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

the spectrum of the burnside tambara functor on a finite cyclic p group abstract for a finite group g a tambara functor on g is regarded as a g bivariant analog of a commutative ring in this analogy previously we have defined an ideal of a tambara functor in this article we calculate the prime spectrum of the burnside tambara functor when g is a finite cyclic p group for a prime integer 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

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

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

integral hosm semiglobal controller for finite time exact compensation of unmatched perturbations the present technical note studies a class of nonlinear systems with unmatched perturbations the combination of integral high order sliding modes with the hierarchical quasi continuous controller is proposed allowing finite time exact compensation of unmatched perturbations with semiglobal convergence features for both regulation and tracking

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

technical communique quasi continuous hosm control for systems with unmatched perturbations the control of nonlinear systems subject to unmatched perturbations is studied a new design algorithm is proposed based on the block control and quasi continuous higher order sliding modes techniques the proposed method provides for the finite time exact tracking of a smooth desired signal in spite of unmatched perturbations

sampled data fuzzy control for a class of nonlinear systems with missing data and disturbances this paper considers the sampled data fuzzy control of nonlinear systems in strict feedback form with disturbances and random missing input data we propose a novel method in which a state observer and a disturbance observer are combined to construct a sampled data fuzzy output feedback controller the stochastic variables with a bernoulli distributed sequence are used to model missing input data fuzzy logic systems are applied to approximate nonlinearities without requiring prior knowledge the relation between observer gain and sampling period is established the output feedback controller designed guarantees that the nonlinear system is globally stable a simulation example of four degrees of freedom robotic arm is used to demonstrate the effectiveness and applicability of the proposed control scheme

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

robustness of the tuning functions adaptive backstepping design for linear systems we study robustness of the adaptive backstepping design with tuning functions for linear systems under assumptions on unmodeled dynamics and disturbances equal to those for certainty equivalence schemes we address an adaptive scheme not based on the certainty equivalence principle in the process of redesign for robustness we employ only leakage in the estimator we do not employ normalization neither static nor dynamic a fundamental difference between the tuning functions design and the certainty equivalence designs is that the controller in the former is inherently nonlinear while in the latter it is nonlinear only in the parameter estimate as a result achievable robustness results for the tuning functions scheme are not global but regional with a region of attraction inversely proportional to the size of the unmodeled dynamics the tracking error is proportional to the size of the uncertainties

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

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

dynamic switching surfaces for output sliding mode control the robustness properties of sliding mode and h controllers are exploited to produce a dynamic output feedback controller that is insensitive to matched perturbations and attenuates the unmatched ones the assumptions on the plant differ from the standard assumptions of the riccati state space approach to h control the sliding mode controller drives the state into a reduced order manifold for which the equivalent system does satisfy the standard assumptions and hence the standard theory can be applied the resulting riccati equations are of reduced order

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

integral sliding mode control for nonlinear systems with matched and unmatched perturbations we consider the problem of designing an integral sliding mode controller to reduce the disturbance terms that act on nonlinear systems with state dependent drift and input matrix the general case of both matched and unmatched disturbances affecting the system is addressed it is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it guarantees the minimization of the effect of the disturbance terms which takes place when the matched disturbances are completely rejected and the unmatched ones are not amplified a simulation of the proposed technique applied to a dynamically feedback linearized unicycle illustrates its effectiveness even in presence of nonholonomic constraints

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

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

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

nonlinear sliding mode control design an lmi approach abstract this paper presents a novel nonlinear sliding mode control methodology for systems with both matched and unmatched perturbations including parametric uncertainties instead of traditional approaches where uncertainties and nonlinearities are coped with via linear nominal models and linear sliding surfaces the proposed approach incorporates exact convex expressions to represent both the nonlinear surface and the system thus allowing a significant chattering reduction moreover thanks to the convex form of the nonlinear nominal model when combined with the direct lyapunov method it leads to linear matrix inequalities which are efficiently solved via convex optimization techniques illustrative examples are provided

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

observation and output adaptive tracking for a class of nonlinear non minimum phase systems abstractin this paper the output tracking problem for a class of systems with unstable zero dynamics is addressed the state is assumed not measurable the output of the dynamical system to be controlled has to track a signal which is the sum of a known number of sinusoids with unknown frequencies amplitudes and phases the non minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods which are known to generate unstable behaviours of the internal dynamics the proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state therefore a nonlinear observer is needed due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states adaptive indirect methods are applied

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

exact tracking using backstepping control design and high order sliding modes in this technical note a controller ensuring exponential exact tracking in the presence of matched and unmatched disturbances for the nonlinear systems in the block controllable form is proposed the controller is designed using the backstepping procedure and combines the feedback linearization technique with the high order sliding modes the matched and unmatched disturbances are compensated by the injection of a continuous term generated by the robust exact high order sliding modes differentiator the obtained control law is differentiable and can be applied directly to the system simulations verify the performance of the proposed controller

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

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

global properties of the triangular systems in the singular case we introduce a new class of the triangular multi input and multi output control systems of o d e which are not feedback linearizable and investigate its global behavior the triangular form introduced is a generalization of the classes of triangular systems considered before for our class we solve the problem of global robust controllability combining our main result with that of f h clarke yu s ledyaev e d sontag a i subbotin asymptotic controllability implies feedback stabilization ieee trans automat control 42 1997 1394 1407 we obtain a corollary on the global discontinuous sampled stabilization an example showing that global smooth stabilization can be irrelevant to the singular case is considered to prove our main result we apply a certain back stepping algorithm and combine the technique proposed in v i korobov s s pavlichkov w h schmidt global robust controllability of the triangular integro differential volterra systems j math anal appl 309 2005 743 760 with solving a specific problem of global practical stabilization by means of a discontinuous time varying feedback law

adaptive dynamic surface control a simplified algorithm for adaptive backstepping control of nonlinear systems in this paper we propose a new algorithm for adaptive backstepping control of non linear uncertain systems current backstepping algorithms require repeated differentiations of the modelled non linearities the addition of n first order low pass filters allows the algorithms to be implemented without differentiating any model non linearities the uncertainties are assumed to be linear in the unknown constant parameters the combined adaptive backstepping first order filter system is proven to be semi globally stable for sufficiently fast filters by a singular perturbation approach