topologies on measured groupoids abstract if an analytic borel group g has a quasiinvariant measure it is known that g is actually a locally compact group with the original borel structure being generated by the topology and the original measure being equivalent to haar measure in this paper a variation is given on the known proof which then extends to show that an analytic measured groupoid has a compact and also a locally compact inessential reduction which is a topological groupoid in the compact case it is proved that every almost homomorphism agrees a e with a strict homomorphism also the topology is used to show that every measured groupoid has a complete countable section 7 and that every locally compact equivalence relation has a complete transversal 3 these are further used to show that some results of feldman et al 7 apply in general and that a locally compact groupoid with continuous haar system has sufficiently many non singular borel g sets provided that the orbit measures are atom free 23

zappa szep products of semigroups and their c algebras abstract zappa szep products of semigroups provide a rich class of examples of semigroups that include the self similar group actions of nekrashevych we use li s construction of semigroup c algebras to associate a c algebra to zappa szep products and give an explicit presentation of the algebra we then define a quotient c algebra that generalises the cuntz pimsner algebras for self similar actions we indicate how known examples previously viewed as distinct classes fit into our unifying framework we specifically discuss the baumslag solitar groups the binary adding machine the semigroup n n and the a x b semigroup z z

herz schur multipliers of dynamical systems abstract we extend the notion of a herz schur multiplier to the setting of non commutative dynamical systems given a c algebra a a locally compact group g and an action of g on a we define transformations on the reduced crossed product of a by which in the case a c reduce to the classical herz schur multipliers we introduce schur a multipliers establish a characterisation that generalises the classical descriptions of schur multipliers and present a transference theorem in the new setting identifying isometrically the herz schur multipliers of the dynamical system a g with the invariant part of the schur a multipliers we discuss special classes of herz schur multipliers in particular those associated to a locally compact abelian group g and its canonical action on the c algebra c of the dual group

rotational surfaces in mathbb l 3 and solutions of the nonlinear sigma model the gauss map of non degenerate surfaces in the three dimensional minkowski space are viewed as dynamical fields of the two dimensional o 2 1 nonlinear sigma model in this setting the moduli space of solutions with rotational symmetry is completely determined essentially the solutions are warped products of orbits of the 1 dimensional groups of isometries and elastic curves in either a de sitter plane a hyperbolic plane or an anti de sitter plane the main tools are the equivalence of the two dimensional o 2 1 nonlinear sigma model and the willmore problem and the description of the surfaces with rotational symmetry a complete classification of such surfaces is obtained in this paper indeed a huge new family of lorentzian rotational surfaces with a space like axis is presented the description of this new class of surfaces is based on a technique of surgery and a gluing process which is illustrated by an algorithm

toeplitz operators and solvable c algebras on hermitian symmetric spaces bounded symmetric domains cartan domains and exceptional domains are higher dimensional generalizations of the open unit disc in this note we give a structure theory for the c algebra t generated by all toeplitz operators tf h p fh with continuous symbol function g c s on the shilov boundary 5 of a bounded symmetric domain d of arbitrary rank r here h belongs to the hardy space h s and p l s h s is the szego projection for domains of rank 1 and tube domains of rank 2 the structure of t has been determined in 1 2 in these cases toeplitz operators are closely related to pseudodifferential operators for the open unit disc t is the c algebra generated by the unilateral shift the structure theory for the general case 12 is based on the fact that d can be realized as the open unit ball of a unique jordan triple system z 7 theorem 4 1 denoting the jordan triple product by uv w a tripotent e g z satisfies ee e e tripotents generalize the partial isometries of matrix algebras and determine the boundary structure of d c z cf 7 theorem 6 3 our principal result 12 cf also 3 4 8 is the following

ideal structure of uniform roe algebras of coarse spaces abstract let c u x e be the uniform roe algebra of a coarse space x e with uniformly locally finite coarse structure by a controlled truncation technique we show that the controlled propagation operators in an ideal i of c u x e are exactly the controlled truncations of elements in i it follows that the lattice of the ideals of the uniform roe algebra c u x e in which controlled propagation operators are dense the lattice of the invariant open subsets in the unit space of the groupoid g x introduced by skandalis tu and yu the lattice of the ideals of the coarse structure e and the lattice of the ideals of the coarse space x are mutually isomorphic these lattices also give rise to a type of classification for the ideals of c u x e

on c algebras generated by isometries with twisted commutation relations in the theory of c algebras interesting noncommutative structures arise as deformations of the tensor product e g the rotation algebra a as a deformation of c s1 c s1 we deform the tensor product of two toeplitz algebras in the same way and study the universal c algebra t t generated by two isometries u and v such that uv e2 i vu and u v e 2 i vu for r since the second relation implies the first one we also consider the universal c algebra t t generated by two isometries u and v with the weaker relation uv e2 i vu such a weaker case does not exist in the case of unitaries and it turns out to be much more interesting than the twisted tensor product case t t we show that t t is nuclear whereas t t is not even exact also we compute the k groups and we obtain k0 t t z and k1 t t 0 and the same k groups for t t

spectrum and analytical indices of the c algebra of wiener hopf operators we study multivariate generalisations of the classical wiener hopf algebra which is the c algebra generated by the wiener hopf operators given by convolutions restricted to convex cones by the work of muhly and renault this c algebra is known to be isomorphic to the reduced c algebra of a certain restricted action groupoid given by the action of euclidean space on a certain compactification using groupoid methods we construct composition series for the wiener hopf c algebra by a detailed study of this compactification we compute the spectrum and express homomorphisms in k theory induced by the symbol maps which arise by the subquotients of the composition series in analytical terms namely these symbols maps turn out to be given by an analytical family index of a continuous family of fredholm operators in a subsequent paper we also obtain a topological expression of these indices

on the imaging of reflectors in the earth in this paper i present a modification of the beylkin inversion operator this modification accounts for the band limited nature of the data and makes the role of discontinuities in the sound speed more precise the inversion presented here partially dispenses with the small parameter constraint of the born approximation this is shown by applying the proposed inversion operator to upward scattered data represented by the kirchhoff approximation using the angularly dependent geometrical optics reflection coefficient a fully nonlinear estimate of the jump in sound speed may be extracted from the output of this algorithm interpreted in the context of these kirchhoff approximate data for the forward problem the inversion of these data involves integration over the source receiver surface the reflecting surface and frequency the spatial integrals are computed by the method of stationary phase the output is asymptotically a scaled singular function of the reflecting surface the singular function of a

pull backs of algebras and crossed products by certain diagonal actions let g be a locally compact group and p q t a principal g bundle if a is a c algebra with primitive ideal space t the pull back p a of a along p is the balanced tensor product co q c t a if 3 g aut a consists of c t module automorphisms and y g aut co q is the natural action then the automorphism group y 0x 3 of co q 0 a respects the balancing and induces the diagonal action p 3 of g on p a we discuss some examples of such actions and study the crossed product p a x p g we suggest a substitute d for the fixed point algebra prove p a x g is strongly morita equivalent to d and investigate the structure of d in various cases in particular we ask when d is strongly morita equivalent to a sometimes but by no means always and investigate the case where a has continuous trace let b be a c algebra and g a locally compact group acting on b as a strongly continuous automorphism group a our goal here is to study the crossed product c algebra b x g for two classes of diagonal actions for which the induced action of g on b is free the first class includes actions of the form y 0x3 on b co q 0 a where p q t is a principal g bundle y is the dual action of g on co q and 3 g aut a is an action of g on another c algebra a we also consider diagonal actions on algebras which are the pull backs of another algebra a along a principal bundle p q t if a is a c algebra with primitive ideal space t then the pull back p a is the balanced tensor product co q cb t a when 3 g aut a consists of c t module automorphisms the product action ty 0 3 preserves the balancing and the diagonal action p 3 is by definition the induced action on p a in general if f x y and q prima y are continuous then cb y acts on co x by composition with f and on a by composition with q and the daunshofmann theorem we can therefore define the pull back f a of a along f as the c algebraic tensor product co x cb y a the reason for the name is that when a is the algebra of sections of some c bundle e over y there is a natural isomorphism of f a onto the algebra of sections of the pull back f e in 1 we discuss this and other basic properties of pull backs and give some evidence to show they are likely to be of interest in particular we show that if g is abelian and a g aut a is locally unitary in the sense of 18 then the crossed product received by the editors october 20 1983 and in revised form february 15 1984 1980 mathematics subject classification primary 46l40 46l55

c algebras of toeplitz type associated with algebraic number fields we associate with the ring r of algebraic integers in a number field a c algebra mathfrak t r it is an extension of the ring c algebra mathfrak a r studied previously by the first named author in collaboration with x li in contrast to mathfrak a r it is functorial under homomorphisms of rings it can also be defined using the left regular representation of the ax b semigroup r rtimes r times on ell 2 r rtimes r times the algebra mathfrak t r carries a natural one parameter automorphism group sigma t t in mathbb r we determine its kms structure the technical difficulties that we encounter are due to the presence of the class group in the case where r is not a principal ideal domain in that case for a fixed large inverse temperature the simplex of kms states splits over the class group the partition functions are partial dedekind zeta functions we prove a result characterizing the asymptotic behavior of quotients of such partial zeta functions which we then use to show uniqueness of the beta kms state for each inverse temperature beta in 1 2

boundary quotients of c algebras of right lcm semigroups abstract we study c algebras associated to right lcm semigroups that is semigroups which are left cancellative and for which any two principal right ideals are either disjoint or intersect in another principal right ideal if p is such a semigroup its c algebra admits a natural boundary quotient q p we show that q p is isomorphic to the tight c algebra of a certain inverse semigroup associated to p and thus is isomorphic to the c algebra of an etale groupoid we use this to give conditions on p which guarantee that q p is simple and purely infinite and give applications to self similar groups and zappa szep products of semigroups

velocity inversion using a stratified reference we present an inversion algorithm for backscattered stacked seismic data which will reconstruct the velocity profile in realistic earth conditions the basic approach follows that of the original constant reference speed cohen and bleistein paper 1979a in that hig hfrequency asymptotics and perturbation methods are used however we use a reference speed which may vary with depth and this greatly enhances the validity of the perturbation assumption and hence the inversion results the new algorithm enjoys the same economies and stability properties of the original algorithm making it very competitive with current migration schemes four major assumptions are made 1 the acoustic wave equation is an adequate model 2 stacked data have amplitude information worth preserving fairly accurately 3 the actual reflectivity coefficients can be adequately modeled as perturbations from a continuous reference velocity which depends only on the depth variable and 4 the subsurface can be adequately

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

nica toeplitz algebras associated with product systems over right lcm semigroups abstract we prove uniqueness of representations of nica toeplitz algebras associated to product systems of c correspondences over right lcm semigroups by applying our previous abstract uniqueness results developed for c precategories our results provide an interpretation of conditions identified in work of fowler and fowler raeburn and apply also to their crossed product twisted by a product system in the new context of right lcm semigroups as well as to a new doplicher roberts type c algebra associated to the nica toeplitz algebra as a derived construction we develop nica toeplitz crossed products by actions with completely positive maps this provides a unified framework for nica toeplitz semigroup crossed products by endomorphisms and by transfer operators we illustrate these two classes of examples with semigroup c algebras of right and left semidirect products

chern character for twisted k theory of orbifolds for an orbifold x and h 3 x z we introduce the twisted cohomology h c x and prove that the non commutative chern character of connes karoubi establishes an isomorphism between the twisted k groups k x c and the twisted cohomology h

c algebras of multiplication operators on bergman spaces soit un domaine borne dans c soit a 2 l espace de bergman de toutes les fonctions analytiques sur qui sont de carre integrable par rapport a la mesure volumetrique et soit c la c algebre engendree par les operateurs de multiplication par les fonctions coordonnee sur on etudie les proprietes de c

an index theorem for wiener hopf operators abstract we study the multivariate generalisation of the classical wiener hopf algebra which is the c algebra generated by the wiener hopf operators given by convolutions restricted to convex cones by the work of muhly and renault this c algebra is known to be isomorphic to the reduced c algebra of a certain restricted action groupoid it admits a composition series and therefore a symbol calculus using groupoid methods we obtain in the framework of kasparov s bivariant kk theory a topological expression of the index maps associated to these symbol maps in terms of geometric topological data of the underlying convex cone this generalises an index theorem by upmeier concerning wiener hopf operators on symmetric cones our result covers a wide class of cones containing polyhedral and homogeneous cones

compact quantum groups and groupoidc algebras abstract we study simple compact matrix quantum groups in the context of groupoid c algebras and obtain explicit descriptions of the structure of the c algebra of quantum su n and a concrete formula for its haar functional

on c algebras of irreversible algebraic dynamical systems abstract extending the work of cuntz and vershik we develop a general notion of independence for commuting group endomorphisms based on this concept we initiate the study of irreversible algebraic dynamical systems which can be thought of as irreversible analogues of the dynamical systems considered by schmidt to each irreversible algebraic dynamical system we associate a universal c algebra and show that it is a uct kirchberg algebra under natural assumptions moreover we discuss the structure of the core subalgebra which turns out to be closely related to generalized bunce deddens algebras in the sense of orfanos we also construct discrete product systems of hilbert bimodules for irreversible algebraic dynamical systems which allow us to view the associated c algebras as cuntz nica pimsner algebras besides we prove a decomposition theorem for semigroup crossed products of unital c algebras by semidirect products of discrete left cancellative monoids

projections over quantum homogeneous odd dimensional spheres abstract we give a complete classification of isomorphism classes of finitely generated projective modules or equivalently unitary equivalence classes of projections over the c algebra c s q 2 n 1 of the quantum homogeneous sphere s q 2 n 1 then we explicitly identify as concrete elementary projections the quantum line bundles l k over the quantum complex projective space c p q n associated with the quantum hopf principal u 1 bundle s q 2 n 1 c p q n

the ring structure for equivariant twisted k theory we prove under some mild conditions that the equivariant twisted k theory group of a crossed module admits a ring structure if the twisting 2 cocycle is 2multiplicative we also give an explicit construction of the transgression map t1 h a h 1 n o a for any crossed module n and prove that any element in the image is multiplicative as a consequence we prove that under some mild conditions for a crossed module n and any e s that the equivariant twisted k theory group k e n admits a ring structure as an application we prove that for a compact connected and simply connected lie group g the equivariant twisted k theory group k c g g is endowed with a canonical ring structurek c g g k j d c g g k i j d c g g where d dimg and c h gog s

c algebras of right lcm monoids and their equilibrium states we study the internal structure of c algebras of right lcm monoids by means of isolating the core semigroup c algebra as the coecient algebra of a fock type module on which the full semigroup c algebra admits a left action if the semigroup has a generalised scale we classify the kms states for the associated time evolution on the semigroup c algebra and provide sucient conditions for uniqueness of the kms state at inverse temperature in a critical interval

nuclearity of semigroup c algebras and the connection to amenability abstract we study c algebras associated with subsemigroups of groups for a large class of such semigroups including positive cones in quasi lattice ordered groups and left ore semigroups we describe the corresponding semigroup c algebras as c algebras of inverse semigroups groupoid c algebras and full corners in associated group crossed products these descriptions allow us to characterize nuclearity of semigroup c algebras in terms of faithfulness of left regular representations and amenability of group actions moreover we also determine when boundary quotients of semigroup c algebras are uct kirchberg algebras this leads to a unified approach to cuntz algebras and ring c algebras

the brauer group of a locally compact groupoid we define the brauer group br g of a locally compact groupoid g to be the set of morita equivalence classes of pairs a consisting of an elementary c bundle a over g 0 satisfying fell s condition and an action of g on a by isomorphisms when g is the transformation groupoid x h then br g is the equivariant brauer group br h x in addition to proving that br g is a group we prove three isomorphism results first we show that if g and h are equivalent groupoids then br g and br h are isomorphic this generalizes the result that if g and h are groups acting freely and properly on a space x say g on the left and h on the right then br g x h and br h g x are isomorphic secondly we show that the subgroup br0 g of br g consisting of classes a with a having trivial dixmier douady invariant is isomorphic to a quotient e g of the collection tw g of twists over g finally we prove that br g is isomorphic to the inductive limit ext g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of the groups e g x where x varies over all principal g spaces x and g x is the imprimitivity groupoid associated to x

on c algebra of a semigroup of partial isometries abstract a c algebra associated to strongly continuous one parameter semigroups of partial isometries is introduced as a groupoid c algebra c g a one to one correspondence between non degenerate representations of c g and the semigroups is established it is proved also that c g contains an ideal j isomorphic to c 0 0 k and c g j c 0 r where k is the algebra of compact operators the c algebra c g is shown to be generated by one unbounded affiliated element whose image under each non degenerate representation is the infinitesimal generator of the corresponding semigroup

toeplitz algebras associated to endomorphisms of ore semigroups in this paper we consider the toeplitz algebra associated to actions of ore semigroups on c algebras in particular we consider injective and surjective actions of such semigroups we use the theory of groupoid dynamical systems to represent the toeplitz algebra as a groupoid crossed product we also discuss the k theory of the toeplitz algebra in some examples for instance we show that for the semigroup of positive matrices the k theory of the associated toeplitz algebra vanishes

c envelopes of semicrossed products by lattice ordered abelian semigroups abstract a semicrossed product is a non selfadjoint operator algebra encoding the action of a semigroup on an operator or c algebra we prove that when the positive cone of a discrete lattice ordered abelian group acts on a c algebra the c envelope of the associated semicrossed product is a full corner of a crossed product by the whole group by constructing a c cover that itself is a full corner of a crossed product and computing the shilov ideal we obtain an explicit description of the c envelope this generalizes a result of davidson fuller and kakariadis from z n to the class of all discrete lattice ordered abelian groups

semigroup crossed products and the toeplitz algebras of nonabelian groups abstract we consider the quasi lattice ordered groups g p recently introduced by nica we realise their universal toeplitz algebra as a crossed product b p p by a semigroup of endomorphisms and show that the toeplitz representation is faithful precisely when an amenability condition is satisfied we then show directly that many interesting free products are amenable the final result contains theorems of cuntz and dinh on the uniqueness of toeplitz cuntz algebras as special cases

toeplitz operators and weighted wiener hopf operators pseudoconvex reinhardt and tube domains the notion of weighted wiener hopf operators is introduced their relationship with toeplitz operators acting on the space of holomorphic functions which are square integrable with respect to a given symmetric measure is discussed the groupoid approach is used in order to present a general program for studying the c algebra generated by weighted wiener hopf operators associated with a solid cone of a second countable locally compact hausdorff group this is applied to the case when the group is the dual of a connected locally compact abelian lie group and the measure is well behaved in order to produce a geometric groupoid which is independent of the representation

regular representation of groupoid c algebras and applications to inverse semigroups the analogue of the left regular representation of a locally compact groupoid is constructed in the hausdoras well as in the non hausdorcase a necessary and su cient condition for a locally compact groupoid with a cocycle to be morita equi valent to a group action is obtained as an application the c algebras of a class of inverse semigroups is shown to be morita equivalent to crossed products of groups by abelian c

ring c algebras we associate reduced and full c algebras to arbitrary rings and study the inner structure of these ring c algebras as a result we obtain conditions for them to be purely infinite and simple we also discuss several examples originally our motivation comes from algebraic number theory

semigroup c algebras of ax b semigroups we study semigroup c algebras of ax b semigroups over integral domains the goal is to generalize several results about c algebras of ax b semigroups over rings of algebraic integers we prove results concerning k theory and structural properties like the ideal structure or pure infiniteness our methods allow us to treat ax b semigroups over a large class of integral domains containing all noetherian integrally closed domains and coordinate rings of affine varieties over infinite fields

amenability of groupoids arising from partial semigroup actions and topological higher rank graphs we consider the amenability of groupoids g equipped with a group valued cocycle c g q with amenable kernel c 1 e we prove a general result which implies in particular that g is amenable whenever q is amenable and if there is countable set d g such that c g u d q for all u g 0 we show that our result is applicable to groupoids arising from partial semigroup actions we explore these actions in detail and show that these groupoids include those arising from directed graphs higher rank graphs and even topological higher rank graphs we believe our methods yield a nice alternative groupoid approach to these important constructions

a computer implementation of 2 5 d common shot inversion the computer implementation of a two and one half dimensional 2 5 d constant density prestack inversion formalism with laterally and depth dependent background propagation speed is a kirchhoff type inversion summing data from a line of receivers over traveltime curves in the depth dependent background medium with weights determined from born kirchhoff inversion theory this theory predicts that the output will be a reflector map with peak amplitudes on each reflector being in known proportion to the angularly dependent geometrical optics reflection coefficient the 2 5 d feature provides for out of plane spreading correction consistent with the prescribed background medium the method is applied to a synthetic data set and to a physically modeled data set generated at the seismic acoustic laboratory the graphical output demonstrates the validity of the formalism as a kirchhoff migration parameter estimation for the synthetic data confirmed the theory parameter estimation for the experimental data wa

groupoid cohomology and extensions we show that haefliger s cohomology for etale groupoids moore s cohomology for locally compact groups and the brauer group of a locally compact groupoid are all particular cases of sheaf or cech cohomology for topological simplicial spaces

graded brauer groups of a groupoid with involution abstract we define a group brr g containing in a sense the graded complex and orthogonal brauer groups of a locally compact groupoid g equipped with an involution when the involution is trivial we show that the new group naturally provides a generalisation of donovan karoubi s graded orthogonal brauer group gbro more generally it is shown to be a direct summand of the well known graded complex brauer group in addition we prove that brr g identifies with a direct sum of a real cohomology group and the abelian group extr g s 1 of real graded s 1 central extensions a cohomological picture is then given

a new approach to recent constructions of c algebras from modular index theory abstract we present a new approach to c algebras recently constructed in the context of modular index theory by carey phillips putnam and rennie it turns out that their constructions can be identified with full corners of ideals in semigroup c algebras this new point of view leads to a systematic analysis of these algebras and their canonical maximal abelian subalgebras

toeplitz algebras and rotational automorphisms associated to polydiscs introduction given a bounded symmetric domain d in cm with d being normalized to be circular and to contain the origin upmeier 22 showed that there is a natural way to associate a c algebra to it this c algebra called the toeplitz c algebra of d and denoted 35 is a solvable c algebra with a composition series jk o k n l of length n where n is the rank of the symmetric domain 22 theorem 3 12 we observe that there is a natural group action on 3 by the compact group g of all biholomorphic automorphisms of d which lie in the connected component of the identity and which fix the origin proposition 1 1 every element 0 in g preserves the solvable series jk o k n l of 3 d we thereby obtain a composition series jk x0 z for the crossed product c algebra 3 xo z in this paper we show by introducing the notion of stratification of composition series see section 2 that the series jk x0 z is exactly the maximal radical series of 3 x0 z section 3 and thus obtain an isomorphism invariant for the latter c algebra when is the polydisc d we determine the k theory of the series jk xo z and their subquotients section 4 techniques from k theory using strong morita equivalence yield a complete classification of the c algebras 3 xo z where d is the n dimensional polydisc up to isomorphism for all 0 in g tn

toeplitz c algebras on bounded symmetric domains in this paper we develop a structure theory for the toeplitz c algebra y for an arbitrary bounded symmetric domain d in c classical or exceptional as the main result it is shown that 5y is a c algebra of type i which is solvable i e admits a finite composition sequence of closed ideals sk in 7 such that the subquotients fk i k are continuous fields of elementary c algebras of compact operators the length of this composition sequence coincides with the rank r of d as a hermitian symmetric space for 0 k r the spectral components sk of ay parametrizing the irreducible representations of y are realized in terms of the boundary components complex analytic faces of d the structure theory for y is based on the fact that the tangent space z c c of d carries a jordan algebraic structure z is a jordan triple system with triple product uv w describing the geometry of d in algebraic terms for example d is the open unit ball with respect to the so called spectral norm on z and the boundary components of d are in 1 1 correspondence with the tripotents e e z partial isometries satisfying ee e 4 e in particular the shilov boundary s of d consists of all tripotents of maximal rank r the jordan theoretic description of d was used in 17 to determine an explicit peter weyl decomposition of the hardy space h2 s cf 15 in terms of the norm functions generalized determinants associated with the jordan triple

three dimensional born inversion with an arbitrary reference recent work of g beylkin helped set the stage for very general seismic inversions we have combined these broad concepts for inversion with classical high frequency asymptotics and perturbation methods to bring them closer to practically implementable algorithms applications include inversion schemes for both stacked and unstacked seismic data basic assumptions are that the data have relative true amplitude and that a reasonably accurate background velocity c x y z is available the perturbation from this background is then sought since high frequency approximations are used throughout the resulting algorithms essentially locate discontinuities in velocity an expression for a full 3 d velocity inversion can be derived for a general data surface in this degree of generality the formula does not represent a computationally feasible algorithm primarily because a key jacobian determinant is not expressed in practical terms in several important cases however this shortcoming can be overcome and

crossed products byc0 x actions abstract suppose thatghas a representation grouph thatgab g g g is compactly generated and thatais ac algebra for which the complete regularization of prim a is a locally compact hausdorff spacex in a previous article we showed that there is a bijection z f between the collection of exterior equivalence classes of locally inner actions g aut a and the collection of principalgab bundlesz together with continuous functionsf x h2 g t in this paper we compute the crossed productsa gin terms of the dataz f andc h

wiener hopf operators on ordered homogeneous spaces i abstract the c algebra w p of wiener hopf operators related to an ordered homogeneous space g h is shown to be the homomorphic image of a groupoid c algebra to obtain this groupoid c algebra we construct an ordered compactification of g h the regularity of this compactification permits to show that w p contains the ideal of compact operators

a dixmier douady theorem for fell algebras abstract we generalise the dixmier douady classification of continuous trace c algebras to fell algebras to do so we show that c diagonals in fell algebras are precisely abelian subalgebras with the extension property and use this to prove that every fell algebra is morita equivalent to one containing a diagonal subalgebra we then use the machinery of twisted groupoid c algebras and equivariant sheaf cohomology to define an analogue of the dixmier douady invariant for fell algebras and to prove our classification theorem

the boundary quotient for algebraic dynamical systems abstract we introduce the notion of accurate foundation sets and the accurate refinement property for right lcm semigroups for right lcm semigroups with this property we derive a more explicit presentation of the boundary quotient in the context of algebraic dynamical systems we also analyse finiteness properties of foundation sets which lead us to a very concrete presentation based on starling s recent work we provide sharp conditions on certain algebraic dynamical systems for pure infiniteness and simplicity of their boundary quotient

on lorentzian surfaces with h2 k in minkowski 3 space abstract a well known classical result classifies the surfaces in 3 space r 3 with the mean curvatures h and the gauss curvatures k satisfying h 2 k as pieces of planes or two spheres corresponding results are given here for lorentzian surfaces in minkowski 3 space this work is done by proving that all the lorentzian surfaces with h 2 k in minkowski 3 space are null scrolls locally and can be classified into three cases two of which have no counterparts in euclidean space

prestack kirchhoff inversion of common offset data in trying to resolve complex geologic structures the pitfalls in employing the cdp method become evident additionally stacking multioffset traces corrupts the amplitudes necessary for stratigraphic analysis in order to preserve whatever structural and amplitude information is in the data prestack processing should be performed given common offset data and the velocity above a reflector prestack acoustic kirchhoff inversion resolves the location of the interface when amplitude information has been preserved in the data the method additionally calculates the reflection coefficient at each interface point for band limited seismic data the inversion operator produces a sinc like picture of the reflector with the peak amplitude of this band limited singular function equal to the angularly dependent reflection coefficient the inversion development is based upon high frequency kirchhoff data which are inserted into a general 3 d inversion operator asymptotically evaluating the four resulting integrals by the method of four dimensional stationary phase permits an inversion amplitude function to be chosen so that the inversion operator produces a singular function of support on the reflector weighted by the reflection coefficient specializing the three dimensional inversion operator to two and one half dimensions allows for processing of single lines of common offset data synthetic examples illustrate the accuracy of the method for constant velocity kirchhoff data as well as the problems in applying constant velocity data to multivelocity models

boundary quotients and ideals of toeplitz c algebras of artin groups abstract we study the quotients of the toeplitz c algebra of a quasi lattice ordered group g p which we view as crossed products by a partial actions of g on closed invariant subsets of a totally disconnected compact hausdorff space the nica spectrum of g p our original motivation and our main examples are drawn from right angled artin groups but many of our results are valid for more general quasi lattice ordered groups we show that the nica spectrum has a unique minimal closed invariant subset which we call the boundary spectrum and we define the boundary quotient to be the crossed product of the corresponding restricted partial action the main technical tools used are the results of exel laca and quigg on simplicity and ideal structure of partial crossed products which depend on amenability and topological freeness of the partial action and its restriction to closed invariant subsets when there exists a generalised length function or controlled map defined on g and taking values in an amenable group we prove that the partial action is amenable on arbitrary closed invariant subsets the topological freeness of the boundary action depends on topological freeness of the restriction to a certain lattice subgroup of g the core of g p which often turns out to be trivial our main results are obtained for right angled artin groups with trivial centre that is those with no cyclic direct factor they include a presentation of the boundary quotient in terms of generators and relations that generalises cuntz s presentation of o n a proof that the boundary quotient is purely infinite and simple and a parametrisation of the ideals of the toeplitz c algebra in terms of subsets of the standard generators of the artin group

amenability reiter s condition and liouville property abstract we show that the liouville property and reiter s condition are equivalent for semigroupoids this result applies to semigroups as well as semigroup actions in the special case of measured groupoids and locally compact groupoids our result proves kaimanovich s conjecture of the equivalence of amenability and the liouville property

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

bjorling problem for timelike surfaces in the lorentz minkowski space abstract we solve the bjorling problem for timelike surfaces in the lorentz minkowski space through a split complex representation formula obtained for this kind of surface our approach uses the split complex numbers and natural split holomorphic extensions as applications we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate bjorling problems in the lorentz minkowski space

toeplitz operators on bounded symmetric domains in this paper jordan algebraic methods are applied to study toeplitz operators on the hardy space h2 s associated with the shilov boundary s of a bounded symmetric domain d in c of arbitrary rank the jordan triple system z c associated with d is used to determine the relationship between toeplitz operators and differential operators further it is shown that each jordan triple idempotent e e z induces an irreducible representation e symbol of the c algebra generated by all toeplitz operators tf with continuous symbol function f 0 introduction toeplitz operators on the boundary t aa of the open unit disc a c c play an important role in function theory of one complex variable cf 9 chapter 7 in several dimensions toeplitz operators have been mainly studied for strictly pseudo convex domains d c c 4 13 14 24 28 in particular for the hilbert ball 7 using the relationship with pseudo differential operators another class of domains in c generalizing the unit disc is the class of bounded symmetric domains cartan domains and exceptional domains which have a more complicated boundary structure compared to the strictly pseudo convex case the aim of this paper is the study of toeplitz operators t1 with continuous symbol functionf e c s on the shilov boundary s of a bounded symmetric domain d of arbitrary rank r in the special cases of the hilbert ball r 1 and the lie ball r 2 the structure of the operators ti and of the toeplitz c algebra

two and one half dimensional born inversion with an arbitrary reference multidimensional inversion algorithms are presented for both prestack and poststack data gathered on a single line these algorithms both image the subsurface i e give a migrated section and given relative true amplitude data estimate reflection strength or impedance on each reflector the algorithms are two and one half dimensional 2 5 d in that they incorporate three dimensional 3 d wave propagation in a medium which varies in only two dimensions the use of 3 d sources does not entail any computational penalty and it avoids the serious degradation of amplitude incurred by using the 2 d wave equation our methods are based on the linearized inversion theory associated with the born inversion thus we assume that the sound speed profile is well approximated by a given background velocity plus a perturbation it is this perturbation that we seek to reconstruct we are able to treat the case of an arbitrary continuous background profile however the cost of implementation increases as one

on k theoretic invariants of semigroup c algebras attached to number fields abstract we show that semigroup c algebras attached to a x b semigroups over rings of integers determine number fields up to arithmetic equivalence under the assumption that the number fields have the same number of roots of unity for finite galois extensions this means that the semigroup c algebras are isomorphic if and only if the number fields are isomorphic

helicoidal surfaces with h2 k in minkowski 3 space in this paper we prove that any helicoidal surface with h2 k in minkowski 3 space is locally a generalized umbilical surface i e a surface with the shape operator having the minimal polynomial x a 2 where a is constant we also give the representation formulas for these helicoidal surfaces

null scrolls as solutions of a sigma model the two dimensional o 2 1 nonlinear sigma model with boundary is considered we calibrate the size of its space of field configurations by exhibiting new and wide classes of solutions we first construct solutions by evolving under a certain group of transformations free elastic curves in any surface either riemannian or lorentzian of constant curvature furthermore we show that any null scroll can provide a solution of this sigma model this surprising phenomenon which obviously has no euclidean counterpart guarantees the existence of an ample class of solutions which are generated by null or lightlike curves evolving through null ruling flows

semigroup c algebras and amenability of semigroups we construct reduced and full semigroup c algebras for left cancellative semigroups our new construction covers particular cases already considered by a nica and also toeplitz algebras attached to rings of integers in number fields due to j cuntz moreover we show how left amenability of semigroups can be expressed in terms of these semigroup c algebras in analogy to the group case

reinhardt domains boundary geometry and toeplitz c algebras abstract in this paper we have found explicitly how the boundary geometry of a reinhardt domain in c 2 determines the structure of its toeplitz c algebra more precisely our main result is an explicit simple algorithm to describe the structure of the toeplitz c algebra of a reinhardt domain d in c 2 satisfying some mild boundary condition in terms of rotation c algebras based on the degree of contact of the boundary curve of c the logarithmic domain of d at each point of intersection with the linear faces of the convex hull of c and the slopes of these faces a consequence of this result is that the toeplitz c algebras t d and t d of d and its pseudoconvex hull d are rarely isomorphic but are always of the same type i e either both are of type i or both are not of type i in other words the isomorphism class of t d is usually changed under taking pseudoconvex hull but the type of t d is not affected