nonlinear fokker planck equations with reaction as gradient flows of the free energy abstract we interpret a class of nonlinear fokker planck equations with reaction as gradient flows over the space of radon measures equipped with the recently introduced hellinger kantorovich distance the driving entropy of the gradient flow is not assumed to be geodesically convex or semi convex we prove new generalized dissipation inequalities which allow us to control the relative entropy by its production we establish the entropic exponential convergence of the trajectories of the flow to the equilibrium along with other applications this result has an ecological interpretation as a trend to the ideal free distribution for a class of fitness driven models of population dynamics our existence theorem for weak solutions under mild assumptions on the nonlinearity is new even in the absence of the reaction term

multi time step domain decomposition and coupling methods for nonlinear parabolic problems abstract in this paper we propose and examine a multi time step algorithm using a feti based domain decomposition method for nonlinear parabolic problems the computational domain is divided into a set of smaller subdomains that may be integrated concurrently with their own time steps the continuity condition at the interface is ensured employing local lagrange multipliers the equation of continuity of primary unknowns at the interface is written only at the so called system time step the subdomain problems are coupled together by requiring the lagrange multipliers on the interface at the intermediate time steps to match a suitable interpolation of the values at the system time steps this allows each subdomain to be solved with its own time step the rigorous nonlinear stability is performed via the energy method several numerical examples will be solved to illustrate the overall performance of the proposed coupling method

hankel integral operators and isometric interpolants on the line abstract the problem of finding an m n continuous isometric matrix valued function with entries from the wiener algebra on the line and with prespecified fourier inverse transform on the half line is studied conditions for existence uniqueness and formulas for the solution of this problem are presented connections are made between the positive factorization indices of certain solutions to this problem and the dimensions of the kernels of hankel operators based on the prespecified data alluded to above the paper uses techniques and results developed in an earlier study of an interpolation problem on the circle the main theorems are in fact continuous analogues of the latter

some existence and nonexistence theorems for solutions of degenerate parabolic equations abstract the initial and boundary value problem for the degenerate parabolic equation v t v f v in the cylinder 0 r n bounded for a certain class of point functions satisfying v 0 e g v v m sign v is considered in the case that f v sign v c 1 v the equation has a global time solution the same is true for 1 provided the measure of is sufficiently small in the case that f v v is nondecreasing a condition is given on the initial state v x 0 which implies that the solution must blow up in finite time the existence of such initial states is discussed

lossless inverse scattering digital filters and estimation theory methods to construct rational solutions of the lossless inverse scattering lis problem for one port passive digital systems are described the first method is recursive and can be viewed as a generalization of the celebrated schur algorithm the second method is global and leads to a parametrization of what we call fundamental solutions from which all lis solutions may be constructed quite a few classical problems in estimation theory and network theory may be viewed as special cases of the lis problem with each fundamental solution there is a solution of a corresponding estimation problem leading to a prediction and a modeling filter for a given stochastic process

exponentially fitted runge kutta methods abstract exponentially fitted runge kutta methods with s stages are constructed which exactly integrate differential initial value problems whose solutions are linear combinations of functions of the form x j exp x x j exp x r or i r j 0 1 j max where 0 j max s 2 1 the lower bound being related to explicit methods the upper bound applicable for collocation methods explicit methods with s 2 3 4 belonging to that class are constructed for these methods a study of the local truncation error is made out of which follows a simple heuristic to estimate the value error and step length control is introduced based on richardson extrapolation ideas some numerical experiments show the efficiency of the introduced methods it is shown that the same techniques can be applied to construct implicit exponentially fitted runge kutta methods

homogenization of degenerate coupled fluid flows and heat transport through porous media we establish a homogenization result for a fully nonlinear degenerate parabolic system with critical growth arising from the heat and moisture flow through a partially saturated porous media existence of a global weak solution of the mesoscale problem is proven by means of a semidiscretization in time a priori estimates and passing to the limit from discrete approximations after that porous material exhibiting periodic spatial oscillations is considered and the two scale convergence as the oscillation period vanishes to a corresponding homogenized problem is rigorously proven

diffusivity versus absorption through the boundary for all 0 1 then we do expect to find that any solution becomes unbounded in finite time see 13 15 63 it is our goal to prove an analogous result for m f 1 for a 1 one can find that if v is a positive solution of

factorization and approximation problems for matrix functions the purpose of this paper is to develop a new approach to certain approximation and factorization problems for matrix valued functions the approach is based on studying properties of maximizing vectors of hankel operators with matrix valued symbols and on the solution of the so called recovery problem for unitary valued matrix functions in the case of scalar functions such problems were studied in detail in pk it turns out however that the case of matrix functions is considerably more complicated than the scalar case in this paper we solve the recovery problem with the help of hankel operators this solution also allows us to give a new approach to wiener hopf factorization problems and obtain some new results another application we consider here is the problem of finding a superoptimal analytic approximation to a matrix function on the unit circle we improve earlier results on hereditary properties of such approximations see py1 and on continuity properties of the operator of superoptimal approximation see py3 recall that for a bounded m x n matrix function b on the unit circle tf the hankel operator hp is defined on the hardy class h2 cn of cn valued functions by hdf padf f e h cn

local continuity and asymptotic behaviour of degenerate parabolic systems abstract we study the local holder continuity and the asymptotic behaviour of solution u u 1 u k of the degenerate system u t i m u m 1 u i for m 1 and i 1 k which describes the population densities of k species whose diffusions are determined by their total population density u u 1 u k for the local holder continuity we adopt the intrinsic scaling and iteration arguments of degiorgi moser and dibenedetto under some regularity conditions we also prove that the population density of i th species with the population m i converges in c s to the function m i m b m x t as t where b m is the barenblatt profile of the standard porous medium equation with l 1 mass m m 1 m k as a consequence of asymptotic behaviour it is shown that each density becomes a concave function after a finite time

boundedness of the gradient for a doubly nonlinear parabolic equation we prove the local boundedness of the gradient for positive solutions to a doubly nonlinear parabolic equation in the case when the standard lebesgue measure has been replaced by a doubling measure which supports a weak poincare inequality

a maximum entropy principle for contractive interpolants abstract in this paper a maximum entropy principle is established for a class of continuous contractive m n matrix valued functions g with preassigned fourier coefficients gj j for j 0 1 the function g in this class which achieves the maximum entropy is characterized in a number of different ways and its entropy is computed in terms of a hankel operator based on the prescribed matrices 0 1 a pair of seemingly new szego type formulas are obtained enroute and some applications to nevanlinna pick interpolation are indicated

variable stepsize chebyshev type methods for the integration of second order i v p s panovsky and richardson a family of implicit chebyshev methods for the numerical integration of second order differential equations j comput appl math 23 1988 35 51 presented a method based on chebyshev approximations for numerically solving the problem y f x y being the steplength constant coleman and booth analysis of a family of chebyshev methods for y f x y j comput appl math 44 1992 95 114 made an analysis of the above method and suggested the convenience to design a variable steplength implementation as far as we know this goal has not been achieved until now later on we extended the above method this journal 2003 and obtained a scheme for numerically solving the equation y 2gy g 2 w 2 f x y the question of how to extend these formulas to variable stepsize procedures is the primary topic of this paper

self improving property of the fast diffusion equation abstract we show that the gradient of the m power of a solution to a singular parabolic equation of porous medium type also known as fast diffusion equation satisfies a reverse holder inequality in suitable intrinsic cylinders relying on an intrinsic calderon zygmund covering argument we are able to prove the local higher integrability of such a gradient for m n 2 n 2 1 our estimates are satisfied for a general class of growth assumptions on the non linearity in this way we extend the theory for m 1 see 16 in the list of references to the singular case in particular an intrinsic metric that depends on the solution itself is introduced for the singular regime

on certain minimal entropy extensions appearing in dilation theory i abstract we consider certain natural isometric intertwining dilations which appear in the context of the commutant lifting theorem these results are based on the authors previous work on a strengthened version of the parrott theorem since our extensions are isometric or coisometric the minimize the classical entropy integral

dissipative chebyshev exponential fitted methods for numerical solution of second order differential equations a family of implicit methods based on intra step chebyshev interpolation has been developed to integrate oscillatory second order initial value problems of the form y t 2g y t g2 w2 y t f t y t the procedure integrates the homogeneous part exactly in the absence of round off errors the chebyshev approach uses stepsizes that are considerably larger than those typically used in runge kutta or multistep methods computational overheads are comparable to those incurred by high order conventional procedures chebyshev interpolation coupled with the exponential fitted nature of the method substantially reduces local errors global error propagation rates are also reduced making these procedures good candidates to be used in long term simulations of perturbed oscillatory systems with a dissipative term

spectral factorization of rectangular rational matrix functions with application to discrete wiener hopf equations the properties of a discrete wiener hopf equation are closely related to the factorization of the symbol of the equation we give a necessary and sufficient condition for existence of a canonical wiener hopf factorization of a possibly nonregular rational matrix function w relative to a contour which is a positively oriented boundary of a region in the finite complex plane the condition involves decomposition of the state space in a minimal realization of w and if it is satisfied we give explicit formulas for the factors the results are generalized by means of centered realizations to arbitrary rational matrix functions the proposed approach can be used to solve discrete wiener hopf equations whose symbols are rational matrix functions which admit canonical factorization relative to the unit circle

existence of weak solutions of doubly nonlinear parabolic equations abstract we deal with a cauchy dirichlet problem with homogeneous boundary conditions on the parabolic boundary of a space time cylinder for doubly nonlinear parabolic equations whose prototype is t u div u m 1 d u p 2 d u f with a non negative lebesgue function f on the right hand side where p 2 n n 2 and m 0 the central objective is to establish the existence of weak solutions under the optimal integrability assumption on the inhomogeneity f the constructed solution is obtained by a limit of approximations i e we use solutions of regularized cauchy dirichlet problems and pass to the limit to receive a solution for the original cauchy dirichlet problem

global solutions for some nonlinear parabolic equations with nonmonotonic peturbations publisher summary this chapter discusses the existence uniqueness and decay property of the solutions of two problems it also presents the sobolev s lemma and gagliardo nirenberg inequality

global and blow up solutions to a p laplacian equation with nonlocal source this paper deals with a p laplacian equation ut div u p 2 u uq x t dx with null dirichlet boundary conditions in a bounded domain rn where p 2 q 1 under appropriate hypotheses we establish local theory of the solution and obtain that the solution either exists globally or blows up in finite time

regularity for parabolic systems of uhlenbeck type with orlicz growth abstract we study the local regularity of p caloric functions or more generally of caloric functions in particular we study local solutions of non linear parabolic systems with homogeneous right hand side where the leading terms have uhlenbeck structure of orlicz type this paper closes the gap of 23 where liebermann proved that if the gradient of a solution is bounded it is holder continuous the crucial step is a novel local estimates for the gradient of the solutions which generalize and improve the pioneering estimates of dibenedetto and friedman 12 10 for the p laplace heat equation

riesz potentials and pointwise estimates of solutions to anisotropic porous medium equation abstract for an anisotropic porous medium equation with l 1 regular lower order terms we prove the local boundedness and continuity of weak solutions in terms of the linear riesz potential of the right hand side of equation

scheifele two step methods for perturbed oscillators two step methods specially adapted to the numerical integration of perturbed oscillators are obtained the formulation of the methods is based on a refinement of classical taylor expansions due to scheifele g scheifele on the numerical integration of perturbed linear oscillating systems z angew math phys 22 1971 186 210 the key property is that those algorithms are able to integrate exactly harmonic oscillators with frequency w the methods depend on a parameter email protected where h is the stepsize based on the b2 series theory of coleman j p coleman order conditions for a class of two step methods for y f x y ima j numer anal 23 2003 197 220 we derive the order conditions of this new type of method the linear stability and phase properties are examined the theory is illustrated with some fourth and fifth order explicit schemes numerical results carried out on an assortment of test problems such as the integration of the orbital motion of earth satellites show the relevance of the theory

holder estimates for nonlinear degenerate parabolic sytems on etablit des estimations de holder pour le gradient d espace u des solutions locales faibles des systemes paraboliques degeneres on etablit la continuite de holder des solutions non negatives d une equation parabolique degeneree

higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth abstract the aim of this paper is to derive the self improving property of integrability for the spatial gradient of solutions to degenerate parabolic obstacle problem with irregular obstacles and p x t nonstandard growth more precisely we prove that the spatial gradient of the solution is integrable to a larger power than the natural one determined by the structural assumptions on the involved differential operator

doubly nonlinear degenerate parabolic systems with coupled nonlinear boundary conditions in this paper we study the global existence and the global nonexistence of doubly nonlinear degenerate parabolic systems with nonlinear boundary conditions we first prove a local existence result by the regularization method next we construct a weak comparison principle then we discuss the large time behavior of solutions by using a modified upper and lower solution methods and constructing various upper and lower solutions necessary and sufficient conditions on the global existence of all positive weak solutions are obtained

homogeneous diffusion in ℝ with power like nonlinear diffusivity we study the nonnegative solutions of the initial value problem ut ur ux p 1ux x u x 0 l1 where p 0 r p 0 the local velocity of propagation of the solutions is identified as v vx vx p 1 where v cu with r p 1 p and c r p r p 1 is the nonlinear potential our main result is the a priori estimate vx vx p 1 x frac 1 2p r t

cauchy problem for fast diffusion equations with a gradient term we study the cauchy problem for fast diffusion equation with a gradient term of the form ut um duq where 0 0 and 0 0 however as q m the optimality of the stipulated assumptions is left open

unit canonical correlations between future and past on considere des processus arma stationnaires x t de rang complet et le cas ou il y a des fonctions lineaires du futur x t t 0 et du passe x t t 0 qui ont une correlation unite on montre que le nombre de paires de ce type lineairement independantes est le nombre de zeros du determinant des fonctions de transfert sur le cercle unite

explicit runge kutta nystro m methods with reduced phase errors for computing oscillating solutions we construct explicit runge kutta nystrom methods for the integration of first and second order differential equations having an oscillatory solution special attention is paid to the phase errors or dispersion of the dominant components in the numerical oscillations when these methods are applied to a linear homogeneous test model rk n methods are constructed which are dispersive of orders up to 10 whereas the algebraic order of accuracy is only 2 or 3 application of these methods to equations describing free and weakly forced oscillations and to semidiscretized hyperbolic equations reveals that the phase errors can significantly be reduced

weak solutions of coupled dual porosity flows in fractured rock mass and structured porous media abstract this paper deals with a fully nonlinear degenerate parabolic system with natural critical growths and under non linear boundary conditions such problems arise from the heat and water flow through a partially saturated fractured rock mass and structured porous media existence of a global weak solution of the problem on an arbitrary interval of time is proved by means of semidiscretization in time deriving suitable a priori estimates based on w 1 p regularity of the approximate solution and by passing to the limit from discrete approximations

controlling the error growth in long term numerical integration of perturbed oscillations in one or several frequencies in this paper we present a simple technique that allows us to limit the error growth in the long term numerical integration of perturbed multi dimensional oscillators while using highly efficient and accurate special multi step codes after laying down the theoretical basis of their behaviour we then illustrate them with some numerical examples including a case with non resonant frequencies seldom found in the related literature

holder estimates for parabolic p x t laplacian systems in this paper we establish the local holder continuity of the spatial gradient of weak solutions to the parabolic p x t laplacian system begin array lll partial t u rm div left a x t du p x t 2 du right 0 end array more precisely we prove that begin array lll du in c rm loc 0 alpha alpha 2 quad rm for some alpha in 0 1 end array provided p and a are holder continuous

the heat flow in nonlinear hodge theory we study the nonlinear hodge systemd 0 and 2 0 for an exterior form on a compact oriented riemannian manifold m where q is a given positive function the solutions are called harmonic forms they are the stationary points on cohomology classes of the functional e me 2 dm with e q q 2 the codifferential of a form is defined as 1 with 2 we evolve a given closed form 0 by the nonlinear heat flow system d for a time dependent exterior form x t on m this system is the differential of the normalized gradient flow u for e with 0 du under a technical assumption on the function 2 q q q we show that the nonlinear heat flow system d with initial condition 0 0 has a unique solution for all times which converges to a harmonic form in the cohomology class of 0 this yields a nonlinear hodge theorem that every cohomology class of m has a unique harmonic representative

doubly nonlinear parabolic equation with nonlinear boundary conditions this paper deals with the existence and nonexistence of global positive solutions of the doubly nonlinear parabolic equation with nonlinear boundary conditions necessary and sufficient conditions in order that all positive solutions exist globally are obtained by using the upper and lower solutions method

new explicit adapted numerov methods for second order oscillatory differential equations this paper is concerned with a novel class of explicit adapted numerov an methods for solving initial value problems of second order oscillatory differential equations of the form y email protected 2y f x y the scheme of the methods incorporate the special structure of the problem carried by the term w 2y so that they can integrate the linear equation y email protected 2y 0 without truncation error a new type of simplifying assumption is proposed on the linear operators related to the quadratures that lead to the an scheme a practical an method of order five and three an methods of order six are derived the phase and stability properties of the new methods are analyzed the results of numerical experiments show the robustness and competence of the new methods compared with some highly efficient codes in the recent literature

a parabolic system model for the formation of porous silicon existence uniqueness and stability in this paper a nonlinear weakly coupled parabolic system is constructed to model porous silicon formation the model considers physical and chemical factors such as charge carriers transport ions transport electrochemical reactions and material balance in order to prove the existence of a unique solution for the proposed parabolic model with zero neumann boundary we use a monotone method based on the upper and lower solutions the asymptotic stability of the steady state solution is also demonstrated and the behavior of this model is shown for specific cases where the analytical stationary solution is known finally a discussion of the results is carried out and we conclude that the proposed model reproduces important qualitative features which are observed experimentally

unitary interpolants factorization indices and infinite hankel block matrices abstract the existence uniqueness and construction of unitary n n matrix valued functions j j j in wiener like algebras on the circle with prescribed matrix fourier coefficients j j for j 0 are studied in particular if j then such an exists with j if and only if 0 1 where v denotes the infinite block hankel matrix j k v j k 0 1 acting in the sequence space l n 2 one of the main results is that the nonnegative factorization indices of every such are uniquely determined by the given data in terms of the dimensions of the kernels of i v v whereas the negative factorization indices are arbitrary it is also shown that there is a unique such if and only if the data forces all the factorization indices to be nonnegative and simple conditions for that and a formula for in terms of certain schmidt pairs of 0 are given the results depend upon a fine analysis of the structure of the kernels of i v v and of the one step extension problem of adamjan arov and krein funct anal appl 2 1968 1 18 isometric interpolants for the nonsquare case are also considered

factorization of all pass matrix functions we consider the factorization of an all pass matrix function e s into proper stable minimum phase factors this is achieved by applying the state space wiener hopf factorization theory of bart et al 1983 to the state space characterization of all pass matrix functions given by glover 1984 important connections are made between the properties of e s as a nehari extension its partial wiener hopf factorization indices and its hankel singular values

a novel family of p stable symmetric extended linear multistep methods for oscillators scheme of phase fitted and p stable symmetric extended linear multistep selm methods order conditions for modified linear multistep methods practical explicit and implicit selm methods eight step selm predictor corrector method of order ten numerical experiments showing the effectiveness of the selm methods a novel family of phase fitted and p stable symmetric extended linear multistep selm methods for solving initial value problems of second order oscillatory differential equations are developed selm methods are naturally p stable the order conditions are presented based on the harmonic fitting condition and order conditions new explicit selm methods of order two order four order six and order eight respectively and implicit selm methods of order four order six order eight and order ten respectively are derived and the local error for each method is obtained a new eight step selm predictor corrector pair of order ten is obtained numerical experiments are accompanied to show the high accuracy and competence of the new selm methods compared with some highly efficient symmetric multistep methods in the literature

hyperbolic phenomena in a strongly degenerate parabolic equation we consider the equation u t u u x x where 0 and where is a strictly increasing function with lim s we solve the associated cauchy problem for an increasing initial function and discuss to what extent the solution behaves qualitatively like solutions of the first order conservation law u t u x equations of this type arise for example in the theory of phase transitions where the corresponding free energy functional has a linear growth rate with respect to the gradient

frequency evaluation for exponentially fitted runge kutta methods this paper can be seen as a further investigation of the frequency evaluation techniques which are very recently proposed by ixaru et al for exponentially fitted multistep algorithms for first order ordinary differential equations odes the question answered was how the frequencies should be tuned in order to have a maximal benefit from exponentially fitted methods in a previous paper this frequency evaluation algorithm was successfully applied in a direct way to a second order exponentially fitted runge kutta efrk method of collocation type but such a direct application is impossible for higher order efrk methods to overcome this difficulty we develop an efficient extension of ixaru s frequency evaluation algorithm for the exponentially fitted radauiia method of third order it is an adaption of ixaru s algorithm in the sense that instead being applied globally it is applied stagewise numerical experiments illustrate the properties of the developed algorithm

phase fitted and amplification fitted two step hybrid methods for y f x y this paper provides a theoretical framework for a new type of phase fitted and amplification fitted two step hybrid ftsh methods which is introduced by the author in h van de vyver a phase fitted and amplification fitted explicit two step hybrid method for second order periodic initial value problems internat j modern phys c 17 2006 663 675 the methods constitute a modification of dissipative two step hybrid methods in the sense that two free parameters are added to eliminate the phase lag and the amplification error the methods are useful only when a good estimate of the frequency of the problem is known in advance the parameters depend on the product of the estimated frequency and the stepsize the algebraic order zero stability stability and phase properties are examined the theory is illustrated with sixth order explicit ftsh methods numerical results carried out on an assortment of test problems show the relevance of the theory

local calderon zygmund estimates for parabolic minimizers abstract we establish local calderon zygmund estimates for parabolic minimizers u to certain variational inequalities the formal corresponding parabolic partial differential equation would be t u div f z u d u u f z u d u div f p 2 f h with p 2 n n 2 however since we do not impose any condition on the existence of the derivative u f the pde above may not have any meaning at all for proving the calderon zygmund estimates we thus remain solely on the level of parabolic minimizers precisely for q p we prove that d u l loc q if u is locally holder continuous and f l loc q and h l loc q for a q depending on q

travelling waves in a convection diffusion equation abstract we study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1 d euclidean space the diffusion coefficient depends on the gradient in analogy with the p laplacian and may be degenerate unconditional stability is established with respect to initial data perturbations in l 1 r

structure of model uncertainty for a weakly corrupted plant in this paper we investigate the structure of the transfer function set which includes all the transfer functions deduced from the plant available information it is shown that when an upper bound of the plant transfer function s h sup spl infin norm has been supplied and the noise contaminating the time domain identification experiment data is not too significant such a transfer function set can be parameterized by a linear fractional transformation of two transfer function matrices one of them is a fixed transfer function matrix which is completely determined by the plant available information and the noise magnitude the other is a norm bounded structure fixed free transfer function matrix moreover it is shown that the problem of analytically obtaining the fixed complexity nominal model that best approximates this transfer function set is as difficult as the spl mu synthesis problem

holder zygmund estimates for degenerate parabolic systems abstract we consider energy solutions of the inhomogeneous parabolic p laplacian system t u div d u p 2 d u div g we show in the case p 2 that if the right hand side g is locally in l bmo then u is locally in l c 1 where c 1 is the 1 holder zygmund space this is the borderline case of the calderon zygmund theory we provide local quantitative estimates we also show that finer properties of g are conserved by du e g holder continuity moreover we prove a new decay for gradients of p caloric solutions for all 2 n n 2 p

a pseudo monotonicity adapted to doubly nonlinear elliptic parabolic equations the case where b is an unbounded linear operator was considered 1rst by bardos and br7 ezis 4 in the nonlinear case raviart 20 grange and mignot 13 dibenedetto and showalter 11 proved existence results assuming that a and b are at least monotone operators and b is compact alt and luckhaus 1 investigated the case of a non compact operator b assuming a is strongly monotone their work was extended more recently by ka cur 14 filo and ka cur 12 or zadrzy7 nska and zajb aczkowski 26 berm7 udez et al 7 devoted their work to the case where b is compact and strongly monotone and a is pseudo monotone we are interested in the same case excepted that b is no longer assumed to be strongly monotone thus the equation may

exponentially fitted explicit runge kutta nystrom methods exponentially fitted runge kutta nystrom efrkn methods for the numerical integration of second order ivps with oscillatory solutions are derived these methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions exp t exp t c or equivalently sin t cos t when i r explicit efrkn methods with two and three stages and algebraic orders 3 and 4 are constructed in addition a 4 3 embedded pair of explicit efrkn methods based on the fsal technique is obtained which permits to introduce an error and step length control with a small cost added some numerical experiments show the efficiency of our explicit efrkn methods when they are compared with other exponential fitting type codes proposed in the scientific literature

unitary interpolants and factorization indices of matrix functions abstract for an n n bounded matrix function we study unitary interpolants u i e unitary valued functions u such that u j j j u for which the toeplitz operator t u is fredholm we give a new approach based on superoptimal singular values and thematic factorizations we describe wiener hopf factorization indices of u in terms of superoptimal singular values of and thematic indices of f where f is a superoptimal approximation of by bounded analytic matrix functions the approach essentially relies on the notion of a monotone thematic factorization introduced in ap in the last section we discuss hereditary properties of unitary interpolants in particular for matrix functions of class h c we study unitary interpolants u of class qc