analytical solutions to a class of nonlinear schrodinger equations with cal pt like potentials we present closed form solutions to a certain class of one and two dimensional nonlinear schr odinger equations involving potentials with broken and unbroken pt symmetry in the one dimensional case these solutions are given in terms of jacobi elliptic functions hyperbolic and trigonometric functions some of these solutions are possible even when the corresponding pt symmetric potentials have a zero threshold in two dimensions hyperbolic secant type solutions are obtained for a nonlinear schr odinger equation with a nonseparable complex potential

new abstract hardy spaces the aim of this paper is to propose an abstract construction of spaces which keep the main properties of the already known hardy spaces h1 we construct spaces through an atomic or molecular decomposition we prove some results about continuity from these spaces into l1 and some results about interpolation between these spaces and the lebesgue spaces we also obtain some results on weighted norm inequalities finally we present partial results in order to understand a characterization of the duals of hardy spaces

multilinear calderon zygmund theory abstract a systematic treatment of multilinear calderon zygmund operators is presented the theory developed includes strong type and endpoint weak type estimates interpolation a multilinear t 1 theorem and a variety of results regarding multilinear multiplier operators

duality of hardy and bmo spaces associated with operators with heat kernel bounds the introduction and development of hardy and bmo spaces on euclidean spaces r in the 1960s and 1970s played an important role in modern harmonic analysis and applications in partial differential equations these spaces were studied extensively in 32 22 18 19 31 and many others an l function f on r is in the hardy spaceh r if the area integral function of the poisson integral e t f satisfies

hermite spectral methods with a time dependent scaling for parabolic equations in unbounded domains hermite spectral methods are investigated for linear diffusion equations and nonlinear convection diffusion equations in unbounded domains when the solution domain is unbounded the diffusion operator no longer has a compact resolvent which makes the hermite spectral methods unstable to overcome this difficulty a time dependent scaling factor is employed in the hermite expansions which yields a positive bilinear form as a consequence stability and spectral convergence can be established for this approach the present method plays a similar role in the stability of the similarity transformation technique proposed by funaro and kavian math comp 57 1991 pp 597 619 however since coordinate transformations are not required the present approach is more efficient and is easier to implement in fact with the time dependent scaling the resulting discretization system is of the same form as that associated with the classical straightforward but unstable hermite spectral method numerical experiments are carried out to support the theoretical stability and convergence results

abstract hardy sobolev spaces and interpolation the purpose of this work is to describe an abstract theory of hardy sobolev spaces on doubling riemannian manifolds via an atomic decomposition we study the real interpolation of these spaces with sobolev spaces and finally give applications to riesz inequalities

a new generalized laguerre spectral approximation and its applications a new family of generalized laguerre polynomials is introduced various orthogonal projections are investigated some approximation results are established as an example of their important applications the mixed spherical harmonic generalized laguerre approximation is developed a mixed spectral scheme is proposed for a three dimensional model problem its convergence is proved numerical results demonstrate the high accuracy of this new spectral method

use of abstract hardy spaces real interpolation and applications to bilinear operators this paper can be considered as the sequel of bernicot and zhao j func anal 255 1761 1796 2008 where the authors have proposed an abstract construction of hardy spaces h1 they shew an interpolation result for these hardy spaces with the lebesgue spaces here we describe a more precise result using the real interpolation theory and we clarify the use of hardy spaces then with the help of the bilinear interpolation theory we then give applications to study bilinear operators on lebesgue spaces these ideas permit us to study singular operators with singularities similar to those of bilinear calderon zygmund operators in a far more abstract framework as in the euclidean case

rational legendre pseudospectral approach for solving nonlinear differential equations of lane emden type lane emden equation is a nonlinear singular equation in the astrophysics that corresponds to the polytropic models in this paper a pseudospectral technique is proposed to solve the lane emden type equations on a semi infinite domain the method is based on rational legendre functions and gauss radau integration the method reduces solving the nonlinear ordinary differential equation to solve a system of nonlinear algebraic equations the comparison of the results with the other numerical methods shows the efficiency and accuracy of this method

lyapunov schmidt reduction algorithm for three dimensional discrete vortices abstract we address the persistence and stability of three dimensional vortex configurations in the discrete nonlinear schrodinger equation and develop a symbolic package based on wolfram s mathematica for computations of the lyapunov schmidt reduction method the lyapunov schmidt reduction method is a theoretical tool which enables us to study continuations and terminations of the discrete vortices for small coupling between lattice nodes as well as the spectral stability of the persistent configurations the method was developed earlier in the context of the two dimensional lattice and applied to the onsite and offsite configurations called the vortex cross and the vortex cell by using semianalytical computations d e pelinovsky p g kevrekidis d frantzeskakis physica d 212 2005 20 53 p g kevrekidis d e pelinovsky proc r soc a 462 2006 2671 2694 the present treatment develops a full symbolic computational package which takes a desired waveform at the anticontinuum limit of uncoupled sites performs a required number of lyapunov schmidt reductions and outputs the predictions on whether the configuration persists for finite coupling in the three dimensional lattice and whether it is stable or unstable it also provides approximations for the eigenvalues of the linearized stability problem we report a number of applications of the algorithm to important multisite three dimensional configurations such as the simple cube the double cross and the diamond for each configuration we identify exactly one solution which is stable for small coupling between lattice nodes

vertical versus conical square functions we study the difference between vertical and conical square functions in the abstract and also in the specific case where the square functions come from an elliptic operator trans amer math soc 364 2012 no 10 5469 5489

on the rational second kind chebyshev pseudospectral method for the solution of the thomas fermi equation over an infinite interval in this paper we propose a pseudospectral method for solving the thomas fermi equation which is a nonlinear singular ordinary differential equation on a semi infinite interval this approach is based on the rational second kind chebyshev pseudospectral method that is indeed a combination of tau and collocation methods this method reduces the solution of this problem to the solution of a system of algebraic equations the slope at origin is provided with high accuracy comparison with some numerical solutions shows that the present solution is effective and highly accurate

a generalization of the wiener rational basis functions on infinite intervals part ii numerical investigation in part i we introduced the generalized wiener rational basis functions and here in part ii we continue our investigation with numerical experiments wiener s generalized basis can utilize the fast fourier transform for integer values of the decay parameter s we outline two algorithms for doing so in addition the issue of galerkin representations for polynomial nonlinearities of expansions is addressed the wiener basis set is compared against domain truncation methods fourier and chebyshev polynomials hermite functions sinc interpolations and mapped chebyshev expansions and we show that for both exponentially and algebraically decaying functions the wiener approximation is as good as or superior to these alternatives in addition we carry out preliminary investigations regarding tuning of the decay parameter s numerical simulations of korteweg de vries type equations show the effectiveness of the wiener expansion we also explore the practical use of the wiener basis functions on the semi infinite interval which is compared against laguerre function methods and other jacobi polynomial mappings

existence and stability of pt symmetric states in nonlinear two dimensional square lattices abstract solitons and vortices symmetric with respect to simultaneous parity p and time reversing t transformations are considered on the square lattice in the framework of the discrete nonlinear schrodinger equation the existence and stability of such pt symmetric configurations is analyzed in the limit of weak coupling between the lattice sites when predictions on the elementary cell of a square lattice i e a single square can be extended to a large yet finite array of lattice cells in particular we find all examined vortex configurations are unstable with respect to small perturbations while a branch extending soliton configurations is spectrally stable our analytical predictions are found to be in good agreement with numerical computations

discrete vector on site vortices we study discrete vortices in coupled discrete nonlinear schrodinger equations we focus on the vortex cross configuration that has been experimentally observed in photorefractive crystals stability of the single component vortex cross in the anti continuum limit of small coupling between lattice nodes is proved in the vector case we consider two coupled configurations of vortex crosses namely the charge one vortex in one component coupled in the other component to either the charge one vortex forming a double charge vortex or the charge negative one vortex forming a so called hidden charge vortex we show that both vortex configurations are stable in the anti continuum limit if the parameter for the inter component coupling is small and both of them are unstable when the coupling parameter is large in the marginal case of the discrete two dimensional manakov system the double charge vortex is stable while the hidden charge vortex is linearly unstable analytical predictions are corroborated with numerical observations that show good agreement near the anti continuum limit but gradually deviate for larger couplings between the lattice nodes

weighted norm inequalities off diagonal estimates and elliptic operators part i general operator theory and weights this is the first part of a series of four articles in this work we are interested in weighted norm estimates we put the emphasis on two results of different nature one is based on a good inequality with two parameters and the other uses calderon zygmund decomposition these results apply well to singular non integral operators and their commutators with bounded mean oscillation functions singular means that they are of order 0 non integral that they do not have an integral representation by a kernel with size estimates even rough so that they may not be bounded on all lp spaces for 1 p 8 pointwise estimates are then replaced by appropriate localized lp lq estimates we obtain weighted lp estimates for a range of p that is different from 1 8 and isolate the right class of weights in particular we prove an extrapolation theorem a la rubio de francia for such a class and thus vector valued estimates

laguerre pseudospectral approximation to the thomas fermi equation we propose an iterative method to solve the nonlinear thomas fermi equation based on laguerre pseudospectral approximation different from the direct use of pseudospectral methods for solving the problem in the literature we represent the solution of the thomas fermi equation as sum of two parts due to its singularity at the origin both parts regard the initial slope as a parameter unknown to be determined one singular part is a power series expansion the other smooth part satisfies a nonlinear two point boundary value problem we use a laguerre pseudospectral method to discretize and solve it numerically by the newton iteration moreover an introduced new boundary condition is employed innovatively to construct an outer iteration to determine the initial slope we show numerically this separation of solution as two parts is necessary for improvement of accuracy by direct laguerre approximations of the thomas fermi equation comparisons of our numerical results with those obtained by other methods show effectiveness and accuracy of our approach

on maximal l p regularity abstract the aim of this paper is to propose weak assumptions to prove maximal l q regularity for cauchy problem d u d t t l u t f t mainly we only require off diagonal estimates on the real semigroup e t l t 0 to obtain maximal l q regularity the main idea is to use one kind of hardy space h 1 adapted to this problem and then use interpolation results these techniques permit us to prove weighted maximal regularity too

modified laguerre pseudospectral method refined by multidomain legendre pseudospectral approximation a modified laguerre pseudospectral method is proposed for differential equations on the half line the numerical solutions are refined by multidomain legendre pseudospectral approximation numerical results show the spectral accuracy of this approach some approximation results on the modified laguerre and legendre interpolations are established the convergence of proposed method is proved

the spectral method for high order problems with proper simulations of asymptotic behaviors at infinity in this paper we investigate new spectral and multidomain spectral methods for high order problems we introduce a family of new generalized laguerre functions which are mutually orthogonal with the weight function x a d x c d 0 a and c being arbitrary real numbers the corresponding quasi orthogonal approximation and laguerre gauss radau type interpolation are proposed the spectral and multidomain spectral schemes are provided for several model problems which not only fit the mixed inhomogeneous boundary conditions on the fixed boundary exactly but also match the asymptotic behaviors at infinity reasonably numerical results demonstrate the efficiency of suggested algorithms and confirm the analysis well

mixed laguerre legendre pseudospectral method for incompressible fluid flow in an infinite strip in this paper we investigate the mixed laguerre legendre interpolation approximation and its application some approximation results are established a mixed laguerre legendre pseudospectral scheme is constructed for incompressible fluid flow in an infinite strip its stability and convergence are proved numerical results show the efficiency of this new approach

multilinear interpolation between adjoint operators abstract multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak type estimates a typical situation occurs when one knows that a multilinear operator satisfies a weak l q estimate for a single index q which may be less than one and that all the adjoints of the multilinear operator are of similar nature and thus they also satisfy the same weak l q estimate under this assumption in this note we give a general multilinear interpolation theorem which allows one to obtain strong type boundedness for the operator and all of its adjoints for a large set of exponents the key point in the applications we discuss is that the interpolation theorem can handle the case q 1 when q 1 weak l q has a predual and such strong type boundedness can be easily obtained by duality and multilinear interpolation cf interpolation spaces an introduction springer new york 1976 math ann 319 2001 151 in function spaces and applications lund 1986 lecture notes in mathematics vol 1302 springer berlin new york 1988 j amer math soc 15 2002 469 proc amer math soc 21 1969 441

time dependent hermite galerkin spectral method and its applications a time dependent hermite galerkin spectral method thgsm is investigated in this paper for the nonlinear convection diffusion equations in the unbounded domains the time dependent scaling factor and translating factor are introduced in the definition of the generalized hermite functions ghf as a consequence the thgsm based on these ghf has many advantages not only in theoretical proofs but also in numerical implementations the stability and spectral convergence of our proposed method have been established in this paper the korteweg de vries burgers kdvb equation and its special cases including the heat equation and the burgers equation as the examples have been numerically solved by our method the numerical results are presented and it surpasses the existing methods in accuracy our theoretical proof of the spectral convergence has been supported by the numerical results

abstract hardy spaces with variable exponents abstract in this paper we introduce the definition of abstract hardy spaces with variable exponents via the atomic decomposition and molecular decomposition we prove the continuity from our variable hardy space h a t o p into l p where p r n 0 1 0 p p 1 moreover we investigate the bilinear theory finally we give an application of the abstract hardy spaces with variable exponents

a rational spectral method for the kdv equation on the half line a petrov galerkin method using orthogonal rational functions is proposed for the korteweg de vries kdv equation on the half line with initial boundary values the nonlinear term and the right hand side term are treated by chebyshev rational interpolation explicitly and the linear terms are computed with the galerkin method implicitly such an approach is applicable using fast algorithms numerical results are presented for problems with both exponentially and algebraically decaying solutions respectively highlighting the performance of the proposed method

jacobi and laguerre quasi orthogonal approximations and related interpolations in this paper we investigate jacobi quasi orthogonal approximation and generalized jacobi gauss lobatto interpolation we also propose laguerre quasi orthogonal approximation and generalized laguerre gauss radau interpolation a series of sharp results on these approximations are established which are applicable to spectral and pseudospectral methods for mixed nonhomogeneous boundary value problems of high order

on spectral methods for volterra type integro differential equations this paper considers the spectral methods for a volterra type integro differential equation firstly the volterra type integro differential equation is equivalently restated as two integral equations of the second kind secondly a legendre collocation method is used to solve them then the error analysis is conducted based on the l norm in addition numerical results are presented to confirm our analysis

mixed spectral method for three dimensional exterior problems using spherical harmonic and generalized laguerre functions in this paper we develop the mixed spectral method for three dimensional exterior problems using spherical harmonic and generalized laguerre functions some basic approximation results are established the mixed spectral schemes are proposed for two model problems their convergences are proved numerical results demonstrate the efficiency of this new approach

rational scaled generalized laguerre function collocation method for solving the blasius equation in this paper we propose a collocation method for solving the blasius equation the blasius equation is a third order nonlinear ordinary differential equation this approach is based on a rational scaled generalized laguerre function collocation method we also present the comparison of this work with some well known results and show that the present solution is accurate

the laguerre spectral method for solving neumann boundary value problems in this paper we propose a laguerre spectral method for solving neumann boundary value problems this approach differs from the classical spectral method in that the homogeneous boundary condition is satisfied exactly moreover a tridiagonal matrix is employed instead of the full stiffness matrix encountered in the classical variational formulation of such problems for analyzing the numerical errors some basic results on laguerre approximations are established the convergence is proved the numerical results demonstrate the efficiency of this approach

stable and efficient spectral methods in unbounded domains using laguerre functions stable and efficient spectral methods using laguerre functions are proposed and analyzed for model elliptic equations on regular unbounded domains it is shown that spectral galerkin approximations based on laguerre functions are stable and convergent with spectral accuracy in the usual not weighted sobolev spaces efficient accurate and well conditioned algorithms using laguerre functions are developed and implemented numerical results indicating the spectral convergence rate and effectiveness of these algorithms are presented

generalized laguerre interpolation and pseudospectral method for unbounded domains in this paper error estimates for generalized laguerre gauss type interpolations are derived in nonuniformly weighted sobolev spaces weighted with omega alpha beta x x alpha e beta x alpha 1 beta 0 generalized laguerre pseudospectral methods are analyzed and implemented two model problems are considered the proposed schemes keep spectral accuracy and with suitable choice of basis functions lead to sparse and symmetric linear systems

hardy and bmo spaces associated to divergence form elliptic operators consider a second order divergence form elliptic operator l with complex bounded measurable coefficients in general operators based on l such as the riesz transform or square function may lie beyond the scope of the calderon zygmund theory they need not be bounded in the classical hardy bmo and even some l p spaces in this work we develop a theory of hardy and bmo spaces associated to l which includes in particular a molecular decomposition maximal and square function characterizations duality of hardy and bmo spaces and a john nirenberg inequality

laguerre galerkin method for nonlinear partial differential equations on a semi infinite interval summary a laguerre galerkin method is proposed and analyzed for the burgers equation and benjamin bona mahony bbm equation on a semi infinite interval by reformulating these equations with suitable functional transforms it is shown that the laguerre galerkin approximations are convergent on a semi infinite interval with spectral accuracy an efficient and accurate algorithm based on the laguerre galerkin approximations to the transformed equations is developed and implemented numerical results indicating the high accuracy and effectiveness of this algorithm are presented

jacobi spectral method for differential equations with rough asymptotic behaviors at infinity abstract in this paper we change differential equations on the half line to certain singular problems on finite interval and then use a specific jacobi approximation for solving the resulting problems numerically theoretical analysis and numerical results demonstrate the efficiency of this method

a generalized laguerre hermite pseudospectral method for computing symmetric and central vortex states in bose einstein condensates a generalized laguerre hermite pseudospectral method is proposed for computing symmetric and central vortex states in bose einstein condensates becs in three dimensions with cylindrical symmetry the new method is based on the properly scaled generalized laguerre hermite functions and a normalized gradient flow it enjoys three important advantages i it reduces a three dimensional 3d problem with cylindrical symmetry into an effective two dimensional 2d problem ii it solves the problem in the whole space instead of in a truncated artificial computational domain and iii it is spectrally accurate extensive numerical results for computing symmetric and central vortex states in becs are presented for one dimensional 1d bec 2d bec with radial symmetry and 3d bec with cylindrical symmetry

bilinear oscillatory integrals and boundedness for new bilinear multipliers abstract we consider bilinear oscillatory integrals i e pseudo product operators whose symbol involves an oscillating factor lebesgue space inequalities are established which give decay as the oscillation becomes stronger this extends the well known linear theory of oscillatory integral in some directions the proof relies on a combination of time frequency analysis of coifman meyer type with stationary and non stationary phase estimates as a consequence of this analysis we obtain lebesgue estimates for new bilinear multipliers defined by non smooth symbols

efficient spectral galerkin method ii direct solvers of second and fourth order equations using chebyshev polynomials efficient direct solvers based on the chebyshev galerkin methods for second and fourth order equations are presented they are based on appropriate base functions for the galerkin formulation that lead to discrete systems with special structured matrices that can be efficiently inverted numerical results indicate that the direct solvers presented in this paper are significantly more accurate and efficient than those based on the chebyshev tau method

hardy spaces and divergence operators on strongly lipschitz domains of rn abstract let be a strongly lipschitz domain of r n consider an elliptic second order divergence operator l including a boundary condition on and define a hardy space by imposing the non tangential maximal function of the extension of a function f via the poisson semigroup for l to be in l1 under suitable assumptions on l we identify this maximal hardy space with h 1 r n if r n with h r 1 under the dirichlet boundary condition and with h z 1 under the neumann boundary condition

efficient spectral collocation methods for a class of linear fredholm integro differential equations on the half line abstract in this paper an extension of the legendre spectral collocation method has been proposed for the numerical solution of a class of linear fredholm integro differential equation on the half line the properties of mapped legendre functions are first presented these properties together with the legendre gauss points are then utilized to reform the fredholm integro differential equation in semi infinite interval into a singular equation in finite interval and to reduce it to the solution of a simple matrix equation besides in order to show the efficiency and accuracy of the proposed method some numerical examples are considered and solved through a survey of three approaches namely exponential rational and logarithmic legendre functions collocation methods furthermore a comparison of the results shows that using exponential functions leads to more accurate results and faster convergence

combined hermite spectral finite difference method for the fokker planck equation the convergence of a class of combined spectral finite difference methods using hermite basis applied to the fokker planck equation is studied it is shown that the hermite based spectral methods are convergent with spectral accuracy in weighted sobolev space numerical results indicating the spectral convergence rate are presented a velocity scaling factor is used in the hermite basis and is shown to improve the accuracy and effectiveness of the hermite spectral approximation with no increase in workload some basic analysis for the selection of the scaling factors is also presented

multilinear operators with non smooth kernels and commutators of singular integrals we obtain endpoint estimates for multilinear singular integral operators whose kernels satisfy regularity conditions significantly weaker than those of the standard calder6n zygmund kernels as a consequence we deduce endpoint l 1 x l 1 to weak l 1 m estimates for the mth order commutator of calderon our results reproduce known estimates for m 1 2 but are new for m 3 we also explore connections between the 2nd order higher dimensional commutator and the bilinear hilbert transform and deduce some new off diagonal estimates for the former

new function spaces of bmo type the john nirenberg inequality interpolation and applications in this paper we introduce and develop some new function spaces of bmo bounded mean oscillation type on spaces of homogeneous type or measurable subsets of spaces of homogeneous type the new function spaces are defined by variants of maximal functions associated with generalized approximations to the identity and they generalize the classical bmo space we show that the john nirenberg inequality holds on these spaces and they interpolate with lp spaces by the complex interpolation method we then give applications on lp boundedness of singular integrals whose kernels do not satisfy the hormander condition 2005 wiley periodicals inc

the spectral methods for parabolic volterra integro differential equations in this paper we study the numerical solutions to parabolic volterra integro differential equations in one dimensional bounded and unbounded spatial domains in a bounded domain the given parabolic volterra integro differential equation is converted to two equivalent equations then a legendre collocation method is used to solve them and finally a linear algebraic system is obtained for an unbounded case we use the algebraic mapping to transfer the problem on a bounded domain and then apply the same presented approach for the bounded domain in both cases some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method

the sinc collocation method for solving the thomas fermi equation a numerical technique for solving nonlinear ordinary differential equations on a semi infinite interval is presented we solve the thomas fermi equation by the sinc collocation method that converges to the solution at an exponential rate this method is utilized to reduce the nonlinear ordinary differential equation to some algebraic equations this method is easy to implement and yields very accurate results

accurate solution of the thomasfermi equation using the fractional order of rational chebyshev functions in this paper the nonlinear singular thomasfermi differential equation for neutral atoms is solved using the fractional order of rational chebyshev orthogonal functions frcs of the first kind ftn t l on a semi infinite domain where l is an arbitrary numerical parameter first using the quasilinearization method the equation be converted into a sequence of linear ordinary differential equations ldes and then these ldes are solved using the frcs collocation method using 300 collocation points we have obtained a very good approximation solution and the value of the initial slope y 0 1 5880710226113753127186845094239501095 highly accurate to 37 decimal places

efficient spectral galerkin method i direct solvers of second and fourth order equations using legendre polynomials this paper presents some efficient algorithms based on the legendre galerkin approximations for the direct solution of the second and fourth order elliptic equations the key to the efficiency of these algorithms is to construct appropriate base functions which lead to systems with sparse matrices for the discrete variational formulations the complexities of the algorithms are a small multiple of n d 1 operations for a d dimensional domain with n 1 d unknowns while the convergence rates of the algorithms are exponential for problems with smooth solutions in addition the algorithms can be effectively parallelized since the bottlenecks of the algorithms are matrix matrix multiplications

chebyshev rational spectral and pseudospectral methods on a semi infinite interval a weighted orthogonal system on the half line based on the chebyshev rational functions is introduced basic results on chebyshev rational approximations of several orthogonal projections and interpolations are established to illustrate the potential of the chebyshev rational spectral method a model problem is considered both theoretically and numerically error estimates for the chebyshev rational spectral and pseudospectral methods are established preliminary numerical results agree well with the theoretical estimates and demonstrate the effectiveness of this approach

persistence and stability of discrete vortices in nonlinear schrodinger lattices abstract we study discrete vortices in the two dimensional nonlinear schrodinger lattice with small coupling between lattice nodes the discrete vortices in the anti continuum limit of zero coupling represent a finite set of excited nodes on a closed discrete contour with a non zero charge using the lyapunov schmidt reductions we analyze continuation and termination of the discrete vortices for small coupling between lattice nodes an example of a square discrete contour is considered that includes the vortex cell also known as the off site vortex we classify families of symmetric and asymmetric discrete vortices that bifurcate from the anti continuum limit we predict analytically and confirm numerically the number of unstable eigenvalues associated with each family of such discrete vortices

a laguerre legendre spectral method for the stokes problem in a semi infinite channel a mixed spectral method is proposed and analyzed for the stokes problem in a semi infinite channel the method is based on a generalized galerkin approximation with laguerre functions in the x direction and legendre polynomials in the y direction the well posedness of this method is established by deriving a lower bound on the inf sup constant numerical results indicate that the derived lower bound is sharp rigorous error analysis is also carried out