representations of the lie superalgebra and parastatistics fock spaces the algebraic structure generated by the creation and annihilation operators of a system of m parafermions and n parabosons satisfying the mutual parafermion relations is known to be the lie superalgebra osp 2m 1 vertical bar 2n the fock spaces of such systems are then certain lowest weight representations of osp 2m 1 vertical bar 2n in the current paper we investigate what happens when the number of parafermions and parabosons becomes infinite in order to analyze the algebraic structure and the fock spaces we first need to develop a new matrix form for the lie superalgebra b n n osp 2n 1 vertical bar 2n and construct a new gelfand zetlin basis of the fock spaces in the finite rank case the new structures are appropriate for the situation n infinity the algebra generated by the infinite number of creation and annihilation operators is b infinity infinity a well defined infinite rank version of the orthosymplectic lie superalgebra the fock spaces are lowest weight representations of b infinity infinity with a basis consisting of particular row stable gelfand zetlin patterns

periodic solutions of a class of nonlinear difference equations via critical point method in this paper we obtain some new sufficient conditions for the existence of nontrivial m periodic solutions of the following nonlinear difference equation d p n dx n 1 d f n x n n z by using the critical point method where f zxr r is continuous in the second variable m 2 is a given positive integer p n m p n for any n z and f t m z f t z for any t z zxr 1 d 1 and d 0

fast scattered data approximation with neumann and other boundary conditions abstract an important problem in applications such as signal and image procesing is the approximation of a function f from a finite set of randomly scattered data f x j a common and powerful approach is to construct a trigonometric least squares approximation based on the set of exponentials e 2 i kx this leads to fast numerical algorithms but suffers from disturbing boundary effects due to the underlying periodicity assumption on the data which is rarely satisfied in practice to overcome this drawback we impose neumann boundary conditions on the data this implies the use of cosine polynomials cos kx as basis functions we show that using cosine polynomials leads to a least squares problem involving certain toeplitz plus hankel matrices and derive estimates on the condition number of these matrices unlike other toeplitz plus hankel matrices these matrices cannot be diagonalized by the discrete cosine transform dct but they still allow a fast matrix vector multiplication via dct which gives rise to fast conjugate gradient type algorithms we show how the results can be generalized to higher dimensions we also consider anti symmetric boundary conditions leading to sine polynomials as proper trigonometric basis finally we demonstrate the performance of the proposed methods by an application to a two dimensional geophysical scattered data problem

computationally attractive reconstruction of bandlimited images from irregular samples an efficient method for the reconstruction of bandlimited images and the approximation of arbitrary images from nonuniform sampling values is developed the novel method is based on the observation that the reconstruction problem can be formulated as linear system of equations using two dimensional 2 d trigonometric polynomials where the matrix is of block toeplitz type with toeplitz blocks this system is solved iteratively by the conjugate gradient cg method we show that the use of so called adaptive weights in the establishment of the block toeplitz matrix can be seen as efficient preconditioning the superiority of the new method over conventional approaches is demonstrated by numerical experiments

multiple solutions for a discrete boundary value problem involving the p laplacian multiple solutions for a discrete boundary value problem involving the p laplacian are established our approach is based on critical point theory

character formulas for irreducible modules of the lie superalgebras sl m n kac distinguished between typical and atypical finite dimensional irreducible representations of the lie superalgebras sl m n and provided an explicit character formula appropriate to all the typical representations here the range of validity of some character formulas for atypical representations that have been proposed are discussed several of them are of the kac weyl type but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl 3 4 having ruled out therefore all such formulas a completely new extension of the kac weyl character formula is proposed the validity of this formula in the case of all covariant tensor irreducible representations is proved and some evidence in support of the conjecture that it covers all irreducible representations of sl m n is presented

a new algorithm for solving toeplitz systems of equations abstract we present some recurrences that are the basis for an algorithm to invert an n n toeplitz system of linear equations with computational complexity o n log 2 n the recurrences used are closely related to the zohar trench and bareiss algorithms but do not have any obvious connection with other asymptotically fast algorithms for the inversion of toeplitz systems

efficient sampling set selection for bandlimited graph signals using graph spectral proxies we study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs a frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators that take into account the underlying graph connectivity smoothly varying signals defined on the nodes are of particular interest in various applications and tend to be approximately bandlimited in the frequency basis sampling theory for graph signals deals with the problem of choosing the best subset of nodes for reconstructing a bandlimited signal from its samples most approaches to this problem require a computation of the frequency basis i e the eigenvectors of the variation operator followed by a search procedure using the basis elements this can be impractical in terms of storage and time complexity for real datasets involving very large graphs we circumvent this issue in our formulation by introducing quantities called graph spectral proxies defined using the powers of the variation operator in order to approximate the spectral content of graph signals this allows us to formulate a direct sampling set selection approach that does not require the computation and storage of the basis elements we show that our approach also provides stable reconstruction when the samples are noisy or when the original signal is only approximately bandlimited furthermore the proposed approach is valid for any choice of the variation operator thereby covering a wide range of graphs and applications we demonstrate its effectiveness through various numerical experiments

gel fand zetlin basis for a class of representations of the lie superalgebra mathfrak gl infty infty a new so called odd gel fand zetlin basis is introduced for the irreducible covariant tensor representations of the lie superalgebra gl n n the related gel fand zetlin patterns are based upon the decomposition according to a particular chain of subalgebras of gl n n this chain contains only genuine lie superalgebras of type gl k l with k and l nonzero apart from the final element of the chain which is gl 1 0 gl 1 explicit expressions for a set of generators of the algebra on this gel fand zetlin basis are determined the results are extended to an explicit construction of a class of irreducible highest weight modules of the general linear lie superalgebra gl infinity infinity

multiple homoclinic solutions for the discrete p laplacian via critical point theory abstract we introduce a variational framework for a second order difference equation on z driven by the discrete p laplacian and involving a coercive weight function and a positive parameter by means of critical point theory we prove the existence of at least two nontrivial homoclinic solutions for big enough

gel fand zetlin basis and clebsch gordan coefficients for covariant representations of the lie superalgebra gl m n a gel fand zetlin basis is introduced for the irreducible covariant tensor representations of the lie superalgebra gl m n explicit expressions for the generators of the lie superalgebra acting on this basis are determined furthermore clebsch gordan coefficients corresponding to the tensor product of any covariant tensor representation of gl m n with the natural representation v 1 0 0 of gl m n with highest weight 1 0 0 are computed both results are steps for the explicit construction of the parastatistics fock space

multiple solutions for discrete boundary value problems a recent multiplicity theorem for the critical points of a functional defined on a finite dimensional hilbert space established by ricceri is extended an application to dirichlet boundary value problems for difference equations involving the discrete p laplacian operator is presented

positive solutions for a discrete two point nonlinear boundary value problem with p laplacian abstract in the framework of variational methods we use a two non zero critical points theorem to obtain the existence of two positive solutions to dirichlet boundary value problems for difference equations involving the discrete p laplacian operator

the eigenvalues of matrices that occur in certain interpolation problems the eigenvalues of the matrices that occur in certain finite dimensional interpolation problems are directly related to their well posedness and strongly depend on the distribution of the interpolation knots that is on the sampling set we study this dependency as a function of the sampling set itself and give accurate bounds for the eigenvalues of the interpolation matrices the bounds can be evaluated in as few as four arithmetic operations and therefore they greatly simplify the assessment of sampling sets regarding numerical stability the accuracy and usefulness of the bounds are illustrated with examples

multiple positive solutions of singular and nonsingular discrete problems via variational methods we employ the critical point theory to establish the existence of multiple solutions of some regular as well as singular discrete boundary value problems 2004 elsevier ltd all rights reserved msc 34b16 39a10

matrix elements for type 1 unitary irreducible representations of the lie superalgebra gl m n using our recent results on eigenvalues of invariants associated to the lie superalgebra gl m n we use characteristic identities to derive explicit matrix element formulae for all gl m n generators particularly non elementary generators on finite dimensional type 1 unitary irreducible representations we compare our results with existing works that deal with only subsets of the class of type 1 unitary representations all of which only present explicit matrix elements for elementary generators our work therefore provides an important extension to existing methods and thus highlights the strength of our techniques which exploit the characteristic identities

parastatistics and conformal field theories in two dimensions the relation between parafermion field theories of order q and the corresponding fermion field theories with so q symmetry is studied it is shown that these theories are related but not identical the explicit relation between the states and the observables of the two classes of theories are given without using the klein transformations the formalism is applied to the free conformally invariant parafermion theories in two dimensions their virasoro algebra and so n kac moody algebra are given the equivalence of their canonical form of the energy momentum tensor with the sugawara sommerfield form is also elucidated

a levinson galerkin algorithm for regularized trigonometric approximation trigonometric polynomials are widely used for the approximation of a smooth function from a set of nonuniformly spaced samples if the samples are perturbed by noise a good choice for the polynomial degree of the trigonometric approximation becomes an essential issue to avoid overfitting and underfitting of the data standard methods for trigonometric least squares approximation assume that the degree for the approximating polynomial is known a priori which is usually not the case in practice we derive a multilevel algorithm that recursively adapts to the least squares solution of suitable degree we analyze under which conditions this multilevel approach yields the optimal solution the proposed algorithm computes the solution in at most mathcal o rm m 2 operations m being the polynomial degree of the approximation and r being the number of samples by solving a family of nested toeplitz systems it is shown how the presented method can be extended to multivariate trigonometric approximation we demonstrate the performance of the algorithm by applying it in echocardiography to the recovery of the boundary of the left ventricle of the heart

recovery of signals from nonuniform samples using iterative methods an iterative method to recover a bandlimited signal from its ideal nonuniform samples is proposed the convergence of iterations is proved and general regions for convergence are found it is shown that the iterative method is also applicable to other forms of nonuniform sampling i e natural sampling and interpolated sampling such as sample and hold signal simulation results show that this method works effectively and fairly fast and the errors after a few iterations are negligible if a particular sufficient condition is satisfied or the sampling rate is higher than the nyquist rate

the parafermion fock space and explicit mathfrak so 2n 1 representations the defining relations triple relations of n pairs of parafermion operators f j j 1 n are known to coincide with a set of defining relations for the lie algebra in terms of 2n generators with the common hermiticity conditions this means that the parafermions of order p correspond to a finite dimensional unitary irreducible representation w p of with highest weight although the dimension and the character of w p is known by classical formulae there is no explicit basis of w p available in which the parafermion operators have a natural action in this paper we construct an orthogonal basis for w p and present the explicit actions of the parafermion generators on these basis vectors we use group theoretical techniques in which the subalgebra of plays a crucial role a set of gelfand zetlin patterns of will be used to label the basis vectors of w p and also in the explicit action matrix elements certain clebsch gordan coefficients are essential

efficient reconstruction algorithms using shifted lattices in this paper we consider sampling theory for irregular sampling sets of minimal density which are structured an efficient method for the reconstruction of band limited discrete signals from sampling sets which are unions of shifted lattices is developed these sets are not necessarily periodic a signal can be reconstructed from its samples provided the sampling set and the spectrum of the signal satisfy certain compatibility conditions while explicit reconstruction formulas for unions of sampling lattices are possible it is more convenient to use a recursive algorithm a numerical example utilizing nonperiodic sampling sets implemented in matlab is given the theory and the related algorithm has been applied to speech and image processing examples

numerical analysis of the non uniform sampling problem we give an overview of recent developments in the problem of reconstructing a band limited signal from nonuniform sampling from a numerical analysis view point it is shown that the appropriate design of the finite dimensional model plays a key role in the numerical solution of the nonuniform sampling problem in the one approach often proposed in the literature the finite dimensional model leads to an ill posed problem even in very simple situations the other approach that we consider leads to a well posed problem that preserves important structural properties of the original infinite dimensional problem and gives rise to efficient numerical algorithms furthermore a fast multilevel algorithm is presented that can reconstruct signals of unknown bandwidth from noisy nonuniformly spaced samples we also discuss the design of efficient regularization methods for ill conditioned reconstruction problems numerical examples from spectroscopy and exploration geophysics demonstrate the performance of the proposed methods

on the eigenvalues of matrices for the reconstruction of missing uniform samples in this correspondence we derive the relationship between the eigenvalues associated with the matrices of the minimum dimension time domain and frequency domain approaches used for reconstructing missing uniform samples the dependency of the eigenvalues of the weighted toeplitz matrix on positive weights are explored simple bounds for the maximum and minimum eigenvalues of the weighted toeplitz matrix are also presented alternative matrices possessing the same nonzero eigenvalues as that of the weighted toeplitz matrix are provided we verify the theory by the examples presented

the parafermion fock space and explicit so 2n 1 representations the defining relations triple relations of n pairs of parafermion operators f j j 1 n are known to coincide with a set of defining relations for the lie algebra so 2n 1 in terms of 2n generators with the common hermiticity conditions this means that the parafermions of order p correspond to a finite dimensional unitary irreducible representation w p of so 2n 1 with highest weight p 2 p 2 p 2 although the dimension and the character of w p is known by classical formulae there is no explicit basis of w p available in which the parafermion operators have a natural action in this paper we construct an orthogonal basis for w p and present the explicit actions of the parafermion generators on these basis vectors we use group theoretical techniques in which the u n subalgebra of so 2n 1 plays a crucial role a set of gelfand zetlin patterns of u n will be used to label the basis vectors of w p and also in the explicit action matrix elements certain u n clebsch gordan coefficients are essential

a class of infinite dimensional representations of the lie superalgebra mathfrak o mathfrak s mathfrak p 2m 1 2n and the parastatistics fock space an orthogonal basis of weight vectors for a class of infinite dimensional representations of the orthosymplectic lie superalgebra osp 2m 1 vertical bar 2n is introduced these representations are particular lowest weight representations v p with a lowest weight of the form p 2 p 2 vertical bar p 2 p 2 p being a positive integer explicit expressions for the transformation of the basis under the action of algebra generators are found since the relations of algebra generators correspond to the defining relations of m pairs of parafermion operators and n pairs of paraboson operators with relative parafermion relations the parastatistics fock space of order p is also explicitly constructed furthermore the representations v p are shown to have interesting characters in terms of supersymmetric schur functions and a simple character formula is also obtained

invariants and reduced matrix elements associated with the lie superalgebra gl m n we construct explicit formulae for the eigenvalues of certain invariants of the lie superalgebra gl m n using characteristic identities we discuss how such eigenvalues are related to reduced wigner coefficients and the reduced matrix elements of generators and thus provide a first step to a new algebraic derivation of matrix element formulae for all generators of the algebra

irregular sampling theorems and series expansions of band limited functions abstract we present a new approach to the problem of irregular sampling of band limited functions that is based on the approximation and factorization of convolution operators a special case of our main result is the following theorem if r n is compact g l 1 rn a band limited function with g t 0 on and xi i i and yj j j are two discrete sets in rn which are dense enough then every band limited function f lwp 1 p our methods work a for a very general class of function spaces not only weighted lwp spaces b in all dimensions even in general locally compact abelian groups c to provide the correct behavior of the coefficients in contrast to the traditional estimates currently used by engineers furthermore the method is constructive and stable with respect to input errors such as round off errors truncation effors jitter errors or aliasing errors

reconstruction algorithms in irregular sampling a constructive solution of the irregular sampling problem for band limited functions is given we show how a band limited function can be com pletely reconstructed from any random sampling set whose density is higher than the nyquist rate and give precise estimates for the speed of convergence of this iteration method variations of this algorithm allow for irregular sampling with derivatives reconstruction of band limited functions from local averages and irregular sampling of multivariate band limited functions in the irregular sampling problem one is asked whether and how a band limited function can be completely reconstructed from its irregularly sam pled values f xi this has many applications in signal and image processing seismology meteorology medical imaging etc finding constructive solutions of this problem has received considerable attention among mathematicians and engineers the mathematical literature provides several uniqueness results 1 2 17 18 19 it is now part of the folklore that for stable sampling the sampling rate must be at least the nyquist rate 18 these results as deep as they are have had little impact for the applied sciences because they were not constructive if the sampling set is just a perturbation of the regular oversampling then a reconstruction method has been obtained in a seminal paper by duffin and schaeffer 6 see also 29 if for some l 0 a 0 and o 0 the sampling points xk k e z satisfy a xk ok a k i then the norm equivalence a ir f x 2dx with w n o this norm equivalence implies that it is possible to reconstruct through an iterative procedure the so called frame method most of the later work on constructive methods consists of variations of this method 3 21 22 26 the above conditions on the sampling set exclude random irregular sampling sets e g sets with regions of higher sampling density a partial but undesirable remedy to handle highly irregular sampling sets would be to force the above conditions by throwing away information on part of the points and accept a very slow convergence of the iteration

a discrete theory of irregular sampling abstract we derive algorithms for the iterative reconstruction of discrete band limited signals from their irregular samples they converge at a geometric rate and all constants are computable explicitly we also treat the related problem of interpolation of trigonometric polynomials and give estimates for the condition number of certain positive definite toeplitz matrices

efficient numerical methods in non uniform sampling theory summary we present a new second generation reconstruction algorithm for irregular sampling i e for the problem of recovering a band limited function from its non uniformly sampled values the efficient new method is a combination of the adaptive weights method which was developed by the two first named authors and the method of conjugate gradients for the solution of positive definite linear systems the choice of adaptive weights can be seen as a simple but very efficient method of preconditioning further substantial acceleration is achieved by utilizing the toeplitztype structure of the system matrix this new algorithm can handle problems of much larger dimension and condition number than have been accessible so far furthermore if some gaps between samples are large then the algorithm can still be used as a very efficient extrapolation method across the gaps

acceleration of the frame algorithm shows how polynomial acceleration techniques which have been developed for the solution of large linear systems can be employed to improve and accelerate the frame algorithm these methods permit a reduction in the number of necessary iterations by an order of magnitude when the frame algorithm is slow the author gives several examples from the theory of irregular sampling from wavelet theory and from gabor theory where these methods are probably mandatory for efficient reconstruction

the paraboson fock space and unitary irreducible representations of the lie superalgebra mathfrak osp 1 2n it is known that the defining relations of the orthosymplectic lie superalgebra mathfrak osp 1 2n are equivalent to the defining triple relations of n pairs of paraboson operators b pm i in particular with the usual star conditions this implies that the parabosons of order p correspond to a unitary irreducible infinite dimensional lowest weight representation v p of mathfrak osp 1 2n apart from the simple cases p 1 or n 1 these representations had never been constructed due to computational difficulties despite their importance in the present paper we give an explicit and elegant construction of these representations v p and we present explicit actions or matrix elements of the mathfrak osp 1 2n generators the orthogonal basis vectors of v p are written in terms of gelfand zetlin patterns where the subalgebra mathfrak u n of mathfrak osp 1 2n plays a crucial role our results also lead to character formulas for these infinite dimensional mathfrak osp 1 2n representations furthermore by considering the branching mathfrak osp 1 2n supset mathfrak sp 2n supset mathfrak u n we find explicit infinite dimensional unitary irreducible lowest weight representations of mathfrak sp 2n and their characters

a braided look at green ansatz for parabosons bosons and parabosons are described as associative superalgebras with an infinite number of odd generators bosons are shown to be a quotient superalgebra of parabosons establishing thus an even algebra epimorphism which is an immediate link between their simple modules parabosons are a super hopf algebra the super hopf algebraic structure of parabosons combined with the projection epimorphism previously stated provides a braided interpretation of the green ansatz device and of the parabosonic fock like representations this braided interpretation combined with an old problem leads to the construction of straightforward generalizations of the green ansatz

reconstruction of irregularly sampled discrete time bandlimited signals with unknown sampling locations the purpose of this paper is to develop methods that can reconstruct a bandlimited discrete time signal from an irregular set of samples at unknown locations we define a solution to the problem using first a geometric and then an algebraic point of view we find the locations of the irregular set of samples by treating the problem as a combinatorial optimization problem we employ an exhaustive method and two descent methods the random search and cyclic coordinate methods the numerical simulations were made on three types of irregular sets of locations random sets sets with jitter around a uniform set and periodic nonuniform sets furthermore for the periodic nonuniform set of locations we develop a fast scheme that reduces the computational complexity of the problem by exploiting the periodic nonuniform structure of the sample locations in the dft

the newcommand z mathbb z z_2 times z_2 graded lie superalgebra newcommand pso mathfrak pso pso 2m 1 vert 2n and new parastatistics representations when the relative commutation relations between a set of m parafermions and n parabosons are of relative parafermion type the underlying algebraic structure is the classical orthosymplectic lie superalgebra lsa osp 2m 1 2n the relative commutation relations can also be chosen differently of relative paraboson type in this second case the underlying algebraic structure is no longer an ordinary lsa but a z 2 x z 2 graded lsa denoted here by pso 2m 1 2n the identification of this new algebraic structure was performed by tolstoy amongst others in the present paper we investigate the subalgebra structure of pso 2m 1 2n this allows us to study the parastatistics lock spaces for this new set of m n para operators as they correspond to lowest weight representations of pso 2m 1 2n our main result is the construction of these lock spaces with a complete labeling of the basis vectors and an explicit action of the para operators on these basis vectors

irregular sampling toeplitz matrices and the approximation of entire functions of exponential type in many applications one seeks to recover an entire function of exponential type from its non uniformly spaced samples whereas the mathematical theory usually addresses the question of when such a function in l 2 r can be recovered numerical methods operate with a finite dimensional model the numerical reconstruction or approximation of the original function amounts to the solution of a large linear system we show that the solutions of a particularly efficient discrete model in which the data are fit by trigonometric polynomials converge to the solution of the original infinite dimensional reconstruction problem this legitimatizes the numerical computations and explains why the algorithms employed produce reasonable results the main mathematical result is a new type of approximation theorem for entire functions of exponential type from a finite number of values from another point of view our approach provides a new method for proving sampling theorems

local set based graph signal reconstruction signal processing on graph is attracting more and more attentions for a graph signal in the low frequency subspace the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the smoothness of the graph signal in this paper the concept of local set is introduced and two local set based iterative methods are proposed to reconstruct bandlimited graph signal from sampled data in each iteration one of the proposed methods reweights the sampled residuals for different vertices while the other propagates the sampled residuals in their respective local sets these algorithms are built on frame theory and the concept of local sets based on which several frames and contraction operators are proposed we then prove that the reconstruction methods converge to the original signal under certain conditions and demonstrate the new methods lead to a significantly faster convergence compared with the baseline method furthermore the correspondence between graph signal sampling and time domain irregular sampling is analyzed comprehensively which may be helpful to future works on graph signals computer simulations are conducted the experimental results demonstrate the effectiveness of the reconstruction methods in various sampling geometries imprecise priori knowledge of cutoff frequency and noisy scenarios

parabolic radon transform sampling and efficiency a good choice of the sampling in the transform domain is essential for a successful application of the parabolic radon transform the parabolic radon transform is computed for each temporal frequency and is essentially equivalent to the nonuniform fourier transform this leads to new and useful insights in the parabolic radon transform using nonuniform fourier theory we derive a minimum sampling interval for the curvature parameter and a maximum curvature range for which stability is guaranteed for general irregular sampling a significantly smaller sampling interval requires stabilization if diagonal stabilization is used no gain in resolution is obtained in contrast to conventional implementations the curvature sampling interval is proposed to be inversely proportional to the temporal frequency this results in improved quality of the transform and yields significant savings in computation time

sampling in paley wiener spaces on combinatorial graphs a notion of paley wiener spaces on combinatorial graphs is introduced it is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets such uniqueness sets are described in terms of poincare wirtinger type inequalities a reconstruction algorithm of paley wiener functions from uniqueness sets which uses the idea of frames in hilbert spaces is developed special consideration is given to the n dimensional lattice homogeneous trees and eigenvalue and eigenfunction problems on finite graphs

existence of homoclinic constant sign solutions for a difference equation on the integers we consider a difference equation involving the discrete p laplacian operator depending on a positive real parameter l we prove under convenient assumptions that for l big enough the equations admit at least one homoclinic constant sign solution in z our method consists in two parts first we prove the existence of two dirichlet type solutions for the equation in the discrete interval n n for all n n big enough then we show that such solutions converge to a homoclinic solution in z as n

discrete irregular sampling with larger gaps abstract discrete irregular sampling is the problem of recovering a band limited discrete signal from its nonuniformly sampled values we introduce a new method for discrete irregular sampling it features a new sampling geometry where the sampling points are chosen to come in pairs a frequency domain formulation reduces the problem to a system of linear equations for which the matrix is of toeplitz type and is positive definite as soon as there are enough samples an explicit estimate of the condition number of that matrix is given under some condition on the maximum sampling gap this condition allows gaps larger than the nyquist gap we recombine the new method and the conjugate method to deduce an efficient iterative reconstruction scheme for band limited discrete signals numerical results are provided to illustrate the efficiency of the method