences of composition operators on the bergman spaces abstract as is well known on the weighted bergman spaces over the unit disk compactness of differences of two composition operators is characterized by certain cancellation property of the inducing maps at every bad boundary point which makes each composition operator in the difference fail to be compact recently the second and third authors obtained a result implying that double difference cancellation is not possible for linear combinations of three composition operators in this paper we obtain a complete characterization for compact double differences formed by four composition operators applying our characterization we easily recover known results on linear combinations of two or three composition operators as another application we also show that double difference cancellation is possible for linear combinations of four composition operators by constructing an explicit example of a compact double difference formed by two noncompact differences in spite of such an example our characterization also shows that double difference cancellation may occur in the global sense only and that genuine double difference cancellation is not possible in a certain local sense

topological structure of the set of composition operators on the weighted bergman space abstract we investigate the topological connectedness of the set of composition operators on the weighted bergman space a 2 under the uniform operator topology one of our main results is to first find a necessary and sufficient condition for two composition operators on a 2 to be linearly connected in the case of one variable as a corollary we show that two composition operators on a 2 with compact difference must lie in the same path component

the random walk representation of classical spin systems and correlation inequalities ferromagnetic lattice spin systems can be expressed as gases of random walks interacting via a soft core repulsion by using a mixed spinrandom walk representation we present a unified approach to many recently established correlation inequalities as an application of these inequalities we obtain a simple proof of the mass gap for the 4 2 quantum field model we also establish new upper bounds on critical temperatures

green s and dirichlet spaces associated with fine markov processes this is the second paper in a series devoted to green s and dirichlet spaces in the first paper we have investigated green s space k and the dirichlet space h associated with a symmetric markov transition function pt x b now we assume that p is a transition function of a fine markov process x and we prove that a the space h can be built from functions which are right continuous along almost all paths b the positive cone k in k can be identified with a cone m of measures on the state space c the positive cone h in h can be interpreted as the cone of green s potentials of measures m to every measurable set b in the state space e there correspond a subspace k b of k and a subspace h b of h the orthogonal projections of k onto k and of h onto h b can be expressed in terms of the hitting probabilities of b by the markov process x as the main tool we use additive functionals of x corresponding to measures m

the estimation of normalized fuzzy weights abstract the estimation of a normalized set of positive fuzzy weights constitutes the most important aspects in the fuzzy multiple attribute decision making process a systematic treatment of this problem is carried out in this paper the concept of fuzzy normalization is first defined and the meaning of consistency in a fuzzy environment is discussed based on these definitions and discussions the various approaches in the literature are examined and several improvements or new approaches are proposed numerical examples are used to evaluate and to compare the various existing and the newly proposed approaches

a fuzzy approach to deriving priorities from interval pairwise comparison judgements abstract in this paper we study the problem of priority elicitation in the analytic hierarchy process and propose a new approach to deriving crisp priorities from interval pairwise comparison judgements by introducing linear or non linear membership functions representing the decision maker s degree of satisfaction with various crisp priority vectors the interval judgements are transformed into fuzzy inequality constraints the interval prioritisation problem is then formulated as a fuzzy mathematical programming problem for obtaining an optimal crisp priority vector that maximises the overall degree of satisfaction the proposed approach yields linear or non linear mathematical programs capable of deriving priorities from consistent and inconsistent interval judgements the presence of a consistency index that measures the level of inconsistency of interval judgements is an attractive feature of our approach another feature which does not exist in the known prioritisation methods is the opportunity for additional prioritisation of the initial judgements numerical examples are given and comparisons with other interval prioritisation methods are carried out

linear sums of two composition operators on the fock space abstract linear sums of two composition operators of the multi dimensional fock space are studied we show that such an operator is bounded only when both composition operators in the sum are bounded so cancelation phenomenon is not possible on the fock space in contrast to what have been known on other well known function spaces over the unit disk we also show the analogues for compactness and for membership in the schatten classes for linear sums of more than two composition operators the investigation is left open

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

random fields associated with multiple points of the brownian motion abstract let xt be the brownian motion in r d the random set t1 tn z xtl xtn z in r d n is empty a s except in the following cases a n 1 d 1 2 b d 2 n 2 3 c d 3 n 2 in each of these cases a family of random measures m concentrated on is constructed takes values in a certain class of measures on r d measures m characterize the time space location of self intersections for brownian paths if n d 1 then m dt dz dz nz dt where n2 is the local time at z in the case n 2 the set can be identified with the set of brownian loops the measure m explodes on the diagonal t1 t2 and to study small loops a random distribution which regularizes m is constructed

differences of composition operators between weighted type spaces of holomorphic functions on the unit ball of cn we consider differences of composition operators between weighted type or little weighted type spaces of analytic functions on the unit ball with weighted sup norms and give estimates for the distance of these differences to the space of compact operators we also study the boundedness and compactness of these operators

cancellation properties of composition operators on bergman spaces abstract the compact difference of two composition operators on the bergman spaces over the unit disc is characterized in 11 in terms of certain cancellation property of the inducing maps at every bad boundary points which make each single composition operator not to be compact in this paper we completely characterize the compactness of a linear combination of three composition operators on the bergman space as one consequence of this characterization we show that there is no cancellation property for the compactness of double difference of composition operators more precisely we show that if i are distinct and none of c i is compact then c 1 c 2 c 3 c 1 is compact if and only if both c 1 c 2 and c 3 c 1 are compact

deriving priorities from fuzzy pairwise comparison judgements a new approach for deriving priorities from fuzzy pairwise comparison judgements is proposed based on cuts decomposition of the fuzzy judgements into a series of interval comparisons the assessment of the priorities from the pairwise comparison intervals is formulated as an optimisation problem maximising the decision maker s satisfaction with a specific crisp priority vector a fuzzy preference programming method which transforms the interval prioritisation task into a fuzzy linear programming problem is applied to derive optimal crisp priorities aggregating the optimal priorities which correspond to different cut levels enables overall crisp scores of the prioritisation elements to be obtained a modification of the linear fuzzy preference programming method is also proposed to derive priorities directly from fuzzy judgements without applying cut transformations the formulation of the prioritisation problem as an optimisation task is similar to the previous approach but it requires the solution of a non linear optimisation program the second approach also derives crisp priorities and has the advantage that it does not need additional aggregation and ranking procedures both proposed methods are illustrated by numerical examples and compared to some of the existing fuzzy prioritisation methods

compact differences of composition operators on large weighted bergman spaces abstract while there have been extensive studies regarding the theory of composition operators in standard bergman spaces there have not been many results pertaining to large bergman spaces due to a lack of useful tools in this paper we obtain a complete characterization of the compact differences of composition operators in bergman spaces with weight of z e 1 1 z using a newly defined riemannian distance moreover we discuss the compact differences of composition operators in bergman spaces with general weights

components of linear fractional composition operators abstract we determine when two linear fractional composition operators on the hardy space h 2 belong to the same component in the collection of all composition operators on h 2 we show that two such composition operators in the same component may fail to have compact difference which answers a question raised by joel shapiro and carl sundberg