local well posedness for the maxwell schrodinger equation time local well posedness for the maxwell schrodinger equation in the coulomb gauge is studied in sobolev spaces by the contraction mapping principle the lorentz gauge and the temporal gauge cases are also treated by the gauge transform

a canonical factorization for meromorphic herglotz functions on the unit disk and sum rules for jacobi matrices we prove a general canonical factorization for meromorphic herglotz functions on the unit disk whose notable elements are that there is no restriction other than interlacing on the zeros and poles for their blaschke product to converge and there is no singular inner function we use this result to provide a significant simplification in the proof of killip simon ann math 158 2003 253 of their result characterizing the spectral measures of jacobi matrices j with j j 0 hilbert schmidt we prove a nonlocal version of case and step by step sum rules

matrix orthogonal polynomials on the unit circle the properties of matrix orthogonal polynomials on the unit circle are investigated beginning with their recurrence formulas the techniques of scattering theory and banach algebras are used in the investigation a matrix generalization of a theorem of baxter is proved

on new relations between spectral properties of jacobi matrices and their coefficients we study the spectral properties of jacobi matrices by using higher order trace formulae we obtain a result relating the properties of the elements of jacobi matrices and the corresponding spectral measures complicated expressions for traces of some operators can be magically simplified allowing us to apply induction arguments our theorems are generalizations of a recent result of r killip and b simon 17

on the instability of flow in a streamwise corner the linear stability of an incompressible laminar flow in the blending boundary layer between the boundary layer in a 90 streamwise corner and a blasius boundary layer well away from the corner is examined using a locally parallel flow approximation it is shown that the magnitude of the cross flow in the boundary layer is too small to be a significant factor in the observed early transition in the blending layer however the influence of the outer boundary conditions associated with oblique modes of disturbances which are anti symmetric about the bisector plane are shown to have a profound effect on the stability of the flow as a result the square root of the critical streamwise reynolds number r er associated with a spanwise location is significantly reduced as the corner is approached being r er 54 approximately for spanwise distance of z 6 x r 1 from the corner compared with r er 322 approximately for z 20 x r 1 where x measures downstream distance from the leading edges and r 2 is the streamwise reynolds number at r 600 the growth rate of the most amplified mode of disturbance at the former location is over six times greater than that at the latter the corresponding wave angle at the two locations is respectively 44 and 5 approximately

inverse spectral analysis with partial information on the potential ii the case of discrete spectrum we discuss results where the discrete spectrum or partial information on the discrete spectrum and partial information on the potential q of a one dimensional schrodinger operator h d 2 dx 2 q determine the potential completely included are theorems for finite intervals and for the whole line in particular we pose and solve a new type of inverse spectral problem involving fractions of the eigenvalues of h on a finite interval and knowledge of q over a corresponding fraction of the interval the methods employed rest on weyl m function techniques and densities of zeros of a class of entire functions

non modal stability and breakdown in corner and three dimensional boundary layers two classes of three dimensional boundary layer are studied namely the flow in the neighbourhood of a corner of general apex angle and the flow over a wall with spanwise varying porosity stre

generalized strichartz inequalities for the wave equation strichartz inequalities for the wave equation u f are estimates of the solution u of the cauchy problem for that equation in the form of space time integral norms in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data

global existence and asymptotic behavior of solutions for the maxwell schrodinger equations in three space dimensions in this paper we study the global existence and asymptotic behavior of solutions for the maxwell schrodinger equations under the coulomb gauge condition in three space dimensions with the final states given att this leads to the construction of the modified wave operator for certain scattered data it is also shown that for the initial data in the range of the modified wave operator the initial value problem of the maxwell schrodinger equations has the global solutions in time

smoothing effects for schrodinger equations with electro magnetic potentials and applications to the maxwell schrodinger equations abstract we consider schrodinger equations in r 1 2 with electro magnetic potentials the potentials belong to h 1 and typically they are time independent or determined as solutions to inhomogeneous wave equations we prove kato type smoothing estimates for solutions we also apply this result to the maxwell schrodinger equations in the lorentz gauge and prove unique solvability of this system in the energy space

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

matrix measures moment spaces and favard s theorem for the interval 0 1 and 0 abstract in this paper we study the moment spaces corresponding to matrix measures on compact intervals and on the nonnegative line 0 a representation for nonnegative definite matrix polynomials is obtained which is used to characterize moment points by properties of generalized hankel matrices we also derive an explicit representation of the orthogonal polynomials with respect to a given matrix measure which generalizes the classical determinant representation of the one dimensional case moreover the coefficients in the recurrence relations can be expressed explicitly in terms of the moments of the matrix measure these results are finally used to prove a refinement of the well known favard theorem for matrix measures which characterizes the domain of the underlying measure of orthogonality by properties of the coefficients in the recurrence relationships

meromorphic continuations of finite gap herglotz functions and periodic jacobi matrices we find a necessary and sufficient condition for a herglotz function m to be the borel transform of the spectral measure of an exponential decaying perturbation of a periodic jacobi matrix the condition is in terms of meromorphic continuation of m to a natural riemann surface and the structure of its zeros and poles

on space time means and everywhere defined scattering operators for nonlinear klein gordon equations on demontre l existence d operateurs de diffusion definis partout pour certaines equations de klein gordon non lineaires

self similar viscous incompressible flow along an unbounded corner the self similar viscous flow of incompressible fluid along the right angle unbounded corner with nonzero streamwise pressure gradient is considered the corner layer equations for this case are derived and their asymptotic series are analyzed it is shown that self similar corner layer equations have two solutions even at a zero streamwise pressure gradient the numerical procedure for the integration of corner layer equations is developed and numerical calculations are performed at several values of power exponent for a streamwise pressure gradient distribution

kotani theory for one dimensional stochastic jacobi matrices we consider families of operators h on l2 given by h u n u n 1 u n 1 v n u n wherev is a stationary bounded ergodic sequence we prove analogs of kotani s results including that for a e ac h is the essential closure of the set ofe where e the lyaponov index vanishes and the result that ifv is non deterministic then ac is empty

crossed products of c algebras and spectral analysis of quantum hamiltonians we study spectral properties of a hamiltonian by analyzing the structure of certain c algebras to which it is affiliated the main tool we use for the construction of these algebras is the crossed product of abelian c algebras generated by the classical potentials by actions of groups we show how to compute the quotient of such a crossed product with respect to the ideal of compact operators and how to use the resulting information in order to get spectral properties of the hamiltonians this scheme provides a unified approach to the study of hamiltonians of anisotropic and many body systems including quantum fields

stability of the laminar boundary layer in a streamwise corner this work examines the stability of viscous incompressible flow along a streamwise corner often called the corner boundary layer problem the semi infinite boundary value problem satisfied by small amplitude disturbances in the blending boundary layer region is obtained the mean secondary flow induced by the corner exhibits a flow reversal in this region uniformly valid first approximations to solutions of the governing differential equations are derived uniformity at infinity is achieved by a suitable choice of the large parameter and use of an appropriate langer variable approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two dimensional boundary layer profiles viscous incompressible laminar flow along a streamwise corner formed by the intersection of two solid surfaces is often referred to as the corner boundary layer problem in the theoretical model of this problem two flat plates which are infinite in the streamwise and spanwise directions intersect such that the line of intersection the corner line is normal to the plane containing their leading edges the basic flow is along the line of intersection most theoretical work assumes a rectangular corner this situation is shown in figure 1

well posedness for the nonlinear klein gordon schrodinger equations with heterointeractions in this paper we study the well posedness of solution to a certain system of nonlinear klein gordon schrodinger equations in three space dimensions basing on the strichartz estimates we obtain the global existence uniqueness of the solutions and continuous dependence with respect to initial data in the sobolev spaces of low regularities by setting appropriate contraction and taking difference estimates

computation of separated duct flows using the boundary layer equations a semi inverse method based on boundary laye r equations for simulation of duct flows with strong viscous inviscid interaction is developed an improved interaction formula based on the matching of parameters in viscous and inviscid zones is proposed using this method the laminar and turbulent flows in plane channels swirl flow in annular channels and a bypass flow with downstream mixing of the trailing edge of a splitter were calculated the results for the plane channel and bypass flows are in good agreement with known experimental and theoretical data the influence of swirl and parameters of the bypass flow on the separation zone structure were investigated a new type of self similar solution for swirl boundary layer equations was obtained nomenclature c mass concentration h duct height iteration number k turbulence model coefficients l characteristic length m velocity ratio n density ratio p pressure re reynolds number u l v r wall coordinate sc

perturbations of orthogonal polynomials with periodic recursion coefficients the results of denisov rakhmanov szeg shohat nevai and killip simon are extended from asymptotically constant orthogonal polynomials on the real line oprl and unit circle opuc to asymptotically periodic oprl and opuc the key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations

regular articlegeneralized strichartz inequalities for the wave equation we make a synthetic exposition of the generalized strichartz inequalities for the wave equation obtained in 6 together with the limiting cases recently obtained in 13 with as simple proofs as possible the proofs combine stationary phase estimates dyadic decompositions the hardy littlewood inequality or the holder inequality in time and abstract duality and interpolation arguments

the effects of freestream pressure gradient on a corner boundary layer the incompressible boundary layer in the corner formed by two intersecting perpendicular semi infinite planes is investigated the freestream flow aligned with the corner is of the form xn x repr

the orr sommerfeld equation on infinite intervals numerical and asymptotic methods have been developed the last several years to solve the orr sommerfeld os stability equation for boundary layers and other unbounded domain flows these are surveyed and some of the abstract mathematical questions they raise are mentioned there has been a conventional wisdom among fluid dynamicists that it has not been proved that the eigenvalues of the os equations are complete on an unbounded domain there is something to this since without the continuous spectrum which occurs for boundary layer flows the eigenvalues are not complete however much has been proved concerning the nature of the spectrum and the expansion properties of the generalized eigenfunctions the results of miklavcic and williams and of bakenko and herron form the core of the survey

kato type estimates for nls equation in a scalar field and unique solvability of nkgs system in energy space abstract we consider schrodinger equation in r 2 1 with nonlinear scalar potential the potentials are time independent or determined as solutions to inhomogeneous wave equations by constructing a modified propagator we derive kato type smoothing estimates for the nonlinear schrodinger nls equation with the help of these results we prove the unique solvability of the nonlinear klein gordon schrodinger nkgs system for all time in the energy space

long range scattering for the maxwell schrodinger system in the lorenz gauge without any restriction on the size of data abstract this paper concerns the scattering theory for the maxwell schrodinger ms system in the lorenz gauge or more precisely the existence of the modified wave operators for this system in r 3 1 space time we construct solutions to the ms system which behave as free maxwell and schrodinger waves with prescribed asymptotic states when t without any restriction on the size thereof since this system belongs to the borderline between the short range case and the long range case we need modification of phase for the schrodinger function

finite range perturbations of finite gap jacobi and cmv operators abstract necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range perturbation of a jacobi or cmv operator from a finite gap isospectral torus the special case of eventually periodic operators solves an open problem of simon 28 d 2 7 we also solve the inverse resonance problem it is shown that an operator is completely determined by the set of its eigenvalues and resonances and we provide necessary and sufficient conditions on their configuration for such an operator to exist

particle image velocimetry measurement of laminar boundary layer in a streamwise corner measurement of velocity profiles along a laminar boundary layer in a streamwise corner was carried out by using particle image velocimetry in contrast to conventional hot wire anemometry to make the measurement successful the laser light source for particle image velocimetry was placed at a far downstream station and a light sheet was emitted in parallel to the corner intersection line the platewas tilted at very small angles relative to the freestream to realize the laminar flow starting from the corner leading edge discussions on the characteristic features of the velocity profile in the bisector plane are given based on the measurement data it was found that the measured velocity profiles correspond to the blasius branch solution of the theoretical corner layer equations

an asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc the paper investigates high reynolds number stationary instabilities in the boundary layer on a rotating disc the investigation demonstrates that in addition to the inviscid mode found by gregory stuart walker phil trans r soc lond a 248 155 1955 at high reynolds numbers there is a stationary short wavelength mode this mode has its structure fixed by a balance between viscous and coriolis forces and cannot be described by an inviscid theory the asymptotic structure of the wavenumber and orientation of this mode is obtained and a similar analysis is given for the inviscid mode the expansion procedure provides the capacity of taking non parallel effects into account in a self consistent manner the inviscid solution of gregory et al is modified to take account of viscous effects the expansion procedure used is again capable of taking non parallel effects into account the results obtained suggest why the inviscid approach of gregory et al should give a good approximation to the experimentally measured orientation of the vortices the results also explain partly why the inviscid analysis should not give such a good approximation to the wavenumber of the vortices the asymptotic analysis of both modes provides a starting point for the corresponding nonlinear problems

a note on the matrix valued q d algorithm and matrix orthogonal polynomials on 0 1 and 0 in this note a matrix version of the q d algorithm is introduced it is shown that the algorithm may be used to obtain the coefficients of the recurrence relations for matrix orthogonal polynomials on the interval 0 and 0 1 from its moment generating functional the algorithm is illustrated by several examples which generalize classical orthogonal polynomials on the real line

orthogonal matrix polynomials and quadrature formulas we prove that the nodes of a quadrature formula for a matrix weight with the highest degree of precision must necessarily be the zeros of a certain orthonormal matrix polynomial with respect to the matrix weight and the quadrature coefficients are then the coefficients in the partial fraction decomposition of the ratio between the inverse of this orthonormal matrix polynomial and the associated polynomial of the second kind we also extend this result for quadrature formulas with degree of precision one unit smaller than the highest possible

similarity and stability of the laminar boundary layer in a streamwise corner the study of laminar viscous flow along the line of intersection of two solid surfaces at right angles is examined in its present state and outstanding differences between various experimental and theoretical results are analysed new experimental results are presented in which the stability of the corner boundary layer is examined in terms of the degree of streamwise similarity of its velocity profiles conclusive evidence is found that the layer does not exist in stable laminar form when the streamwise pressure gradient is zero and the reynolds number much above about 10 4 the new results also help to explain the differences between various experimental results and between theory and experiment which have characterized the corner boundary layer problem for several years by extrapolation an approximate prediction is obtained of what the velocity profile of the corner boundary layer would be in the limiting case of zero pressure gradient if the layer were stable in that state the predicted profile is compared with the results of current theories

pseudo canonical systems with rational weyl functions explicit formulas and applications abstract the paper extends earlier results of the authors for canonical systems with spectral functions of which the absolutely continuous part has a rational derivative to a class of differential systems with skew selfadjoint potentials the corresponding direct and inverse spectral problems are solved explicitly using state space methods from mathematical system theory applications to nonlinear integrable partial differential equations are included

the cauchy problem for the coupled maxwell schrodinger equations the cauchy problem for the coupled maxwell schrodinger equations in rd in the lorentz gauge is considered the viscosity method is used to establish local existence in one and two space dimensions global solutions are obtained

global existence and uniqueness of solutions to the maxwell schrodinger equations the time local and global well posedness for the maxwell schrodinger equations is considered in sobolev spaces in three spatial dimensions the strichartz estimates of koch and tzvetkov type are used for obtaining the solutions in the sobolev spaces of low regularities one of the main results is that the solutions exist time globally for large data

energy convergence for singular limits of zakharov type systems we prove existence and uniqueness of solutions to the klein gordon zakharov system in the energy space h1 l2 on some time interval which is uniform with respect to two large parameters c and these two parameters correspond to the plasma frequency and the sound speed in the simultaneous high frequency and subsonic limit we recover the nonlinear schrodinger system at the limit we are also able to say more when we take the limits separately

a connection between orthogonal polynomials on the unit circle and matrix orthogonal polynomials on the real line szego s procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on 1 1 is generalized to nonsymmetric measures it generates the so called semi orthogonal functions on the linear space of laurent polynomials and leads to a new orthogonality structure in the module this structure can be interpreted in terms of a 2 2 matrix measure on 1 1 and semi orthogonal functions provide the corresponding sequence of orthogonal matrix polynomials this gives a connection between orthogonal polynomials on the unit circle and certain classes of matrix orthogonal polynomials on 1 1 as an application the strong asymptotics of these matrix orthogonal polynomials is derived obtaining an explicit expression for the corresponding szego s matrix function

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

almost periodic schrodinger operators iii the absolutely continuous spectrum in one dimension we studyh d2 dx2 v x withv x limit periodic e g v x ancos x 2n with an we prove that for a genericv and for generican in the explicit example h is a cantor nowhere dense perfect set for a dense set the spectrum is both cantor and purely absolutely continuous and therefore purely recurrent absolutely continuous

the inverse periodic problem for hill s equation with a finite gap potential let h q d d q x be the hill s operator with a periodic potential q of period one consider the following inverse problem find all potentials q x with the same periodic spectrum as a given potential p x two explicit solutions are known for finite gap potentials its and matveev 6 give an explicit formula in terms of theta functions their solution was generalized by mckean and trubowitz lo to infinite gap potentials finkel et al 5 give a second formula which expresses q in terms of the base potential p the dirichlet eigenfunctions of p and the floquet solutions of p the formula involves no algebraic geometry in this paper we represent finite gap potentials q as rational functions of the base potential p and the derivatives ofp the representation makes use of the finkel isaacson trubowitz fit formula

a strong szegő theorem for jacobi matrices we use a classical result of golinskii and ibragimov to prove an analog of the strong szeg theorem for jacobi matrices on l 2 mathbb n in particular we consider the class of jacobi matrices with conditionally summable parameter sequences and find necessary and sufficient conditions on the spectral measure such that sum k n infty b k and sum k n infty a k 2 1 lie in l 2 1 the linearly weighted l 2 space