shift invariant spaces on lca groups in this article we extend the theory of shift invariant spaces to the context of lca groups we introduce the notion of h invariant space for a countable discrete subgroup h of an lca group g and show that the concept of range function and the techniques of fiberization are valid in this context as a consequence of this generalization we prove characterizations of frames and riesz bases of these spaces extending previous results that were known for rd and the lattice zd

averaged lagrangians and the mean effects of fluctuations in ideal fluid dynamics we begin by placing the generalized lagrangian mean glm equations for a compressible adiabatic fluid into the euler poincare ep variational framework of fluid dynamics for an averaged lagrangian we then state the ep averag ing result that glm equations arise from glm hamilton s principles in the ep framework next we derive a new set of approximate small amplitude glm equations gm equations at second order in the fluctuating displacement of a lagrangian trajectory from its mean position these equations express the linear and nonlinear back reaction effects on the eulerian mean fluid quantities by the fluctuating displacements of the lagrangian trajectories in terms of their eulerian second moments the derivation of the gm equations uses the linearized relations between eulerian and lagrangian fluctuations in the tradition of lagrangian stability analysis for fluids the gm derivation also uses the method of averaged lagrangians in the tradition of wave mean flow interaction wmfi the gm ep motion equations for compressible and incompressible ideal fluids are compared with the euler alpha turbulence closure equations an alpha model is a glm or gm fluid theory with a taylor hypothesis closure thc such closures are based on the linearized fluctuation relations that determine the dynamics of the lagrangian statistical quantities in the euler alpha closure equations we use the ep averaging result to bridge between the glm equations and the euler alpha closure equations hence combining the small amplitude approximation with thc yields in new gm turbulence closure equations for compressible fluids in the ep variational framework 2002 elsevier science b v all rights reserved

exponential bases paley wiener spaces and applications abstract we investigate the connection between translation bases for paley wiener spaces and exponential fourier bases for a domain we apply these results to the characterization of vector valued time frequency translations of a paley wiener window signal

groupe de chow de codimension deux des varietes definies sur un corps de nombres un theoreme de finitude pour la torsion letx be a smooth projective variety defined over a number field and let ch2 x denote the chow group of codimension two cycles modulo rational equivalence we show that if the cohomology grouph2 x ox vanishes then the torsion subgroup of ch2 x is a finite group this result covers all previous results in this direction the hypothesish2 x ox 0 is used to lift line bundles

class field theory for arithmetic schemes let x be a regular arithmetic scheme i e a regular integral separated scheme flat and of finite type over spec mathbb z generalising classical class field theory for number fields we define a class group cx and show there is a natural surjective map c x rightarrow pi 1 ab x whose kernel is the connected component of 0

characterization of the closedness of the sum of two shift invariant spaces abstract we first present a formula for the supremum cosine angle between two closed subspaces of a separable hilbert space under the assumption that the generators form frames for the subspaces we then characterize the conditions that the sum of two not necessarily finitely generated shift invariant subspaces of l 2 r d be closed if the fibers of the generating sets of the shift invariant subspaces form frames for the fiber spaces a e which is satisfied if the shift invariant subspaces are finitely generated or if the shifts of the generating sets form frames for the respective subspaces then the characterization is given in terms of the norms of possibly infinite matrices in particular if the shift invariant subspaces are finitely generated then the characterization is given wholly in terms of the norms of finite matrices

non abelian class field theory for arithmetic surfaces let open image in new window be a regular arithmetic surface assume that for all irreducible curves open image in new window there are given open normal subgroups of 1 c which fulfill a compatibility condition at all closed points x open image in new window we then show that these data uniquely determine a normal subgroup of 1 open image in new window this is used to construct abelian class field theory for arithmetic surfaces using only k0 and k1 groups of local and global fields

aliasing and oblique dual pair designs for consistent sampling abstract in this paper we study some aspects of oblique duality between finite sequences of vectors f and g lying in finite dimensional subspaces w and v respectively we compute the possible eigenvalue lists of the frame operators of oblique duals to f lying in v we compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for f with norm restrictions as an application we show that these optimal duals are the closest to being tight frames and therefore have their spectrum as concentrated as possible among oblique duals with norm restrictions we obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces v and w has in oblique duality we apply this analysis to compute those rigid rotations u for w such that the canonical oblique dual of u f minimize every convex potential we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations u for w such that the canonical oblique dual pair associated to u f minimize the aliasing we point out that these two last problems are intrinsic to oblique duality within the context of consistent sampling

some equations relating multiwavelets and multiscaling functions abstract the local trace function introduced in dutkay the local trace function of shift invariant spaces j operat theory 52 2 2004 267 291 is used to derive equations that relate multiwavelets and multiscaling functions in the context of a generalized multiresolution analysis without appealing to filters a construction of normalized tight frame ntf wavelets is given particular instances of the construction include ntf and orthonormal wavelet sets

unramified class field theory of arithmetical surfaces let k be an algebraic number field 9k its ring of integers and v a non empty open subscheme of spec ck let x be a projective smooth geometrically irreducible scheme over k and x a regular proper flat scheme over v such that x x vk x the purpose of this paper is to give an explicit description of the abelian fundamental groups ab x and 7t b x using some idele class groups attached to x and x by a k theoretical method its outline is as follows in general for a noetherian scheme z and i 0 or 1 we define the group ski z to be the cokernel of

properties of oblique dual frames in shift invariant systems abstract gramian analysis is used to study properties of a shift invariant system x b k k z n where b is an invertible n n matrix and a finite or countable subset of l 2 r n under the assumption that the system forms a frame for the closed subspace m of l 2 r n in particular the relationship between various features of such system such as being a frame for the whole space l 2 r n being a riesz sequence and having a unique shift generated dual of type i or ii is discussed in details several interesting examples are presented

on the structure and interpolation properties of quasi shift invariant spaces abstract the structure of certain types of quasi shift invariant spaces which take the form v x span l 2 x j j z for an infinite discrete set x x j r is investigated additionally the relation is explored between pairs x and y such that interpolation of functions in v x via interpolants in v y solely from the samples of the original function is possible and stable some conditions are given for which the sampling problem is stable and for which recovery of functions from their interpolants from a family of spaces v y is possible

uncertainty principles in finitely generated shift invariant spaces with additional invariance author s tessera romain wang haichao abstract we consider finitely generated shift invariant spaces sis with additional invariance in l 2 r d we prove that if the generators and their translates form a frame then they must satisfy some stringent restrictions on their behavior at infinity part of this work non trivially generalizes recent results obtained in the special case of a principal shift invariant spaces in l 2 r whose generator and its translates form a riesz basis

wavelet frames for not necessarily reducing affine subspaces ii the structure of affine subspaces abstract this is a continuation of the investigation into the theory of wavelet frames for general affine subspaces the main focus of this paper is on the structural properties of affine subspaces we show that every affine subspace is the orthogonal direct sum of at most three purely non reducing subspaces while every reducing subspace with respect to the dilation and translation operators is the orthogonal direct sum of two purely non reducing ones this result is obtained through considering the basic question as to when the orthogonal complement of an affine subspace in another one is still affine motivated by the fundamental question as to whether every affine subspace is singly generated and by a recent result that every singly generated purely non reducing subspace admits a singly generated wavelet frame we prove that every affine subspace can be decomposed into the direct sum of a singly generated affine subspace and some space of small size as a consequence we establish a connection between the above mentioned two questions

a generalization of serre s condition mathrm f f with applications to the finiteness of unramified cohomology in this paper we introduce a condition mathrm f m on a field k for a positive integer m that generalizes serre s condition f and which still implies the finiteness of the galois cohomology of finite galois modules annihilated by m and algebraic k tori that split over an extension of degree dividing m as well as certain groups of etale and unramified cohomology various examples of fields satisfying mathrm f m including those that do not satisfy f are given

affine and quasi affine frames for rational dilations in this paper we extend the investigation of quasi affine systems which were originally introduced by ron and shen j funct anal 148 1997 408 447 for integer expansive dilations to the class of rational expansive dilations we show that an affine system is a frame if and only if the corresponding family of quasi affine systems are frames with uniform frame bounds we also prove a similar equivalence result between pairs of dual affine frames and dual quasi affine frames finally we uncover some fundamental differences between the integer and rational settings by exhibiting an example of a quasi affine frame such that its affine counterpart is not a frame

the structure of shift invariant subspaces of l2 rn using the range function approach to shift invariant spaces in l2 rn we give a simple characterization of frames and riesz families generated by shifts of a countable set of generators in terms of their behavior on subspaces of l2 zn this in turn gives a simplified approach to the analysis of frames and riesz families done by gramians and dual gramians we prove a decomposition of a shift invariant space into the orthogonal sum of spaces each of which is generated by a quasi orthogonal generator as an application of this fact we characterize shift preserving operators in terms of range operators and prove some facts about the dimension function

construction and reconstruction of tight framelets and wavelets via matrix mask functions abstract the paper develops construction procedures for tight framelets and wavelets using matrix mask functions in the setting of a generalized multiresolution analysis gmra we show the existence of a scaling vector of a gmra such that its first component exhausts the spectrum of the core space near the origin the corresponding low pass matrix mask has an especially advantageous form enabling an effective reconstruction procedure of the original scaling vector we also prove a generalization of the unitary extension principle for an infinite number of generators this results in the construction scheme for tight framelets using low pass and high pass matrix masks generalizing the classical mra constructions we prove that our scheme is flexible enough to reconstruct all possible orthonormal wavelets as an illustration we exhibit a pathwise connected class of non msf non mra wavelets sharing the same wavelet dimension function

constrained walks and self avoiding walks implications for protein structure determination we prove that n step walks and self avoiding walks on the 2d honeycomb 2d square 3d diamond and 3d cubic lattices can be uniquely characterized canonized with no more than n euclidian distances we also demonstrate that these canonical distances can be obtained with o n physical measurements finally while the protein folding problem on lattices is known to be strongly np hard we prove that lattice protein structures of size n matching o n canonical distance measurements can be determined in linear time

linear combinations of frame generators in systems of translates abstract a finitely generated shift invariant space v is a closed subspace of l 2 r d that can be generated by the integer translates of a finite number of functions a set of frame generators for v is a set of functions whose integer translates form a frame for v in this note we give necessary and sufficient conditions in order that a minimal set of frame generators can be obtained by taking linear combinations of the given frame generators surprisingly the results are very different from the recently studied case when the property to be a frame is not required

approximation from shift invariant subspaces of l 2 ℝ d a complete characterization is given of closed shift invariant subspaces of l2 rd which provide a specified approximation order when such a space is principal i e generated by a single function then this characterization is in terms of the fourier transform of the generator as a special case we obtain the classical strang fix conditions but without requiring the generating function to decay at infinity the approximation order of a general closed shift invariant space is shown to be already realized by a specifiable principal subspace

riemannian metrics on positive definite matrices related to means abstract the riemannian metric on the manifold of positive definite matrices is defined by a kernel function in the form k d h k i j i j 1 tr p i hp j k when i i p i is the spectral decomposition of the foot point d and the hermitian matrices h k are tangent vectors for such kernel metrics the tangent space has an orthogonal decomposition the pull back of a kernel metric under a mapping d g d is a kernel metric as well several riemannian geometries of the literature are particular cases for example the statistical metric for multivariate gaussian distributions and the quantum fisher information in the paper the case x y m x y is mostly studied when m x y is a mean of the positive numbers x and y there are results about the geodesic curves and geodesic distances the geometric mean the logarithmic mean and the root mean are important cases

subspaces of l2 g invariant under translation by an abelian subgroup abstract for a second countable locally compact group g and a closed abelian subgroup h we give a range function classification of closed subspaces in l 2 g invariant under left translation by h for a family a l 2 g this classification ties with a set of conditions under which the translations of a by h form a continuous frame or a riesz sequence when g is abelian our work relies on a fiberization map for the more general case we introduce an analogue of the zak transform both transformations intertwine translation with modulation and both rely on a new group theoretic tool for a closed subgroup g we produce a measure on the space g of right cosets that gives a measure space isomorphism g g outside of the group setting we consider a more general problem for a measure space x and a hilbert space h we investigate conditions under which a family of functions in l 2 x h multiplies with a basis like system in l 2 x to produce a continuous frame or a riesz sequence in l 2 x h finally we explore connections with dual integrable representations of lca groups as introduced by hernandez et al in 25

on the spectrums of frame multiresolution analyses we first give conditions for a univariate square integrable function to be a scaling function of a frame multiresolution analysis fmra by generalizing the corresponding conditions for a scaling function of a multiresolution analysis mra we also characterize the spectrum of the central space of an fmra and then give a new condition for an fmra to admit a single frame wavelet solely in terms of the spectrum of the central space of an fmra this improves the results previously obtained by benedetto and treiber and by some of the authors our methods and results are applied to the problem of the containments of fmras in mras we first prove that an fmra is always contained in an mra and then we characterize those mras that contain genuine fmras in terms of the unique low pass filters of the mras and the spectrums of the central spaces of the fmras to be contained this characterization shows in particular that if the low pass filter of an mra is almost everywhere zero free as is the case of the mras of daubechies then the mra contains no fmras other than itself

on progressive functions abstract progressive functions at time t involve only the progressive functions at time before t and some nice compactly supported function at time t we give sufficient conditions and explicit formulas to construct progressive functions with exponential decay and characterize the conditions on which the positive integer translates of a progressive function are orthonormal or a riesz sequence we provide explicit ways for construction of orthonormal progressive functions and for construction of the biorthogonal functions of nonorthogonal progressive functions such progressive functions can be used to construct wavelets with arbitrary smoothness on the half line if they are generated by a smooth refinable compactly supported function

class field theory for a product of curves over a local field we prove that the kernel of the reciprocity map for a product of curves over a p adic field with split semi stable reduction is divisible we also consider the k1 of a product of curves over a number field

minimal generator sets for finitely generated shift invariant subspaces of l2 rn abstract let s be a shift invariant subspace of l 2 r n defined by n generators and suppose that its length l the minimal number of generators of s is smaller than n then we show that at least one reduced family of generators can always be obtained by a linear combination of the original generators without using translations in fact we prove that almost every such combination yields a new generator set on the other hand we construct an example where any rational linear combination fails

spaces invariant under unitary representations of discrete groups abstract we investigate the structure of subspaces of a hilbert space that are invariant under unitary representations of a discrete group we work with square integrable representations and we show that they are those for which we can construct an isometry intertwining the representation with the right regular representation that we call a helson map we then characterize invariant subspaces using a helson map and provide general characterizations of riesz and frame sequences of orbits these results extend to the nonabelian setting several known results for abelian groups they also extend to countable families of generators previous results obtained for principal subspaces

the structure of shift invariant spaces on a locally compact abelian group abstract we investigate shift invariant subspaces of l 2 g where g is a locally compact abelian group we show among other things that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a parseval frame

extra invariance of shift invariant spaces on lca groups this article generalizes recent results in the extra invariance for shift invariant spaces to the context of lca groups let g be a locally compact abelian lca group and k a closed subgroup of g a closed subspace of l2 g is called k invariant if it is invariant under translations by elements of k assume now that h is a countable uniform lattice in g and m is any closed subgroup of g containing h in this article we study necessary and sufficient conditions for an h invariant space to be m invariant as a consequence of our results we prove that for each closed subgroup m of g containing the lattice h there exists an h invariant space s that is exactly m invariant that is s is not invariant under any other subgroup m containing h we also obtain estimates on the support of the fourier transform of the generators of the h invariant space related to its m invariance

the structure of finitely generated shift invariant spaces in l2 rd a simple characterization is given of finitely generated subspaces of l2 rd which are invariant under translation by any multi integer and is used to give conditions under which such a space has a particularly nice generating set namely a basis and more than that a basis with desirable properties such as stability orthogonality or linear independence the last property makes sense only for local spaces i e shift invariant spaces generated by finitely many compactly supported functions and special attention is paid to such spaces as an application we prove that the approximation order provided by a given local space is already provided by the shift invariant space generated by just one function with this function constructible as a finite linear combination of the finite generating set for the whole space hence compactly supported this settles a question of some 20 years standing

kernels of gramian operators for frames in shift invariant subspaces abstract for an invertible n n matrix b and a finite or countable subset of l 2 r n consider the collection x bk k z n generating the closed subspace m of l 2 r n our main objects of interest in this paper are the kernel of the associated gramian g and dual gramian g operator valued functions we show in particular that the orthogonal complement of m in l 2 r n can be generated by a parseval frame obtained from a shift invariant system having m generators where m dim ker g furthermore this parseval frame can be taken to be an orthonormal basis exactly when dim ker g m almost everywhere analogous results in terms of dim ker g are also obtained concerning the existence of a collection of m sequences in the orthogonal complement of the range of analysis operator associated with the frame x whose shifts either form a parseval frame or an orthonormal basis for that orthogonal complement

cycles on curves over global fields of positive characteristic let k be a global field of positive characteristic and let x spec k be a smooth projective curve we study the zero dimensional cycle group v x ker sik 1 x k 1 k and the one dimensional cycle group w x coker k 2 k h 0 zar x k 2 addressing the conjecture that v x is torsion and w x is finitely generated the main idea is to use abhyankar s theorem on resolution of singularities to relate the study of these cycle groups to that of the k groups of a certain smooth projective surface over a finite field

constructive realization of dual systems for generators of multi window spline type spaces multi window spline type spaces arise naturally in many areas among others they have been used as model spaces in the theory of irregular sampling this class of shift invariant spaces is characterized by possessing a riesz basis which consists of a set of translates along some lattice l of a finite family of atoms part of their usefulness relies on the explicit knowledge of the structure of the projection operator on such a space using the existence of a finite family of dual atoms the main goal of this paper is to address the problems arising from the discrepancy between a constructive description and an implementable approximate realization of such concepts using function space concepts e g wiener amalgam spaces we describe how approximate dual atoms can be computed for any given degree of precision as an application of our result we describe the best approximation of hilbert schmidt operators by generalized gabor multipliers using smooth analysis and synthesis windows the kohn nirenberg symbols of the rank one operators formed from analysis and synthesis windows satisfy our general assumptions applications to irregular sampling are given elsewhere

dimensional homotopy t structures in motivic homotopy theory the aim of this work is to construct certain homotopy t structures on various categories of motivic homotopy theory extending works of voevodsky morel deglise and ayoub we prove these t structures possess many good properties some analogous to those of the perverse t structure of beilinson bernstein and deligne we compute the homology of certain motives notably in the case of relative curves we also show that the hearts of these t structures provide convenient extensions of the theory of homotopy invariant sheaves with transfers extending some of the main results of voevodsky these t structures are closely related to gersten weight structures as defined by bondarko

system bandwidth and the existence of generalized shift invariant frames abstract we consider the question whether given a countable family of lattices j j j in a locally compact abelian group g there exist functions g j j j such that the resulting generalized shift invariant system g j j j j is a tight frame of l 2 g this paper develops a new approach to the study of generalized shift invariant system via almost periodic functions based on a novel unconditional convergence property from this theory we derive characterizing relations for tight and dual frame generators we introduce the system bandwidth as a measure of the total bandwidth a generalized shift invariant system can carry and we show that the so called calderon sum is uniformly bounded from below for generalized shift invariant frames without the unconditional convergence property we show counter intuitively that even orthonormal bases can have arbitrary small system bandwidth our results show that the question of existence of frame generators for a general lattice system is rather subtle and depends on analytical and algebraic properties of the lattice system

explicit solution for a gaussian wave packet impinging on a square barrier the collision of a quantum gaussian wave packet with a square barrier is solved explicitly in terms of known functions the obtained formula is suitable for performing fast calculations or asymptotic analysis it also provides physical insight since the description of different regimes and collision phenomena typically requires only some of the terms

on the existence of multiresolution analysis for framelets we show that a compactly supported tight framelet comes from an mra if the intersection of all dyadic dilations of the space of negative dilates which is defined as the shift invariant space generated by the negative scales of a framelet is trivial we also construct examples of non tight framelets which are arbitrarily close to tight frame framelets such that the corresponding space of negative dilates is equal to the entire space l 2

a finer tate duality theorem for local galois symbols abstract let k be a finite extension of q p let a b be abelian varieties over k with good reduction for any integer m 1 we consider the galois symbol k k a b m h 2 k a m b m where k k a b is the somekawa k group attached to a b this map is a generalization of the galois symbol k 2 m k m h 2 k m 2 of the bloch kato conjecture where k 2 m k is the milnor k group of k in this paper we give a geometric description of the image of this generalized galois symbol by looking at the tate duality pairing h 2 k a m b m hom g k a m b m z m where b is the dual abelian variety of b under this perfect pairing we compute the exact annihilator of the image of the galois symbol in terms of an object of integral p adic hodge theory in this way we generalize a result of tate for h 1 moreover our result has applications to zero cycles on abelian varieties

affine systems in l2 rd the analysis of the analysis operator abstract discrete affine systems are obtained by applying dilations to a given shift invariant system the complicated structure of the affine system is due first and foremost to the fact that it is not invariant under shifts affine frames carry the additional difficulty that they are global in nature it is the entire interaction between the various dilation levels that determines whether the system is a frame and not the behaviour of the system within one dilation level we completely unravel the structure of the affine system with the aid of two new notions the affine product and a quasi affine system this leads to a characterization of affine frames the induced characterization of tight affine frames is in terms of exact orthogonality relations that the wavelets should satisfy on the fourier domain several results such as a general oversampling theorem follow from these characterizations most importantly the affine product can be factored during a multiresolution analysis construction and this leads to a complete characterization of all tight frames that can be constructed by such methods moreover this characterization suggests very simple sufficient conditions for constructing tight frames from multiresolution of particular importance are the facts that the underlying scaling function does not need to satisfy any a priori conditions and that the freedom offered by redundancy can be fully exploited in these constructions an

perturbation of frame sequences and its applications to shift invariant spaces abstract we generalize the main result in o christensen h o kim r y kim j k lim perturbation of frame sequences in shift invariant spaces j geom anal 15 2005 181 191 in order to make it comparable with existing results then we compare the special cases of the three results in the literature in the setting of the perturbation of the generating sets of finitely generated shift invariant spaces of l 2 r d

on the well posedness for kadomtsev petviashvili burgers i equation abstract we prove local and global well posedness in h s 0 r 2 s 1 2 for the cauchy problem associated with the kadomtsev petviashvili burgers i equation kpbi by working in bourgain s type spaces this result is almost sharp if one requires the flow map to be smooth

the structure of shift modulation invariant spaces the rational case in this paper we study structural properties of shift modulation invariant smi spaces also called gabor subspaces or weyl heisenberg subspaces in the case when shift and modulation lattices are rationally dependent we prove the characterization of smi spaces in terms of range functions analogous to the well known description of shift invariant spaces c de boor r devore a ron the structure of finitely generated shift invariant spaces in l2 r d j funct anal 119 1994 37 78 m bownik the structure of shift invariant subspaces of l2 r n j funct anal 177 2000 282 309 h helson lectures on invariant subspaces academic press new york london 1964 we also give a simple characterization of frames and riesz sequences in terms on their behavior of the fibers of the range function next we prove several orthogonal decomposition results of smi spaces into simpler blocks called principal smi spaces then this is used to characterize operators invariant under both shifts and modulations in terms of families of linear maps acting on the fibers of the range function we also introduce the fundamental concept of the dimension function for smi spaces as a result this leads to the classification of unitarily equivalent smi spaces in terms of their dimension functions finally we show several results illustrating our fiberization techniques to characterize dual gabor frames

regular families of kernels for nonlinear approximation abstract this article studies sufficient conditions on families of approximating kernels which provide n term approximation errors from an associated nonlinear approximation space which match the best known orders of n term wavelet expansion these conditions provide a framework which encompasses some notable approximation kernels including splines cardinal functions and many radial basis functions such as the gaussians and general multiquadrics examples of such kernels are given to justify the criteria additionally the techniques involved allow for some new results on n term greedy interpolation of sobolev functions via radial basis functions

frames of translates with prescribed fine structure in shift invariant spaces abstract for a given finitely generated shift invariant fsi subspace w l 2 r k we obtain a simple criterion for the existence of shift generated sg bessel sequences e f induced by finite sequences of vectors f w n that have a prescribed fine structure i e such that the norms of the vectors in f and the spectra of s e f are prescribed in each fiber of spec w t k we complement this result by developing an analogue of the so called sequences of eigensteps from finite frame theory in the context of sg bessel sequences that allows for a detailed description of all sequences with prescribed fine structure then given 1 n 0 we characterize the finite sequences f w n such that f i 2 i for 1 i n and such that the fine spectral structure of the shift generated bessel sequences e f has minimal spread i e we show the existence of optimal sg bessel sequences with prescribed norms in this context the spread of the spectra is measured in terms of the convex potential p w induced by w and an arbitrary convex function r r

frames and riesz bases of twisted shift invariant spaces in l2 r2n abstract in this paper twisted shift invariant spaces in l 2 r 2 n are introduced characterizations of orthonormal system and bessel sequence of twisted translates in l 2 r 2 n are obtained in terms of weyl transform these results appear to be totally different from the classical case of characterizations of orthonormal systems and bessel sequences of translates in l 2 r n further characterizations of frames riesz basis in twisted shift invariant spaces in l 2 r 2 n are also obtained

a two phase free boundary problem for a nonlinear diffusion convection equation a two phase free boundary problem associated with a diffusion convection equation is considered the problem is reduced to a system of nonlinear integral equations which admits a unique solution for small times the system admits an explicit two component solution corresponding to a two component shock wave of the burgers equation the stability of such a solution is also discussed

on chow and brauer groups of a product of mumford curves let c1 cd be mumford curves defined over a finite extension of open image in new window and let x c1 cd we shall show the following 1 the cycle map ch0 x n h2d x n d is injective for any non zero integer n 2 the kernel of the canonical map ch0 x hom br x open image in new window defined by the brauer manin pairing coincides with the maximal divisible subgroup in ch0 x