isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

on a class of singular biharmonic problems involving critical exponents abstract this paper deals with the following class of singular biharmonic problems p 2 u v x u q 1 u u 2 2 u in r n u d 2 2 o n 5 where 1 q 1 2 2n n 4 is the critical sobolev exponent 2 denotes the biharmonic operator is open domain not necessarily bounded it may be equal to r n and v is a potential that changes sign in with some points of singularities in some results on the existence of solutions are obtained by combining the mountain pass theorem and hardy inequality with some arguments used by brezis and nirenberg

models for n tuples of noncommuting operators abstract this paper proves versions of the rota model theorem the de branges rovnyak model theorem and the coisometric extension theorem for n tuples of not necessarily commuting operators this generalizes the work of a e frazho j funct anal 48 1982 1 11 for pairs of operators the methods involve applying the single operator results to matrices of operators

quasi multiplicativity of typical cocycles we show that typical in the sense of bonatti and viana ergod theory dyn syst 24 5 1295 1330 2004 and avila and viana port math 64 311 376 2007 holder and fiber bunched text gl d mathbb r valued cocycles over subshifts of finite type are uniformly quasi multiplicative with respect to all singular value potentials we prove the continuity of the singular value pressure and its corresponding necessarily unique equilibrium state for such cocycles and apply this result to repellers moreover we show that the pointwise lyapunov spectrum is closed and convex and establish partial multifractal analysis on the level sets of pointwise lyapunov exponents for such cocycles

tensor algebras overc correspondences representations dilations andc envelopes tensor algebras overc correspondences are noncommutative generalizations of the disk algebra they contain as special cases analytic crossed products semi crossed products and popescu s noncommutative disk algebras in this paper a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved these are used to show that for certainc correspondences thec envelopes in the sense of arveson of the tensor algebras are the cuntz pimsner algebras of the correspondences

isomorphisms of algebras associated with directed graphs given countable directed graphs g and g we show that the associated tensor algebras open image in new window g and open image in new window g are isomorphic as banach algebras if and only if the graphs g are g are isomorphic for tensor algebras associated with graphs having no sinks or no sources the graph forms an invariant for algebraic isomorphisms we also show that given countable directed graphs g g the free semigroupoid algebras open image in new window and open image in new window are isomorphic as dual algebras if and only if the graphs g are g are isomorphic in particular spatially isomorphic free semigroupoid algebras are unitarily isomorphic for free semigroupoid algebras associated with locally finite directed graphs with no sinks the graph forms an invariant for algebraic isomorphisms as well

construction of parseval wavelets from redundant filter systems we consider wavelets in l2 rd which have generalized multiresolutions this means that the initial resolution subspace v0 in l2 rd is not singly generated as a result the representation of the integer lattice zd restricted to v0 has a nontrivial multiplicity function we show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary matrix valued functions on a torus acting on a certain vector bundle specifically we show how the wavelet functions on rd can be constructed directly from the generalized wavelet filters

iterated function systems ruelle operators and invariant projective measures we introduce a fourier based harmonic analysis for a class of discrete dynamical systems which arise from iterated function systems our starting point is the following pair of special features of these systems 1 we assume that a measurable space x comes with a finite to one endomorphism r x x which is onto but not one to one 2 in the case of affine iterated function systems ifss in r d this harmonic analysis arises naturally as a spectral duality defined from a given pair of finite subsets b l in r d of the same cardinality which generate complex hadamard matrices our harmonic analysis for these iterated function systems ifs x is based on a markov process on certain paths the probabilities are determined by a weight function w on x from w we define a transition operator r w acting on functions on x and a corresponding class h of continuous r w harmonic functions the properties of the functions in h are analyzed and they determine the spectral theory of l 2 for affine ifss we establish orthogonal bases in l 2 these bases are generated by paths with infinite repetition of finite words we use this in the last section to analyze tiles in r d

multiple and sign changing solutions for a class of semilinear biharmonic equation abstract in this paper under an improved hardy rellich s inequality we study the existence of multiple and sign changing solutions for a biharmonic equation in unbounded domain by the minimax method and linking theorem

an analogue of the prime number theorem for closed orbits of axiom a flows for an axiom a flow restricted to a basic set we extend the zeta function to an open set containing w s h where h is the topological entropy this enables us to give an asymptotic formula for the number of closed orbits by adapting the wiener ikehara proof of the prime number theorem

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

positivity preserving property for a class of biharmonic elliptic problems the lack of a general maximum principle for biharmonic equations suggests to study under which boundary conditions the positivity preserving property holds we show that this property holds in general domains for suitable linear combinations of dirichlet and navier boundary conditions the spectrum of this operator exhibits some unexpected features radial data may generate nonradial solutions these boundary conditions are also of some interest in semilinear equations since they enable us to give explicit radial singular solutions to fourth order gelfand type problems

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

discrete product systems and twisted crossed products by semigroups a product systemeover a semigrouppis a family of hilbert spaces es s p together with multiplicationses et est we vieweas a unitary valued cocycle onp and consider twisted crossed productsa e pinvolvingeand an action ofpby endomorphisms of ac algebraa whenpis quasi lattice ordered in the sense of nica we isolate a class of covariant representations ofe and consider a twisted crossed productbp e pwhich is universal for covariant representations ofewhenehas finite dimensional fibres and in general is slightly larger in particular whenp nand dim e1 our algebrabn e n is a new infinite analogue of the toeplitz cuntz algebras ton our main theorem is a characterisation of the faithful representations ofbp e p

probability measures on solenoids corresponding to fractal wavelets the measure on generalized solenoids constructed using filters by dutkay and jorgensen in 12 is analyzed further by writing the solenoid as the product of a torus and a cantor set using this decomposition key differences are revealed between solenoid measures associated with classical filters in r d and those associated with filters on inflated fractal sets in particular it is shown that the classical case produces atomic fiber measures and as a result supports both suitably defined solenoid msf wavelets and systems of imprimitivity for the corresponding wavelet representation of the generalized baumslag solitar group in contrast the fiber measures for filters on inflated fractal spaces cannot be atomic and thus can support neither msf wavelets nor systems of imprimitivity

on thermodynamics of rational mapsi negative spectrum we study the pressure spectrum p t of the maximal measure for arbitrary rational maps we also consider its modified version which is defined by means of the variational principle with respect to non atomic invariant measures it is shown that for negative values of t the modified spectrum has all major features of the hyperbolic case analyticity the existence of a spectral gap for the corresponding transfer operator rigidity properties etc the spectrum p t can be computed in terms of their legendre transforms are the hausdorff and the box counting dimension spectra of the maximal measure respectively this work is closely related to a paper 32 by d ruelle

on finding sign changing solutions abstract some parameter depending linking theorems are established which allow to produce a bounded and sign changing palais smale sequence for even functionals a parameter depending fountain theorem is obtained which provides infinitely many bounded and sign changing palais smale sequences a variant mountain pass theorem is built in cones which yields bounded positive and negative palais smale sequences the usual palais smale type compactness condition and its variants are completely not necessary for these theories more exact locations of the critical sequences can be determined the abstract results are applied to the schrodinger equation with or without critical sobolev exponents u v x u u 2 2 u f x u x r n 0 where 2 is the critical sobolev exponent the existence of multiple sign changing solutions is obtained the positive and negative solutions are also gained as by products we will also show that this schrodinger problem with jumping nonlinearity is independent of the fucik spectrum

fundamental solutions and eigenfunction expansions for schrodinger operators i fundamental solutions on considere des developpements en fonctions propres pour des operateurs de schrodinger a n corps avec des potentiels a courte et longue portees on construit l expression de l operateur integral de fourier de la solution fondamentale globale en temps pour l equation de schrodinger correspondante

fundamental solutions and eigenfunction expansions for schrodinger operators ii eigenfunction expansions where we assume that v x satisfies assumptions i and ii of part i namely v x is a real valued function of xern in studying eigenfunction expansions for h we further assume the existence and intertwining property of the modified channel wave operator w or w 9 whose definition will be given in a general form in sect 1 under these assumptions we first construct eigendistributions f for if which expand the range of w and prove a structure theorem for them using the fourier integral operator expression of the fundamental solution e ttb obtained in part i this structure theorem is then used in sect 2 to prove a regularity result for x fj indicating the variables in question the pairing i 9 py g rm pe rm m is taken to satisfy f for pesf rm where is the z inner product for hilbert spaces jf j b j jf denotes the space of bounded operators from 2tf into tf and b j b j j y

symmetric solutions for a class of singular biharmonic elliptic systems involving critical exponents this paper deals with a class of singular biharmonic elliptic systems involving critical exponents in a bounded symmetric domain by using the variational method and the symmetric criticality principle of palais we obtain several existence and multiplicity results of g symmetric solutions for the systems

the algebra of harmonic functions for a matrix valued transfer operator abstract we analyze matrix valued transfer operators we prove that the fixed points of transfer operators form a finite dimensional c algebra for matrix weights satisfying a low pass condition we identify the minimal projections in this algebra as correlations of scaling functions i e limits of cascade algorithms

existence and multiplicity of solutions for fourth order elliptic equations in rn abstract in this paper we study the fourth order elliptic equations 2 u u v x u f x u in r n u h 2 r n where 1 and the nonlinearity f is either superlinear or sublinear at infinity we establish the existence and multiplicity results without the compactness of embedding of the working space which unify and sharply improve the recent results of liu chen and wu j liu s chen x wu existence and multiplicity of solutions for a class of fourth order elliptic equations in r n j math anal appl 395 2012 608 615

on the existence and multiplicity of solutions for a class of singular elliptic problems abstract in this paper we prove the existence and multiplicity of solutions for a class of elliptic problems with singular coefficients we also prove the existence of a sign changing solution for a brezis nirenberg type problem with hardy potential and singular coefficients our proofs are based on the krasnoselskii genus the concentration compactness principle of lions and the linking theorem

commutator methods and a smoothing property of the schrodinger evolution group on montre que le groupe d evolution de schrodinger unitaire a une propriete de lissage dans certains espaces de sobolev ponderes

sign changing critical points from linking type theorems in this paper the relationships between sign changing critical point theorems and the linking type theorems of m schechter and the saddle point theorems of p rabinowitz are established the abstract results are applied to the study of the existence of sign changing solutions for the nonlinear schrodinger equation u v x u f x u u h 1 r n where f x u is a caratheodory function problems of jumping or oscillating nonlinearities and of double resonance are considered

models for noncommuting operators abstract this paper develops a model theory for a pair of noncommuting operators using backward shift operators on a fock space rota s theorem is generalized i e it is shown that any two bounded operators on a hilbert space are simultaneously similar to part of a pair of backward shift operators on a fock space these shift operators and the fock space framework are also used to develop a dilation theory for two noncommuting operators

unwrapping eigenfunctions to discover the geometry of almost invariant sets in hyperbolic maps the numerical approximation of perron frobenius operators allows efficient determination of the physical invariant measure of chaotic dynamical systems as a fixed point of the operator eigenfunctions of the perron frobenius operator corresponding to large subunit eigenvalues have been shown to describe almost invariant dynamics in one dimensional expanding maps we extend these ideas to hyperbolic maps in higher dimensions while the eigendistributions of the operator are relatively uninformative applying a new procedure called unwrapping to regularised versions of the eigendistributions clearly reveals the geometric structures associated with almost invariant dynamics this unwrapping procedure is applied to a uniformly hyperbolic map of the unit square to discover this map s dominant underlying dynamical structure and to the standard map to pinpoint clusters of period 6 orbits

sign changing saddle point abstract in this paper the saddle point theorems are generalized to a new version by showing that there exists a sign changing saddle point besides zero the abstract result is applied to the semilinear elliptic boundary value problem u f x u in u 0 on and the schrodinger equation u v x u f x u x r n u x 0 as x where r n is a bounded domain with smooth boundary the schrodinger operator v has both eigenvalues and essential spectrum the asymptotically linear case is considered which permits double resonance to be happened some existence results of sign changing solutions are established

the differential zeta function for axiom a attractors closed orbit of least period x t an important problem is to construct the meromorphic extensions for these zeta functions a detailed knowledge of the domain of s gives information on the long term behaviour of the flow for example this is a standard approach to deriving asymptotic formulae for closed orbits cf 9 for the case of geodesic flows on surfaces of constant negative curvature the zeta function is known to have a meromorphic extension to the entire complex plane unfortunately an obstruction to a general theory along these lines is the existence of examples of axiom a flows for which d s does not have a meromorphic extension to c in a recent article william parry proposed a modified definition of a zeta function for axiom a attractors he defined the differential zeta function by ns s h i e s t l where the least period x x of a closed orbit is replaced by the expansion xu t along the unstable manifold around the orbit 8 parry also defined the useful notion of a synchronized flow i e one for which the measure of maximal entropy and the srb measure coincide the following remark is taken from page 273 of his article when the flow is synchronized the zeta functions coincide this is the case for example with a geodesic flow on a surface of constant negative curvature one wonders whether synchronization has something to do with the very desirable features of the zeta function of such a geodesic flow in this article we shall give a solution to parry s question which shows that in many cases du s has a meromorphic extension to the entire complex plane our main result can be stated as follows

zeta functions and transfer operators for piecewise monotone transformations given a piecewise monotone transformationt of the interval and a piecewise continuous complex weight functiong of bounded variation we prove that the ruelle zeta function z of t g extends meromorphically to z 1 where lim g tn 1 g tg 1 n and thatz is a pole of if and only ifz 1 is an eigenvalue of the corresponding transfer operator l we do not assume that l leaves a reference measure invariant

harmonic analysis of iterated function systems with overlap an iterated function system ifs is a system of contractive mappings i y y i 1 n finite where y is a complete metric space every such ifs has a unique up to scale equilibrium measure also called the hutchinson measure and we study the hilbert space l2 in this paper we extend previous work on ifss without overlap our method involves systems of operators generalizing the more familiar cuntz relations from operator algebra theory and from subband filter operators in signal processing these cuntz like operator systems were used in recent papers on wavelet analysis by baggett jorgensen merrill and packer contemp math 345 11 25 2004 where they serve as a first step to generating wavelet bases of parseval type alias normalized tight frames i e wavelet bases with redundancy similarly it was shown in work by dutkay and jorgensen rev mat iberoam 22 131 180 2006 that the iterative operator approach works well for generating wavelets on fractals from ifss without overla

type i product systems of hilbert modules abstract christensen and evans showed that in the language of hilbert modules a bounded derivation on a von neumann algebra with values in a two sided von neumann module i e a sufficiently closed two sided hilbert module are inner then they use this result to show that the generator of a normal uniformly continuous completely positive cp semigroup on a von neumann algebra decomposes into a suitably normalized cp part and a derivation like part the backwards implication is left open in these notes we show that both statements are equivalent among themselves and equivalent to a third one namely that any type i tensor product system of von neumann modules has a unital central unit from existence of a central unit we deduce that each such product system is isomorphic to a product system of time ordered fock modules we thus find the analogue of arveson s result that type i product systems of hilbert spaces are symmetric fock spaces on the way to our results we have to develop a number of tools interesting on their own right inspired by a very similar notion due to accardi and kozyrev we introduce the notion of semigroups of completely positive definite kernels cpd semigroups being a generalization of both cp semigroups and schur semigroups of positive definite c valued kernels the structure of a type i system is determined completely by its associated cpd semigroup and the generator of the cpd semigroup replaces arveson s covariance function as another tool we give a complete characterization of morphisms among product systems of time ordered fock modules in particular the concrete form of the projection endomorphisms allows us to show that subsystems of time ordered systems are again time ordered systems and to find a necessary and sufficient criterion when a given set of units generates the whole system as a byproduct we find a couple of characterizations of other subclasses of morphisms we show that the set of contractive positive endomorphisms are order isomorphic to the set of cpd semigroups dominated by the cpd semigroup associated with type i system

infinitely many solutions for fourth order elliptic equations abstract in this paper we study a class of fourth order elliptic equations setting on r n based on the minimax methods in critical point theory we obtain the existence of infinitely many large energy and small energy solutions which unifies and improves the recent results of yin and wu y yin x wu high energy solutions and nontrivial solutions for fourth order elliptic equations j math anal appl 375 2011 699 705

spectral characterization of anomalous diffusion of a periodic piecewise linear intermittent map abstract for a piecewise linear version of the periodic map with anomalous diffusion the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions of the frobenius perron fp operator are explicitly derived the evolution of the averages is controlled by real eigenvalues as well as continuous spectra terminating at the unit circle appropriate scaling limits are shown to give a normal diffusion if the reduced map is in the stationary regime with normal fluctuations a levy flight if the reduced map is in the stationary regime with levy type fluctuations and a transport of ballistic type if the reduced map is in the non stationary regime

linear response and consequences for differentiability of statistical quantities and multifractal analysis in this article we initially prove the differentiability of the topological pressure equilibrium states and their densities with respect to smooth expanding dynamical systems and any smooth potential this is done by proving the regularity of the dominant eigenvalue of the transfer operator with respect to dynamics and potential from that we obtain strong consequences on the regularity of the dynamical system statistical properties that apply in more general contexts indeed we prove that the average and variance obtained from the central limit theorem vary c r 1 with respect to the c r expanding dynamics and c r potential and also there is a large deviations principle exhibiting a c r 1 rate with respect to the dynamics and the potential an application for multifractal analysis is given we also obtained asymptotic formulas for the derivatives of the topological pressure and other thermodynamical quantities

structure of free semigroupoid algebras abstract a free semigroupoid algebra is the wot closure of the algebra generated by a tck family of a graph we obtain a structure theory for these algebras analogous to that of free semigroup algebra we clarify the role of absolute continuity and wandering vectors these results are applied to obtain a lebesgue von neumann wold decomposition of tck families along with reflexivity a kaplansky density theorem and classification for free semigroupoid algebras several classes of examples are discussed and developed including self adjoint examples and a classification of atomic free semigroupoid algebras up to unitary equivalence

hilbert spaces built on a similarity and on dynamical renormalization we develop a hilbert space framework for a number of general multiscale problems from dynamics the aim is to identify a spectral theory for a class of systems based on iterations of a non invertible endomorphism we are motivated by the more familiar approach to wavelet theory which starts with the two to one endomorphism r z z2 in the one torus t a wavelet filter and an associated transfer operator this leads to a scaling function and a corresponding closed subspace v0 in the hilbert space l2 r using the dyadic scaling on the line r one has a nested family of closed subspaces vn n z with trivial intersection and with dense union in l2 r more generally we achieve the same outcome but in different hilbert spaces for a class of non linear problems in fact we see that the geometry of scales of subspaces in hilbert space is ubiquitous in the analysis of multiscale problems e g martingales complex iteration dynamical systems graph iterated function systems of affine type and subshifts in

critical semilinear biharmonic equations in rn an existence theorem is obtained for a fourth order semilinear elliptic problem in r n involving the critical sobolev exponent n 4 n 4 n 4 a preliminary result is that the best constant in the sobolev embedding l 2n n 4 r n is attained by all translations and dilations of 1 x 2 4 n 2 the best constant is found to be

the measure of a measurement we identify a fractal scale s in a family of borel probability measures on the unit interval which arises independently in quantum information theory and in wavelet analysis the scales s we find satisfy s r and s 1 some s 1 we identify these scales s by considering the asymptotic properties of u j j s where j are dyadic subintervals and j 0

constrained von neumann inequalities abstract an equivalent formulation of the von neumann inequality states that the backward shift s on l 2 is extremal in the sense that if t is a hilbert space contraction then p t p s for each polynomial p we discuss several results of the following type if t is a hilbert space contraction satisfying some constraints then s restricted to a suitable invariant subspace is an extremal operator several operator radii are used instead of the operator norm applications to inequalities of coefficients of rational functions positive on the torus are given

a concentration compactness lemma with applications to singular eigenvalue problems let omega subset of or equal to r n be any open set we study the nonlinear eigenvalue problem delta p u lambda v x u p 2 u u epsilon d 0 1 p omega where 1 p n and v is an element of l loc 1 omega may have strong singularities and an indefinite sign the key ingredient is a precised concentration compactness lemma related to v dependent limiting problems this work follows extends and simplifies that of a tertikas 1998 j funct anal 154 42 66 dealing with the positive linear case for omega r n c 1999 academic press

reconstruction of singularities for solutions of schrodinger s equation we determine the behavior in time of singularities of solutions to some schrodinger equations onr n we assume the hamiltonians are of the formh 0 v where h 0 1 2 delta 1 2 sum limits k 1 n omega k 2 x k 2 and wherev is bounded and smooth with decaying derivatives when all k 0 the kernelk t x y of exp ith is smooth inx for every fixed t y when all 1 are equal but non zero the initial singularity reconstructs at times t frac m pi omega 1 and positionsx 1 m y just as ifv 0 k is otherwise regular in the general case the singular support is shown to be contained in the union of the hyperplanes x x js 1 l js y js when j t l j forj j 1 j r

existence and convergence of solutions for nonlinear biharmonic equations on graphs abstract in this paper we first prove some propositions of sobolev spaces defined on a locally finite graph g v e which are fundamental when dealing with equations on graphs under the variational framework then we consider a nonlinear biharmonic equation 2 u u a 1 u u p 2 u on g v e under some suitable assumptions we prove that for any 1 and p 2 the equation admits a ground state solution u moreover we prove that as the solutions u converge to a solution of the equation 2 u u u u p 2 u in u 0 on where x v a x 0 is the potential well and denotes the boundary of

explicit eigenvalue estimates for transfer operators acting on spaces of holomorphic functions abstract we consider transfer operators acting on spaces of holomorphic functions and provide explicit bounds for their eigenvalues more precisely if is any open set in c d and l is a suitable transfer operator acting on bergman space a 2 its eigenvalue sequence n l is bounded by n l a exp a n 1 d where a a 0 are explicitly given

diffusion effusion and chaotic scattering an exactly solvable liouvillian dynamics we study diffusion and chaotic scattering in a chain of baker maps coupled together which forms an area preserving mapping of an infinitely extended strip onto itself this exactly solvable mapping sustains chaotic behaviors and diffusion processes the relationship between the diffusion coefficient the lyapunov exponent and the entropy per unit time is derived the long lived classical resonances of the liouville evolution operator are proved to converge toward the eigenvalues of the phenomenological diffusion equation in this sense there is a quasi isomorphism between the resonance spectrum of the liouville evolution and the eigenvalue spectrum of the phenomenological diffusion equation furthermore we show that a fractal repeller is associated to each non equilibrium state in the isolated and finite multibaker chain the nonequilibrium states are all unstable with respect to the equilibrium validating a weak form of the second principle of thermodynamics for the present dynamical system consequences of nonequilibrium fractals on classical measurements are discussed we then describe the open multibaker chain as a scattering system fractal properties of chaotic scattering are here shown to be related to diffusion in the chain

on some fourth order semilinear elliptic problems in r n the existence of two solutions for a fourth order semilinear elliptic problem involving critical growth from the viewpoint of sobolev embedding was established the basic tools used in the analysis were the mountain pass theorem constrained minimization and concentration compactness principle the existence of positive principle eigenvalues for the corresponding linear elliptic problem was also investigated

the n particle scattering problem asymptotic completeness for short range systems on demontre la completude asymptotique pour des systemes de mecanique quantique a courte portee constitues d un nombre arbitraire de particules

one dimensional gibbs states and axiom a diffeomorphisms on etudie la mecanique statistique en equilibre de systemes reticules classiques a une dimension a interactions a decroissance exponentielle pour de tels systemes les transformees de fourier des fonctions de correlation de paires sont meromorphes dans une bande et les residus des poles peuvent s exprimer en termes de distributions de gibbs on applique ces resultats aux diffeomorphismes de l axiome a de smale

infinitely many solutions to perturbed elliptic equations abstract a new version of perturbation theory is developed which produces infinitely many sign changing critical points for uneven functionals the abstract result is applied to the following elliptic equations with a hardy potential and a perturbation from symmetry u u x 2 f x u p x u in u 0 on and u u q 2 x s u p x u in u 0 on where 0 s 2 is a smooth bounded domain of r n and p x u is not odd in u infinitely many sign changing solutions are obtained

the thermodynamic formalism for expanding maps letf x x be an expanding map of a compact space small distances are increased by a factor 1 a generating function z is defined which countsf periodic points with a weight one can express in terms of nonstandard fredholm determinants of certain transfer operators which can be studied by methods borrowed from statistical mechanics in this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of z gibbs distributions and applications to julia sets are also discussed some new results are proved and some natural conjectures are proposed

applications of the wold decomposition to the study of row contractions associated with directed graphs based on a wold decomposition for families of partial isometries and projections of cuntz krieger toeplitz type we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks we prove a szego type factorization theorem for ckt families which leads to information on the structure of the unit ball in free semigroupoid algebras and show that joint similarity implies joint unitary equivalence for such families for each graph we prove a generalization of von neumann s inequality which applies to row contractions of operators on hilbert space which are related to the graph in a natural way this yields a functional calculus determined by quiver algebras and free semigroupoid algebras we establish a generalization of coburn s theorem for the c algebra of a ckt family and prove a universality theorem for c algebras generated by these families in both cases the c algebras generated by quiver algebras play the universal role

perturbation of embedded eigenvalues in the generalized n body problem we discuss the perturbation of continuum eigenvalues without analyticity assumptions among our results we show that generally a small perturbation removes these eigenvalues in accordance with fermi s golden rule thus generically in a baire category sense the schrodinger operator has no embedded non threshold eigenvalues

an equivariant brauer group and actions of groups onc algebras suppose that g t is a second countable locally compact trans formation group given by a homomorphism l g homeo t and that a is a separable continuous trace c algebra with spectrum t an action g aut a is said to cover l if the induced action of g on t coincides with the original one we prove that the set brg t of morita equivalence classes of such systems forms a group with multiplication given by the balanced tensor product a b a c0 t b and we refer to brg t as the equivariant brauer group we give a detailed analysis of the structure of brg t in terms of the moore cohomology of the group g and the integral cohomology of the space t using this we can characterize the stable continuous trace c algebras with spectrum t which admit actions covering l in particular we prove that if g r then every stable continuous trace c algebra admits an essentially unique action covering l thereby substantially improving results of raeburn and rosenberg

on ruelle perron frobenius operators i ruelle theorem we study ruelle perron frobenius operators for locally expanding and mixing dynamical systems on general compact metric spaces associated with potentials satisfying the dini condition in this paper we give a proof of the ruelle theorem on gibbs measures it is the first part of our research on the subject the rate of convergence of powers of the operator will be presented in a forthcoming paper

action principle in nonequilibrium statistical dynamics we introduce a variational method for approximating distribution functions of dynamics with a liouville operator l in terms of a nonequilibriumaction functional for two independent left and right trial states the method is valid for deterministic or stochastic markov dynamics and for stationary or time dependent distributions a practical rayleigh ritz procedure is advanced whose inputs are a finitely parametrized ansatz for the trial states leading to a parametric action for their evolution the euler lagrange equations of the action principle are hamiltonian in form generally noncanonical this permits a simple identification of fixed points as critical points of the parametric hamiltonian we also establish a variational principle for low order statistics such as mean values and correlation functions by means of the least effective action the latter is a functional of the given variable which is positive and convex as a consequence of h older realizability inequalities its value measures the cost for a fluctuation from the average to occur and in a weak noise limit it reduces to the onsager machlup action in general the effective action is shown to arise from the nonequilibrium action functional by a constrained variation this result provides a rayleigh ritz scheme for calculating just the desired low order statistics with internal consistency checks less demanding than for the full distribution textcopyright 1996 the american physical society

sign changing solutions for p biharmonic equations with hardy potential in the half space abstract in this paper by using the method of invariant sets of descending flow we obtain the existence of positive solutions and sign changing solutions of p biharmonic equations with hardy potential in the half space

certain free products of graph operator algebras abstract we develop a notion of a generalized cuntz krieger family of projections and partial isometries where the range of the partial isometries need not have trivial intersection we associate to these generalized cuntz krieger families a directed graph with a coloring function on the edge set we call such a directed graph an edge colored directed graph we then study the c algebras and the non selfadjoint operator algebras associated to edge colored directed graphs these algebras arise as free products of directed graph algebras with amalgamation we then determine the c envelopes for a large class of the non selfadjoint algebras finally we relate properties of the edge colored directed graphs to properties of the associated c algebra including simplicity and nuclearity using the free product description of these algebras we investigate the k theory of these algebras

meromorphic extensions of generalised zeta functions in this paper we give a full description of the spectrum of the ruelle perron frobenius operator acting on the banach space of holder continuous functions on a subshift of finite type theorem 1 these results are then used to extend the meromorphic domain of generalised zeta functions theorem 2 the most important application of these results is to the domain of the smale zeta function for axiom a flows theorem 3 in the course of this paper we settle questions raised by ruelle and sunada

the resonance spectrum of the cusp map in the space of analytic functions we prove that the frobenius perron operator u of the cusp map f 1 1 1 1 f x 1 2 x which is an approximation of the poincare section of the lorenz attractor has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1 we also prove that for any q 0 1 the spectrum of u in the hardy space in the disk z c z q 1 q is the union of the segment 0 1 and some finite or countably infinite set of isolated eigenvalues of finite multiplicity

infinitely many solutions for fourth order elliptic equations with general potentials abstract this paper is concerned with the following fourth order elliptic equations 2 u u v x u f x u in r n u h 2 r n where u r n r under general assumption on potential v x and f x u is indefinite sign and sublinear as u we establish the existence of infinitely many solutions by using the genus properties in critical point theory recent results from the literature are extended