squared wavefunctions approach to periodic solutions of vector nonlinear schrodinger equation we develop a method of squared wavefunctions for the vector nonlinear schrodinger equation the squared wavefunctions of the octet representation of su 3 group give periodic solutions in terms of weierstrass elliptic functions specific limits of the obtained solution are the plane wave the soliton and cnoidal waves which were previously obtained using the ansatz of stationary motion

a transference principle for general groups and functional calculus on umd spaces let ia be the generator of a c 0 group u s s is an element of r on a banach space x and omega theta u the group type of u we prove a transference principle that allows to estimate parallel to f a parallel to in terms of the l p r x fourier multiplier norm of f i omega if x is a hilbert space this yields new proofs of important results of mcintosh and boyadzhiev de laubenfels if x is a umd space one obtains a bounded h 1 infinity calculus of a on horizontal strips related results for sectorial and parabola type operators follow finally it is proved that each generator of a cosine function on a umd space has bounded h infinity calculus on sectors

analytic solutions for a stefan problem with gibbs thomson correction we provide existence of a unique smooth solution for a class of oneand two phase stefan problems with gibbs thomson correction in arbitrary space dimensions in addition it is shown that the moving interface depends analytically on the temporal and spatial variables of crucial importance for the analysis is the property of maximal lpregularity for the linearized problem which is fully developed in this paper as well

integral criteria for a classification of solutions of linear differential equations are positive continuous function on the interval 0 co by solution we always mean a continuously differentiable function such that r t x t has a continuous derivative satisfying e when the func tion r is continuous but does not have a continuous derivative e can be interpreted as the first order system for the vector x y x rx 381

maximal regularity of the stokes operator in an exterior domain with moving boundary and application to the navier stokes equations consider the navier stokes system on an exterior domain with moving boundary and dirichlet boundary conditions in 2003 saal proved that the stokes operator in a domain with moving boundary has the property of maximal regularity provided that the operator is invertible hence his result can be applied if the domain is bounded or by adding a shift to the stokes operator if the domain is unbounded or the time interval is finite in this paper we will generalize his result to a result global in time if the reference domain is an exterior domain finally we will apply this result to the navier stokes equations to obtain a global in time existence theorem for small data

solutions and laws of conservation for coupled nonlinear schrodinger equations lie group analysis a set of two coupled nonlinear schr odinger equations is systematically analyzed by means of lie group technique the physical situations under consideration include nonlinear propagation in strongly birefringent and multimode optical fibers the most general lie group of point symmetries its lie algebra and a group of adjoint representations that correspond to the lie algebra are identified as a result a complete list of group invariant exact solutions is obtained and compared with earlier results the corresponding laws of conservation are derived employing noether s theorem

a geometrical characterization of banach spaces in which martingale difference sequences are unconditional we study banach space valued martingale transforms and in particular characterize those banach spaces for which the classical theorems of the real valued case carry over for example if b is a banach space and 1 0 and zeta x y leq x y text if x leq 1 leq y

global smooth solutions for a class of parabolic integrodifferential equations the existence and uniqueness of smooth global large data solutions of a class of quasilinear partial integrodifferential equations in one space and one time dimension are proved if the integral kernel behaves like t near t 0 o with a 2 3 an existence and regularity theorem for linear equations with variable coefficients that are related to this type is also proved in arbitrary space dimensions and with no restrictions for o

completely positive measures and feller semigroups on donne d abord une approche unifiee aux mesures completement positives qui jouent un role important dans la theorie des equations de volterra a travers le theoreme de bernstein puis on etudie la solution d une equation de transport liee par une mesure non negative qu elle definit a l equation qui caracterise les noyaux completement positifs on obtient une desorption complete des generateurs de semigroupes de feller induits par de telles mesures on donne une application aux equations de flux thermique lineaire dans des materiaux avec memoire

pointwise convergence for semigroups in vector valued l p spaces suppose that tt t 0 is a symmetric diffusion semigroup on l2 x and denote by widetilde t t t geq0 its tensor product extension to the bochner space l p x mathcal b where mathcal b belongs to a certain broad class of umd spaces we prove a vector valued version of the hopf dunford schwartz ergodic theorem and show that this extends to a maximal theorem for analytic continuations of widetilde t t t geq 0 on l p x mathcal b as an application we show that such continuations exhibit pointwise convergence

some results about complex powers of closed operators the aim of this paper is to give some further results about complex powers of operators a tool that the authors already employed in 2 and s to study some questions of operator theory our first result is essentially a completion of corollary 2 9 of 2 since it gives an estimate for the rate of decrease of a a at infinity when a is a positive operator with bounded imaginary powers we remark that the converse question i e the estimate of the imaginary powers in terms of the amplitude of the spectrum remains open next we prove a result of pertubation if we add to a positive operator

quasi periodic and periodic solutions for coupled nonlinear schrodinger equations of manakov type we consider travelling periodic and quasi periodic wave solutions in coupled nonlinear schrodinger equations in fibre optics these equations can be used to model single mode fibres with strong birefringence and two mode optical fibres recently these equations appear as a model describing pulse pulse interactions in wavelength division multiplexed channels of optical fibre transmission systems in some cases this model reduces to the integrable manakov system ims two phase quasi periodic solutions for the ims are given in terms of two dimensional kleinian functions the reduction of quasi periodic solutions to elliptic functions is discussed new solutions are found in terms of generalized hermite polynomials which are associated with two gap treibich verdier potentials

quasiperiodic and periodic solutions for vector nonlinear schrodinger equations we consider quasiperiodic and periodic cnoidal wave solutions of a set of n component vector nonlinear schrodinger equations vnlses in a biased photorefractive crystal with a drift mechanism of nonlinear response and kerr type nonlinearity n component nonlinear schrodinger equations can be used to model self trapped mutually incoherent wave packets these equations also model pulse pulse interactions in wavelength division multiplexed channels of optical fiber transmission systems quasiperiodic wave solutions for the vnlses in terms of n dimensional kleinian functions are presented periodic solutions in terms of hermite polynomials and generalized hermite polynomials for n component nonlinear schrodinger equations are found

spectral properties of operator logarithms we prove that the spectral height of the logarithm log a of a sectorial operator a equals the spectral angle of a this yields old results of pruss sohr and mcintosh as corollaries then we construct a sectorial operator a on a umd space having bounded imaginary powers such that the group type of a is s is strictly greater than

maximal lp regularity of parabolic problems with boundary dynamics of relaxation type in this paper we investigate vector valued parabolic initial boundary value problems of relaxation type typical examples for such boundary conditions are dynamic boundary conditions or linearized free boundary value problems like in the stefan problem we present a complete lp theory for such problems which is based on maximal regularity of certain model problems

functional calculus for semigroup generators via transference abstract in this article we apply a recently established transference principle in order to obtain the boundedness of certain functional calculi for semigroup generators in particular it is proved that if a generates a c 0 semigroup on a hilbert space then for each 0 the operator a has a bounded calculus for the closed ideal of bounded holomorphic functions on a sufficiently large right half plane that satisfy f z o e re z as z the bound of this calculus grows at most logarithmically as 0 as a consequence f a is a bounded operator for each holomorphic function f on a right half plane with polynomial decay at then we show that each semigroup generator has a so called strong m bounded calculus for all m n and that this property characterizes semigroup generators similar results are obtained if the underlying banach space is a umd space upon restriction to so called bounded semigroups the hilbert space results actually hold in general banach spaces

steckin s theorem transference and spectral decompositions abstract let y be a closed subspace of lp where is an arbitrary measure and 1 sup v n n 0 1 2 in particular every surjective isometry of y can be expressed in the form v eia where a is well bounded of type b i e a has a spectral diagonalization analogous to though weaker than that in the spectral theorem for self adjoint operators this result which fails if y is replaced by an arbitrary reflexive space is obtained by a blend of the transference method of coifman and weiss with steckin s theorem and a recent result in abstract operator theory it has the direct consequence that every uniformly bounded one parameter group on y is the fourier stieltjes transform of a projection valued mapping of r an additional consequence is that every hermitian equivalent operator on y is well bounded of type b in the setting of an arbitrary banach space x power bounded operators with a logarithm of the form ia with a well bounded of type b are studied it is shown that if u is such an operator on x then for every function f of bounded variation on the unit circle n tf n u n converges in the strong operator topology this result which formally is a transference by u of steckin s theorem makes it possible to calculate directly from u a normalized logarithm for u and the spectral projections for the logarithm

properties of the third order trinomial differential equations with delay argument abstract in this paper we study properties of the third order trinomial delay differential equation y t p t y t g t y t 0 by transforming this equation to binomial second third order differential equation employing suitable comparison theorems we establish new results on asymptotic behavior of solutions of the studied equation

solvability of a parabolic problem with non smooth data abstract we study a weak solvability of one linear parabolic problem with a summable right hand side and non smooth coefficients we consider this problem as appropriate operator equation in some banach space methods of the semigroups theory fractional powers of operators and integral operators for solvability of this operator equation are used

the group reduction for bounded cosine functions on umd spaces it is shown that if a generates a bounded cosine operator function on a umd space x t heni a 1 2 generates a bounded c0 group the proof uses a transference prin

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

a joint functional calculus for sectorial operators with commuting resolvents 1 introduction in this paper we are concerned with h 1 functional calculus in the sense of the construction introduced by mcintosh 23 and developed recently by cowling doust mcintosh and yagi 8 given v in 0 p we will use the notation sv fz 2 c n f0g jarg z j vg to denote the open sector of angle 2v around the half line r let x be a complex banach space given a linear operator a on x we denote by d a n a and r a the domain the kernel and the range of a respectively we also denote by j a the spectrum of a and by r a the resolvent set of a

generalized ornstein uhlenbeck semigroups littlewood paley stein inequalities and the p a meyer equivalence of norms abstract let be a nondegenerate gaussian measure on a hilbert space h for an arbitrary selfadjoint nonnegative operator a we consider the semigroup e tl e ta on l p where stands for the second quantization operator we provide an explicit characterization of the domains of i l m 2 in l p in terms of gaussian sobolev spaces thus extending the p a meyer result on equivalence of norms the main tools are the littlewood paley stein inequalities which are proved under minimal assumptions by a purely analytic method following e stein 1970 topics in harmonic analysis princeton univ press princeton nj

positivity and regularity of hyperbolic volterra equations in banach spaces soit x un espace de banach a un operateur lineaire clos non borne dans x a domaine dense d a a l loc 1 r f c j x avec j 0 t et on considere l equation de volterra de type scalaire u t f t 0 t a t au d t j on etudie l existence la positivite la regularite et la compacite ainsi que l integrabilite de l operateur resolvant s t defini par s t x x 0 t a t as xd t 0 x d a pour deux classes particulieres de noyaux a et d operateurs a

analysis of a galerkin approach applied to a system of coupled schrodinger equations abstract we study error and convergence rate of a fully discrete fourier galerkin scheme to approximate the solutions of a system consisting of two coupled cubic schrodinger equations with cross modulation which is a model for the propagation of a nonlinear pulse in a linearly birefringent kerr optical fiber we also establish a result on existence and uniqueness of a solution of the corresponding initial value problem

existence of analytic solutions for the classical stefan problem we prove that under mild regularity assumptions on the initial data the two phase classical stefan problem admits a unique solution that is analytic in space and time

abstract lp estimates for the cauchy problem with applications to the navier stokes equations in exterior domains abstract we apply an abstract perturbation theorem to derive global in time lq estimates for the cauchy problem and lq ls estimates for the nonstationary stokes equations in exterior domains this will be applied to obtain various new global in time estimates for weak solutions of the navier stokes equations

on the regularity of a generalized diffusion problem arising in population dynamics set in a cylindrical domain abstract in this paper we consider a generalized diffusion problem arising in population dynamics to this end we study a fourth order operational equation of elliptic type with various boundary conditions we show existence uniqueness and regularity of a classical solution on a cylindrical domain under some necessary and sufficient conditions on the data this elliptic problem is solved in l p a b x p 1 where a b r and x is a umd banach space our techniques use essentially the functional calculus and the semigroup theory

strong solutions of the navier stokes equations for a compressible fluid of allen cahn type in this work we study the navier stokes allen cahn system a combination of the compressible navier stokes equations with an allen cahn phase field description this model describes two phase patterns in a flowing liquid including phase transformations our purpose is to show the existence and uniqueness of local strong solutions for arbitrary initial data part of the proof is based on methods used in a companion paper which investigated the compressible navier stokes equations

transference principles for semigroups and a theorem of peller a general approach to transference principles for discrete and continuous operator semi groups is described this allows one to recover the classical transference results of calderon coifman and weiss and of berkson gillespie and muhly and the more recent one of the author the method is applied to derive a new transference principle for discrete and continuous operator semigroups that need not be groups as an application functional calculus estimates for bounded operators with at most polynomially growing powers are derived leading to a new proof of classical results by peller from 1982 the method allows for a generalization of his results away from hilbert spaces to lp spaces and involving the concept of boundedness to general banach spaces analogous results for strongly continuous one parameter semi groups are presented as well finally an application is given to singular integrals for one parameter semigroups

the full positive flows of manakov hierarchy hamiltonian structures and conservation laws based on four sets of lenard recursion sequences and zero curvature equation we derive the full positive flows of the manakov hierarchy associated with a 3x3 matrix spectral problem from which some new nonlinear evolution equations are proposed with the help of the darboux transformation soliton solutions of two new nonlinear evolution equations in the manakov hierarchy are constructed as two special reductions the full positive flows of the coupled modified korteweg de vries hierarchy and the sasa satsuma hierarchy are deduced in which some new nonlinear evolution equations are included and then we construct the hamiltonian structures of the manakov hierarchy and infinite conservation laws of several nonlinear evolution equations

domains of fractional powers of the stokes operator in lr spaces soit d un domaine borne de r n n 2 a frontiere lisse s soit 1 r et soit x r la fermeture dans l r d n de tous les champs vectoriels solenoidaux lisses a support compact dans d soit w r m d l espace de sobolev d ordre m et soit le laplacien on considere l operateur de stokes a r p r de domaine d a r w w r 2 d n w 5 0 mx 2 soit a un nombre reel positif pour chaque positif il y a une constante ce a telle que a r z ce a exp im z pour tout z satisfaisant a rez 0 ou a r z est la norme operateur de a r z

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

stability properties of stochastic maximal l p regularity in this paper we consider lp regularity estimates for solutions to stochastic evolution equations which is called stochastic maximal lp regularity our aim is to find a theory which is analogously to dore s theory for deterministic evolution equations he has shown that maximal lp regularity is independent of the length of the time interval implies analyticity and exponential stability of the semigroup is stable under perturbation and many more properties we show that the stochastic versions of these results hold

global properties of generalized ornstein uhlenbeck operators on lp rn rn with more than linearly growing coefficients we show that the realization ap of the elliptic operator au div q u f u vu in lp rn rn p 1 generates a strongly continuous semigroup and we determine its domain d ap u w2 p rn rn f u vu lp rn rn if 1 p the diffusion coefficients q qij are uniformly elliptic and bounded together with their first order derivatives the drift coefficients f can grow as x log x and v can grow logarithmically our approach relies on the monniaux pruss theorem on the sum of noncommuting operators we also prove lp lq estimates and under somewhat stronger assumptions we establish pointwise gradient estimates and smoothing of the semigroup in the spaces w p rn rn 0 1 where 1 p

positive solutions of functional differential equations with singular nonlinear terms soit p i a 0 0 i n des fonctions continues on definit les operateurs differentiels l i 0 i n par l 0 y t y t p 0 t l i y t 1 p i t dl i 1 y t dt 1 i n et on considere les equations l n y t f t y g t 0 l n y t f t y g t 0 ou f a 0 0 et g a 0 sont des fonctions continues et lim t g t on etudie la structure des solutions de ces equations definies et positives au voisinage de l infini

oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations the equation to be considered iswhere pi t 0 i n and q t are continuous and positive on some half line a it is known that always has strictly monotone nonoscillatory solutions defined on a so that of particular interest is the extreme situation in which such strictly monotone solutions are the only possible nonoscillatory solutions of in this paper sufficient conditions are given for this situation to hold for the structure of the solution space of is also studied

dynamical stability of non constant equilibria for the compressible navier stokes equations in eulerian coordinates in this paper we establish global existence and uniqueness of strong solutions to the non isothermal compressible navier stokes equations in bounded domains the initial data have to be near equilibria that may be non constant due to considering large external forces we are able to show exponential stability of equilibria in the phase space and above all to study the problem in eulerian coordinates the latter seems to be a novelty since in works by other authors global strong lp solutions have been investigated only in lagrangian coordinates eulerian coordinates are even declared as impossible to deal with the proof is based on a careful derivation and study of the associated linear problem