consistent estimation of a general nonparametric regression function in time series abstract we propose an estimator of the conditional distribution of x t x t 1 x t 2 and the corresponding regression function e x t x t 1 x t 2 where the conditioning set is of infinite order we establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition

nearest neighbor classification with dependent training sequences the asymptotic classification risk for nearest neighbor procedures is well understood in the case of i i d training sequences in this article we generalize these results to a class of dependent models including hidden markov models in the case where the observed patterns have lebesgue densities the asymptotic risk takes the same expression as in the i i d case for discrete distributions we show that the asymptotic risk depends on the rule used for breaking ties of equal distances

nontrivial solutions of kirchhoff type problems via the yang index abstract we obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the yang index and critical groups

crossed products extensions of lp bounds for amenable actions abstract we will extend earlier transference results due to neuwirth and ricard from the context of noncommutative l p spaces associated with amenable groups to that of noncommutative l p spaces associated with crossed products of amenable actions namely if m g c is a completely bounded fourier multiplier on l p then it extends to the crossed product with similar bounds provided that the action is amenable and trace preserving furthermore our construction also allows to extend g equivariant completely bounded operators acting on the space part to the crossed product provided that the generalized folner sets of the action satisfy certain accretivity property as a corollary we obtain stability results for maximal l p bounds over crossed products we derive using that stability results an application to the boundedness of smooth multipliers in the l p spaces of group algebras

recursive probability density estimation for weakly dependent stationary processes recursive estimation of the univariate probability density function f x for stationary processes x j is considered quadratic mean convergence and asymptotic normality for density estimators f n x are established for strong mixing and for asymptotically uncorrelated processes x j recent results for nonrecursive density estimators are extended to the recursive case

grothendieck s theorem past and present probably the most famous of grothendieck s contributions to banach space theory is the result that he himself described as the fundamental theorem in the metric theory of tensor products that is now commonly referred to as grothendieck s theorem gt in short or sometimes as grothendieck s inequality this had a major impact first in banach space theory roughly after 1968 then later on in c algebra theory roughly after 1978 more recently in this millennium a new version of gt has been successfully developed in the framework of operator spaces or non commutative banach spaces in addition gt independently surfaced in several quite unrelated fields in connection with bell s inequality in quantum mechanics in graph theory where the grothendieck constant of a graph has been introduced and in computer science where the grothendieck inequality is invoked to replace certain np hard problems by others that can be treated by semidefinite programming and hence solved in polynomial time in this expository paper we present a review of all these topics starting from the original gt we concentrate on the more recent developments and merely outline those of the first banach space period since detailed accounts of that are already available for instance the author s 1986 cbms notes

on optimal sequential prediction for general processes this paper considers several aspects of the sequential prediction problem for unbounded nonstationary processes under pth power loss spl lscr sub p u v u v sup p 1 p spl infin in the first part it is shown that bayes prediction schemes are cesaro optimal under general conditions that cesaro optimal prediction schemes are unique in a natural sense and that cesaro optimality is equivalent to a form of weak calibration connections between calibration and stronger forms of optimality are considered extensions of the existence and uniqueness results to generalized prediction and prediction from observations with additive noise are established for binary processes it is shown that thresholding an optimal prediction scheme for the squared loss yields an optimal binary prediction scheme for the hamming loss in the second part of the paper it is shown how to construct from a countable family of prediction schemes a single composite scheme whose asymptotic performance on any suitable process dominates the performance of each member of the family the construction is based on aggregating methods for individual binary sequences using the construction some results of algoet 1994 1995 on the existence of cesaro optimal schemes for families of ergodic processes are rederived in a direct way and extended to unbounded processes

lacunary fourier series for compact quantum groups this paper is devoted to the study of sidon sets lambda p sets and some related notions for compact quantum groups we establish several different characterizations of sidon sets and in particular prove that any sidon set in a discrete group is a strong sidon set in the sense of picardello we give several relations between sidon sets lambda p sets and lacunarities for lp fourier multipliers generalizing a previous work by blendek and michalicek we also prove the existence of lambda p sets for orthogonal systems in noncommutative lp spaces and deduce the corresponding properties for compact quantum groups central sidon sets are also discussed and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central sidon sets several examples are also included

iterative nonparametric estimation of a log optimal portfolio selection function let stock market vectors form a stationary ergodic sequence for fixed d spl isin n a log optimal portfolio selection function of the past d observed vectors is iteratively estimated on the basis of a training sequence by use of gradients and nonparametric regression strong consistency is obtained under a boundedness and spl alpha mixing condition without further assumptions on the distribution

nonparametric output prediction for nonlinear fading memory systems the authors construct a class of elementary nonparametric output predictors of an unknown discrete time nonlinear fading memory system their algorithms predict asymptotically well for every bounded input sequence every disturbance sequence in certain classes and every linear or nonlinear system that is continuous and asymptotically time invariant causal and with fading memory the predictor is based on k sub n nearest neighbor estimators from nonparametric statistics it uses only previous input and noisy output data of the system without any knowledge of the structure of the unknown system the bounds on the input or the properties of noise under additional smoothness conditions the authors provide rates of convergence for the time average errors of their scheme finally they apply their results to the special case of stable linear time invariant lti systems

positive solutions for a quasilinear elliptic equation of kirchhoff type this paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type m w u 2dx du f x u email protected u 0 email protected email protected where w is a smooth bounded domain of n m is a positive function and f has subcritical growth

nonparametric inference for ergodic stationary time series the setting is a stationary ergodic time series the challenge is to construct a sequence of functions each based on only finite segments of the past which together provide a strongly consistent estimator for the conditional probability of the next observation given the infinite past ornstein gave such a construction for the case that the values are from a finite set and recently algoet extended the scheme to time series with coordinates in a polish space the present study relates a different solution to the challenge the algorithm is simple and its verification is fairly transparent some extensions to regression pattern recognition and on line forecasting are mentioned

the fourier algebra of a measured groupoid and its multipliers abstract the classical definitions of the fourier algebras b g and a g of a locally compact group are extended to an arbitrary measured groupoid g dualities are established between b g and a g and the convolution algebras c g and vn g in the framework of operator modules they are used to generalize results of varopoulos and pisier about littlewood functions and completely bounded multipliers

measurable schur multipliers and completely bounded multipliers of the fourier algebras let g be a locally compact group and a g the fourier algebra of g from 17 in 24 herz de ned the space of herz schur multipliers b2 g he claimed that this space coincided with the space he denoted v g in his article 23 but o2ered no proof of this fact the completely bounded multipliers of the fourier algebra mcba g were de ned by de canniere and haagerup in 8 in was shown by bo zejko and fendler 7 that mcba g 1 4 b2 g isometrically unfortunately this result relies on unpublished work of gilbert entitled convolution operators and banach space tensor products i ii and iii but not widely available however there is a proof of the fact that mcba g 1 4 b2 g due to jolissaint 27 which relies on the representation theorem for completely bounded maps applied to the reduced c algebra c r g in this paper we prove an analogue of the fact that mcba g 1 4 b2 g in fact our result obtains that fact in the case that g is a discrete group and improves upon it in the respect that we obtain a complete isometry where both mcba g and b2 g are given natural operator space structures moreover we show that the natural module action of mcba g on the von neumann algebra generated by the left regular representation vn g extends completely isometrically to a normal action of mcba g on all of b l g the space of bounded operators on l g in fact the image of mcba g in the completely bounded normal maps on b l g consists of l1 g bimodule maps and can be characterised as a certain intrinsic invariant part amongst those maps we feel that our approach is interesting in and of itself since it makes systematic use of modern operator space theoretic techniques pioneered by blecher e2ros haagerup paulsen ruan and smith amongst others it thus gives a starting point for obtaining representations of completely bounded multipliers of kac algebras after 29 or of multipliers of locally compact quantum groups after vaes et al see 47 to support our approach in x 3 we describe the space of measurable schur multipliers v1 x for any suitable measure space x we develop the theory of v1 x fully and systematically our main tools for doing this are the results of smith 41 and blecher and smith 5 which characterise the normal completely bounded maps on the space of all bounded operators on a hilbert space which are module maps over a von neumann algebra we make great use of the weak haagerup tensor product of two von neumann algebras which is

universal prediction this paper consists of an overview on universal prediction from an information theoretic perspective special attention is given to the notion of probability assignment under the self information loss function which is directly related to the theory of universal data compression both the probabilistic setting and the deterministic setting of the universal prediction problem are described with emphasis on the analogy and the differences between results in the two settings

infinitely many positive solutions for kirchhoff type problems abstract this paper is concerned with the existence of infinitely many positive solutions to a class of kirchhoff type problem a b u 2 d x u f x u in and u 0 on where is a smooth bounded domain of r n a b 0 0 and f r r is a caratheodory function satisfying some further conditions we obtain a sequence of a e positive weak solutions to the above problem tending to zero in l with f being more general than that of k perera z zhang nontrivial solutions of kirchhoff type problems via the yang index j differential equations 221 2006 246 255 z zhang k perera sign changing solutions of kirchhoff type problems via invariant sets of descent flow j math anal appl 317 2006 456 463

sequential prediction of unbounded stationary time series a simple on line procedure is considered for the prediction of a real valued sequence the algorithm is based on a combination of several simple predictors if the sequence is a realization of an unbounded stationary and ergodic random process then the average of squared errors converges almost surely to that of the optimum given by the bayes predictor an analog result is offered for the classification of binary processes

intermittent estimation for gaussian processes let xn n 0 be a stationary real valued gaussian time series we estimate the conditional expectation e xn 1 x0 xn from a growing number of observations x0 xn in a pointwise consistent way along a sequence of stopping times

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

weakly convergent nonparametric forecasting of stationary time series the conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past several schemes are known for constructing pointwise consistent estimates but they all demand prohibitive amounts of input data we consider real valued time series and construct conditional distribution estimates that make much more efficient use of the input data the estimates are consistent in a weak sense and the question whether they are pointwise consistent is still open for finite alphabet processes one may rely on a universal data compression scheme like the lempel ziv 1978 algorithm to construct conditional probability mass function estimates that are consistent in expected information divergence consistency in this strong sense cannot be attained in a universal sense for all stationary processes with values in an infinite alphabet but weak consistency can some applications of the estimates to on line forecasting regression and classification are discussed

memory universal prediction of stationary random processes we consider the problem of one step ahead prediction of a real valued stationary strongly mixing random process xi sub i spl infin sup spl infin the best mean square predictor of x sub 0 is its conditional mean given the entire infinite past x sub i sub i spl infin sup 1 given a sequence of observations x sub 1 x sub 2 x sub n we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasing dimension for example neural networks and legendre polynomials the proposed estimators select both the model memory and the model dimension in a data driven fashion by minimizing certain complexity regularized least squares criteria when the underlying predictor function has a finite memory we establish that the proposed estimators are memory universal the proposed estimators which do not know the true memory deliver the same statistical performance rates of integrated mean squared error as that delivered by estimators that know the true memory furthermore when the underlying predictor function does not have a finite memory we establish that the estimator based on legendre polynomials is consistent

a simple randomized algorithm for sequential prediction of ergodic time series we present a simple randomized procedure for the prediction of a binary sequence the algorithm uses ideas from previous developments of the theory of the prediction of individual sequences we show that if the sequence is a realization of a stationary and ergodic random process then the average number of mistakes converges almost surely to that of the optimum given by the bayes predictor the desirable finite sample properties of the predictor are illustrated by its performance for markov processes in such cases the predictor exhibits near optimal behavior even without knowing the order of the markov process prediction with side information is also considered

noncommutative maximal ergodic theorems this paper is devoted to the study of various maximal ergodic theorems in noncommutative spaces in particular we prove the noncommutative analogue of the classical dunford schwartz maximal ergodic inequality for positive contractions on and the analogue of stein s maximal inequality for symmetric positive contractions we also obtain the corresponding individual ergodic theorems we apply these results to a family of natural examples which frequently appear in von neumann algebra theory and in quantum probability

riesz transform gaussian bounds and the method of wave equation for an abstract self adjoint operator l and a local operator a we study the boundedness of the riesz transform al on lp for some 0 a very simple proof of the obtained result is based on the finite speed propagation property for the solution of the corresponding wave equation we also discuss the relation between the gaussian bounds and the finite speed propagation property using the wave equation methods we obtain a new natural form of the gaussian bounds for the heat kernels for a large class of the generating operators we describe a surprisingly elementary proof of the finite speed propagation property in a more general setting than it is usually considered in the literature

completely bounded module maps and the haagerup tensor product abstract we obtain a representation theorem for module maps defined on the algebra k h of compact operators this is used to show that the haagerup tensor product of two operator algebras enjoys strong versions of tomita s commutant theorem and the slice map property we also give a general theorem concerning the automatic complete boundedness of module maps

universal schemes for learning the best nonlinear predictor given the infinite past and side information let x sub t be a real valued time series the best nonlinear predictor of x sub 0 given the infinite past x sub spl infin sup 1 in the least squares sense is equal to the conditional mean e x sub 0 x sub spl infin sup 1 previously it has been shown that certain predictors based on growing segments of past observations converge to the best predictor given the infinite past whenever x sub t is a stationary process with values in a bounded interval the present paper deals with universal prediction schemes for stationary processes with finite mean we also discuss universal schemes for learning the conditional mean e x sub 0 x sub spl infin sup 1 y sub spl infin sup 1 y sub 0 from past observations of a stationary pair process x sub t y sub t and schemes for learning the repression function m y e x y y from independent samples of x y

amenable actions of groups the equivalence between different characterizations of amenable actions of a locally compact group is proved in particular this answers a question raised by r j zimmer in 1977

multiplicity of positive solutions for an equation with degenerate nonlocal diffusion abstract we consider an elliptic boundary value problem with degenerate nonlocal term we prove the multiplicity of positive solutions for the problem where the number of solutions doubles the number of zeros of the degenerate term the solutions are also ordered according to their l p norms

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

twisted hilbert transforms vs kakeya sets of directions given a discrete group g and an orthogonal action g o n we study lp convergence of fourier integrals which are frequency supported on the semidirect product ro g given a unit u rn and 1 p 6 2 our main result shows that the twisted directional hilbert transform hu o idg is lp bounded iff the orbit o u is finite this is in sharp contrast with twisted riesz transforms ru o idg which are always bounded our result characterizes fourier summability in lp for this class of groups we also extend de leeuw s compactification theorem to this setting and obtain stronger estimates for functions with lacunary frequency support

bounds for spectral multipliers on nilpotent groups a criterion is given for the lp boundedness of a class of spec tral multiplier operators associated to left invariant homogeneous subelliptic second order differential operators on nilpotent lie groups generalizing a theo rem of hormander for radial fourier multipliers on euclidean space the order of differentiability required is half the homogeneous dimension of the group improving previous results in the same direction

les espaces lp d une algebre de von neumann definies par la derivee spatiale abstract this work answers a question raised by a connes on the spatial theory of von neumann algebras preprint inst hautes etudes sci france and generalizes for a general von neumann algebra the theory of non commutative integration of j dixmier bull soc math france 81 1953 and i segal ann of math 57 1973

weakly universally consistent forecasting of stationary and ergodic time series static forecasting of stationary and ergodic time series is considered i e inference of the conditional expectation of the response variable at time zero given the infinite past it is shown that the mean squared error of a combination of suitably defined localized least squares estimates converges to zero for all distributions where the response variable is square integrable

long term prediction intervals of time series we consider the problem of predicting aggregates or sums of future values of a process based on its past values in contrast with the conventional prediction problem in which one predicts a future value given past values of the process in our setting the number of aggregates can go to infinity with respect to the number of available observations consistency and bahadur representations of the prediction estimators are established a simulation study is carried out to assess the performance of different prediction estimators

sobolev versus holder local minimizers in degenerate kirchhoff type problems abstract in this paper we study the geometry of certain functionals associated to quasilinear elliptic boundary value problems with a degenerate nonlocal term of kirchhoff type due to the degeneration of the nonlocal term it is not possible to directly use classical results such as uniform a priori estimates and sobolev versus holder local minimizers type of results we prove that results similar to these hold true or not depending on how degenerate the problem is we apply our findings in order to show existence and multiplicity of solutions for the associated quasilinear equations considering several different interactions between the nonlocal term and the nonlinearity

plancherel type estimates and sharp spectral multipliers abstract we study general spectral multiplier theorems for self adjoint positive definite operators on l2 x where x is any open subset of a space of homogeneous type we show that the sharp hormander type spectral multiplier theorems follow from the appropriate estimates of the l2 norm of the kernel of spectral multipliers and the gaussian bounds for the corresponding heat kernel the sharp hormander type spectral multiplier theorems are motivated and connected with sharp estimates for the critical exponent for the riesz means summability which we also study here we discuss several examples which include sharp spectral multiplier theorems for a class of scattering operators on r3 and new spectral multiplier theorems for the laguerre and hermite expansions

limits to consistent on line forecasting for ergodic time series this article concerns problems of time series forecasting under the weakest of assumptions related results are surveyed and are points of departure for the developments here some of which are new and others are new derivations of previous findings the contributions in this study are all negative showing that various plausible prediction problems are unsolvable or in other cases are not solvable by predictors which are known to be consistent when mixing conditions hold

sign changing solutions of kirchhoff type problems via invariant sets of descent flow we obtain sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow

existence of solutions for a nonhomogeneous elliptic kircchoff type equation abstract for a bounded domain in r n a bounded caratheodory function g in r and a nonnegative and nonzero locally integrable measurable function h in we give sufficient conditions on the c 1 function m 0 r for the existence of a solution of the nonlocal elliptic problem 1 m u 2 u u g x u h x u p 1 u f x x u x 0 x for every p 1 0 r and f l 2

a polynomially bounded operator on hilbert space which is not similar to a contraction let e 0 we prove that there exists an operator te e2 2 such that for any polynomial p we have iip te ii not similar to a contraction i e there does not exist an invertible operator s f2 e f2 such that jis 1tesii tributed to halmos after his well known 1970 paper ten problems in hilbert space we also give some related finite dimensional estimates department of mathematics texas a m university college station texas 77843 universite paris vi equipe d7analyse case 186 75252 paris cedex 05 france e mail address gipqccr jussieu fr this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 52 47 utc all use subject to http about jstor org terms

positive solutions for a kirchhoff problem with vanishing nonlocal term abstract in this paper we study the kirchhoff problem m u 2 u f u in u 0 on in a bounded domain allowing the function m to vanish in many different points under an appropriated area condition by using a priori estimates truncation techniques and variational methods we prove a multiplicity result of positive solutions which are ordered in the h 0 1 norm

weak factorizations of operators in the group von neumann algebras of certain amenable groups and applications let g be a compact group whose local weight b g has uncountable cofinality let h be an amenable locally compact group and a g h be the fourier algebra of g h we prove that the group von neumann algebra vn g h a g h has the weak uniform a g h factorization property of level b g as a corollary we show that a g h is strongly arens irregular and the topological centre of uc2 g h is equal to the fourier stieltjes algebra b g h