convergence acceleration for boundary value problems with singularities using the e algorithm in the present work we use the e algorithm to accelerate the convergence of finite difference schemes for ordinary differential equations as a model a boundary value problem for a second order differential equation is considered where the right hand side may have different kinds of singularities an asymptotic error expansion is obtained enabling the use of the e algorithm to accelerate the convergence the applicability and the efficiency of the e algorithm are discussed and illustrated by numerical examples

on subalgebras of the car algebra abstract every nuclear unital separable c algebra a is unitally and completely isometrically ismorphic to the range of a unital completely positive projection on the car algbra b m 2 m 2 let c be a nuclearly imbeddable separable unital c algebra in the sense of voiculescu vo13 then there exists a c subalgebra e of the car algebra b such that c is isomorphic to a quotient c algebra of e we include one of the possible proofs that exact c algebras are nuclearly imbeddable proofs of g covariant analogs are outlined for compact g some related results are obtained on non selfadjoint operator algebras the unital separable nuclear c algebras not of type i are mutually cb isomorphic and have cb distance 256 separable lindenstrauss spaces are isometric to quotients of the car algebra by a sum of closed left and a closed right ideal

on restricted perturbations in inverse images and a description of normalizer algebras in c algebras abstract let e and f be banach spaces and t a bounded linear map from e into f using a certain perturbation function t we find a useful sufficient criterion that t maps the closed unit ball onto a closed set applying this to the quotient map from a c algebra a onto its quotient banach space a l r by the sum l r of closed left and right ideals l and r of a we obtain that the closed unit ball of a maps onto the closed unit ball of a l r this gives an independent description of the images of the right normalizer algebra n r d and the normalizer algebra n d n l d n r d of a hereditary c subalgebra d of a by the quotient map from a onto a cl ad cl da we use this to prove a necessary and sufficient criterion for a c algebra b to be a c quotient algebra of a c subalgebra of a c algebra a the latter criterion will be applied in the situation where a equals the car algebra in some forthcoming papers cf section 6 for more details

modules over operator algebras and the maximal c dilation abstract we continue our study of the general theory of possibly nonselfadjoint algebras of operators on a hilbert space and modules over such algebras developing a little more technology to connect nonselfadjoint operator algebra with the c algebraic framework more particularly we make use of the universal or maximal c algebra generated by an operator algebra and c dilations this technology is quite general however it was developed to solve some problems arising in the theory of morita equivalence of operator algebras and as a result most of the applications given here and in a companion paper are to that subject other applications given here are to extension problems for module maps and characterizations of c algebras

the kirchberg wassermann operator system is unique in 1998 kirchberg and wassermann constructed a separable nuclear operator system with the property that the canonical unital homomorphism from the maximal c algebra onto the c envelope is injective we show that such an operator system is unique and completely order isomorphic to the operator system associated with the noncommutative poulsen simplex

the shift invariant discrete wavelet transform and application to speech waveform analysis the discrete wavelet transform may be used as a signal processing tool for visualization and analysis of nonstationary time sampled waveforms the highly desirable property of shift invariance can be obtained at the cost of a moderate increase in computational complexity and accepting a least squares inverse pseudoinverse in place of a true inverse a new algorithm for the pseudoinverse of the shift invariant transform that is easier to implement in array oriented scripting languages than existing algorithms is presented together with self contained proofs representing only one of the many and varied potential applications a recorded speech waveform illustrates the benefits of shift invariance with pseudoinvertibility visualization shows the glottal modulation of vowel formants and frication noise revealing secondary glottal pulses and other waveform irregularities additionally performing sound waveform editing operations i e cutting and pasting sections on the shift invariant wavelet representation automatically produces quiet click free section boundaries in the resulting sound the capabilities of this wavelet domain editing technique are demonstrated by changing the rate of a recorded spoken word individual pitch periods are repeated to obtain a half speed result and alternate individual pitch periods are removed to obtain a double speed result the original pitch and formant frequencies are preserved in informal listening tests the results are clear and understandable

the discrete wavelet transform wedding the a trous and mallat algorithms two separately motivated implementations of the wavelet transform are brought together it is observed that these algorithms are both special cases of a single filter bank structure the discrete wavelet transform the behavior of which is governed by the choice of filters in fact the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact moreover it is shown that the commonly used lagrange a trous filters are in one to one correspondence with the convolutional squares of the daubechies filters for orthonormal wavelets of compact support a systematic framework for the discrete wavelet transform is provided and conditions are derived under which it computes the continuous wavelet transform exactly suitable filter constraints for finite energy and boundedness of the discrete transform are also derived relevant signal processing parameters are examined and it is observed that orthonormality is balanced by restrictions on resolution

tensor products of operator systems abstract the purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems after giving an axiomatic definition of tensor products in this category we examine in detail several particular examples of tensor products including a minimal maximal maximal commuting maximal injective and some asymmetric tensor products we characterize these tensor products in terms of their universal properties and give descriptions of their positive cones we also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system we examine notions of nuclearity for our tensor products which on the category of c algebras reduce to the classical notion we exhibit an operator system s which is not completely order isomorphic to a c algebra yet has the property that for every c algebra a the minimal and maximal tensor product of s and a are equal

complete to overcomplete discrete wavelet transforms theory and applications a new transform is proposed that derives the overcomplete discrete wavelet transform odwt subbands from the critically sampled dwt subbands complete representation this complete to overcomplete dwt codwt has certain advantages in comparison to the conventional approach that performs the inverse dwt to reconstruct the input signal followed by the a spl grave trous or the lowband shift algorithm specifically the computation of the input signal is not required as a result the minimum number of downsampling operations is performed and the use of upsampling is avoided the proposed codwt computes the odwt subbands by using a set of prediction filter matrices and filtering and downsampling operators applied to the dwt this formulation demonstrates a clear separation between the single rate and multirate components of the transform this can be especially significant when the codwt is used in resource constrained environments such as resolution scalable image and video codecs to illustrate the applicability of the proposed transform in these emerging applications a new scheme for the transform calculation is proposed and existing coding techniques that benefit from its usage are surveyed the analysis of the proposed codwt in terms of arithmetic complexity and delay reveals significant gains as compared with the conventional approach

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

the near shift invariance of the dual tree complex wavelet transform revisited abstract the dual tree complex wavelet transform dt c wt is an enhancement of the conventional discrete wavelet transform dwt due to a higher degree of shift invariance and a greater directional selectivity finding its applications in signal and image processing this paper presents a quantitative proof of the superiority of the dt c wt over the dwt in case of modulated wavelets

phase shifting for nonseparable 2 d haar wavelets in this paper we present a novel and efficient solution to phase shifting 2 d nonseparable haar wavelet coefficients while other methods either modify existing wavelets or introduce new ones to handle the lack of shift invariance we derive the explicit relationships between the coefficients of the shifted signal and those of the unshifted one we then establish their computational complexity and compare and demonstrate the superior performance of the proposed approach against classical interpolation tools in terms of accumulation of errors under successive shifting

relative weak injectivity of operator system pairs abstract the concept of a relatively weakly injective pair of operator systems is introduced and studied in this paper motivated by relative weak injectivity in the c algebra category e kirchberg 11 proved that the c algebra c f of the free group f on countably many generators characterises relative weak injectivity for pairs of c algebras by means of the maximal tensor product one of the main results of this paper shows that c f also characterises relative weak injectivity in the operator system category a key tool is the theory of operator system tensor products 9 10

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

a shift invariant discrete wavelet transform this article presents a unifying approach to the derivation and implementation of a shift invariant wavelet transform of one and two dimensional 1 d and 2 d discrete signals starting with mallat s 1989 multiresolution wavelet representation mrwar it presents an analytical process through which a shift invariant orthogonal discrete wavelet transform called the multiscale wavelet representation mswar is obtained the coefficients in the mswar are shown to be inclusive of those in the mrwar with the implication that the derived representation is invertible the computational complexity of the mswar is quantified in terms of the required convolutions and its implementation is shown to be equivalent to the filter upsampling technique

the sign regularity of the auxiliary family g i x x a i ln x b i in convergence acceleration processes using the e algorithm abstract the e algorithm can be successfully applied to accelerate the convergence of the solution of some numerical differential equations provided the respective error expansion satisfies a certain asymptotic determinantal condition in this work it is proved that such condition is fulfilled for any error expansion in which formation enter the auxiliary family h n i ln h n i where h n designates the stepsize of the discretization method

an approximation theorem for nuclear operator systems abstract we prove that an operator system s is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps s m n and m n s such that converges to id s in the point norm topology our proof is independent of the choi effros kirchberg characterization of nuclear c algebras and yields this characterization as a corollary we give an explicit example of a nuclear operator system that is not completely order isomorphic to a unital c algebra

c algebras generated by operator systems an operator systemx such thatx is ac algebra and such that the canonical embedding ofxinx is a unital complete isometry is called ac system ifais a unitalc algebra andlis a closed left ideal ofa thena l l has a natural operator system structure relative to which it is ac system it is shown that any separablec system is of this form for some separablea and that an arbitrary inseparablec system is an inductive limit of separablec systems associated with any operator systemxis a universalc algebrac u x which containsxas a generating subsystem and is maximal among suchc algebras in the sense that any other suchc algebra is canonically a homomorphic image ofc u x ifxis additionally ac system then thec subalgebrac r x ofx generated byxis minimal amongc algebras containingxas a generating subsystem in the sense thatc r x is canonically a homomorphic image of any other suchc algebra it follows that there is a canonical homomorphism c u x c r x which extends the identity map onx whenxis ac algebra of dimension greater than 1 is never injective one of the main results of the paper is that there exists a separable nuclearc systemxcontainingm2 c for which is an isomorphism this implies that for any embedding ofxas an operator subsystem of ac algebraa thec subalgebra ofagenerated byxis isomorphic toc u x moreoverc u m2 c is notc exact andc u m2 c c u x from which it follows thatc u x and hencea are not exactc algebras thusx though a nuclear operator system cannot be embedded in a nuclearc algebra

the advanced oca for 2 d discrete periodized wavelet transformation we develop a novel computation method for the 2 d discrete periodized wavelet transformation dpwt the new algorithm is based on the operator correlation algorithm oca compared with the classical 2 d pyramid algorithm the new advanced operator correlation algorithm aoca has two major advantages it requires half the number of multiplications and can yield the same output snr with half the precision of the dpwt filter coefficients furthermore the modular structure of the adca makes it particularly suitable for a vlsi implementation

richardson extrapolation in boundary value problems for differential equations with nonregular right hand side abstract when the finite difference method is used to solve initial or boundary value problems with smooth data functions the accuracy of the numerical results may be considerably improved by acceleration techniques like richardson extrapolation however the success of such a technique is doubtful in cases were the right hand side or the coefficients of the equation are not sufficiently smooth because the validity of an asymptotic error expansion which is the theoretical prerequisite for the convergence analysis of the richardson extrapolation is not a priori obvious in this work we show that the richardson extrapolation may be successfully applied to the finite difference solutions of boundary value problems for ordinary second order linear differential equations with a nonregular right hand side we present some numerical results confirming our conclusions

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed