towards a matrix theory for unbounded operator matrices sur l espace produit r l 2 r on considere l operateur 7b a a 0 ou d d dx est defini sur d a w 1 r 0 est la mesure de dirac en 0 c l 2 r est un operateur de r dans l 2 r et 7b a a un domaine d 7b a r w 1 r on introduit une fonction caracteristique non commutative donnant une facon efficace pour calculer le spectre de 7b a on obtient des resultats sur la generation de semi groupes par des matrices operateur

semi groupes sous markoviens engendres par des operateurs matriciels we characterize generators of sub markovian semigroups onlp by a version of kato s inequality this will be used to show under precise assumptions that the semigroup generated by a matrix operatora aij 1 i j n on lp n is sub markovian if and only if the semigroup generated by the sum of each rowai1 ain 1 i n is sub markovian the corresponding result on c0 x n characterizes dissipative operator matrices

multivariable extremum seeking for pde dynamic systems in this article we address the design and analysis of multivariable newton based extremum seeking es for static locally quadratic maps subject to actuation dynamics governed by diffusion partial differential equations pdes multi input systems with distinct diffusion coefficients in each individual input channel are dealt with the phase compensation of the dither signals is handled as a trajectory generation problem and the inclusion of a multivariable diffusion feedback controller with a perturbation based averaging based estimate of the hessian s inverse allow to obtain local exponential convergence results to a small neighborhood of the optimal point the stability analysis is carried out using backstepping transformation and averaging in infinite dimensions capturing the infinite dimensional state due the diffusion pdes in addition the generalization of the results for different classes of parabolic reaction advection diffusion pdes wave equations and or first order hyperbolic transport dominated pdes is also discussed as for ordinary differential equations case the proposed newton approach removes the dependence of the algorithm s convergence rate on the unknown hessian of the nonlinear map to be optimized being user assignable unlike the gradient algorithm a numerical example illustrates the performance of our multivariable es for compensating pde based systems

amplitude and kinematic corrections of migrated images for nonunitary imaging operators obtaining migrated images with meaningful amplitudes is a challenging problem when the migration operator is not unitary one possible solution to this problem is iterative inversion however inversion is an expensive process that can be rather difficult to apply especially with 3d data in this paper i propose estimating migrated images similar to the least squares inverse images by approximating the inverse hessian thus avoiding the need for iterative inversion the inverse hessian is approximated with a bank of nonstationary matching filters these filters are not exact impulse responses and are limited in their ability to mimic the full effects of least squares inversion tests on two data sets show that this filtering approach gives results similar to iterative least squares inversion at a lower cost this technique is flexible enough to be applied to images migrated from zero offset or angle domain common image point gathers

zeros of the partition function for a continuum system at first order transitions we extend the circle theorem on the zeros of the partition function to a continuum system we also calculate the exact zeros of the partition function for a finite system where the probability distribution for the order parameter is given by two asymmetric gaussian peaks for the temperature driven first order transition in the thermodynamic limit the locus and the angular density of zeros are given by r mathit e mathrm ensuremath delta mathit c 2 mathit l mathrm ensuremath theta 2 and 2 ensuremath pi g ensuremath theta l 1 3 2 ensuremath delta c l 2 mathrm ensuremath theta 2 respectively in the complex z ensuremath equiv mathit re mathit i mathrm ensuremath theta plane where l is the reduced latent heat ensuremath delta c is the discontinuity in the reduced specific heat and z exp 1 mathit t mathit c t textcopyright 1996 the american physical society

matrix methods for wave equations in analogy to a characterisation of operator matrices generating c0 semigroups due to r nagel 13 we give conditions on its entries in order that a 2 2 operator matrix generates a cosine operator function we apply this to systems of wave equations to second order initial boundary value problems and to overdamped wave equations

complete second order linear differential operator equations in hilbert space and applications in hydrodynamics we study the cauchy problem for a complete second order linear differential operator equation in a hilbert space h of the form d 2 u dt 2 f ik du dt bu f u 0 u 0 u 1 0 u 1 problems of this kind arise e g in hydrodynamics where the coefficients f k and b are unbounded selfadjoint operators it is assumed that f is the dominating operator in the cauchy problem above i e d f d b d f d k we also suppose that f and b are bounded from below but the operator coefficients are not assumed to commute the main results concern the existence of strong solutions to the stated cauchy problem and applications of these results to the cauchy problem associated with small motions of some hydrodynamical systems

eventual norm continuity for neutral semigroups on banach spaces in this paper we prove under suitable hypotheses eventually norm continuity and compactness of the solution semigroups of certain neutral differential equations in banach spaces our approach is based on a general perturbation theorem obtained from closed loop systems of infinite dimensional control systems with unbounded control and observation operators in fact the solution semigroup can be viewed as the semigroup of an appropriate closed loop system in product state spaces

wellposedness and wave propagation for a class of integrodifferential equations in banach space in recent years there has been an increasing interest in the mathematical treatment of problems which originate in the theory of viscoelastic materials in such problems the constitutive relations for these materials incorporate the history of the strain or the strain rate and in the linear theory lead to linear volterra integrodifferential equations with infinite memory in a banach space x the purpose of this paper is to examine the problems of wellposedness and wave propagation for one such equation in particular we are concerned with equations of the form x t 4 x r j f t s x s ds al

modeling of a constant q methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique linear anelastic phenomena in wave propagation problems can be well modeled through a viscoelastic mechanical model consisting of standard linear solids in this paper we present a method for modeling of constant q as a function of frequency based on an explicit closed formula for calculation of the parameter fields several standard linear solids connected in parallel can be tuned through a single parameter to yield an excellent constant q approximation the proposed method enables substantial savings in computations and memory requirements experiments show that the new method also yields higher accuracy in the modeling of q than e g the pade approximant method

least squares migration data domain versus image domain using point spread functions abstract conventional amplitude inversion assumes that the migrated image preserves relative amplitude information however illumination effects caused by complex geologic settings undersampled acquisition geometry and limited recording aperture pose a challenge to even the most advanced imaging algorithms in addition standard depth migration images can suffer from lack of resolution caused by wavelet stretch attenuation and suboptimal deghosting least squares migration lsm can mitigate many of these problems and produce better resolved migration images suitable for avo inversion however whether formulated in the data domain or the image domain lsm is an inversion algorithm and is sensitive to inaccuracies in the source wavelet velocity model data preprocessing and the propagator used practical considerations to mitigate these problems under nonideal conditions and cost reduction strategies differ between the data and image domain formulations the relative merits of each approach are ev

a variational principle for block operator matrices and its application to the angular part of the dirac operator in curved spacetime abstract the operator associated to the angular part of the dirac equation in the kerr newman background metric is a block operator matrix with bounded diagonal and unbounded off diagonal entries the aim of this paper is to establish a variational principle for block operator matrices of this type and to derive thereof upper and lower bounds for the angular operator mentioned above in the last section these analytic bounds are compared with numerical values from the literature

asymptotic stability of the solution of the m mb 1 queueing model by using positive c 0 semigroup theory we study the asymptotic stability of the solution of a bulk queueing model m m b 1

a mixed discrete continuous fragmentation model abstract motivated by the occurrence of shattering mass loss observed in purely continuous fragmentation models this work concerns the development and the mathematical analysis of a new class of hybrid discrete continuous fragmentation models once established the model which takes the form of an integro differential equation coupled with a system of ordinary differential equations is subjected to a rigorous mathematical analysis using the theory and methods of operator semigroups and their generators most notably by applying the theory relating to the kato voigt perturbation theorem honest substochastic semigroups and operator matrices the existence of a unique differentiable solution to the model is established this solution is also shown to preserve nonnegativity and conserve mass

on nonautonomous functional differential equations abstract in this paper we prove a theorem on boundary perturbation of nonautonomous cauchy problems and then apply this result to show the existence and uniqueness of classical solutions of the nonautonomous banach space valued functional differential equation formula

elastic least squares reverse time migration via linearized elastic full waveform inversion with pseudo hessian preconditioning abstracttime domain elastic least squares reverse time migration lsrtm is formulated as a linearized elastic full waveform inversion problem the elastic born approximation and elastic reverse time migration rtm operators are derived from the time domain continuous adjoint state method our approach defines p and s wave impedance perturbations as unknown elastic images our algorithm is obtained using continuous functional analysis in which the problem is discretized at the final stage optimize before discretize approach the discretized numerical versions of the elastic born operator and its adjoint elastic rtm operator pass the dot product test the conjugate gradient least squares method is used to solve the least squares migration quadratic optimization problem in other words the hessian operator for elastic lsrtm is implicitly inverted via a matrix free algorithm that only requires the action of forward and adjoint operators on vectors the diagonal of the pseudo hessian operator is used t

spectral enclosures for a class of block operator matrices abstract we prove new spectral enclosures for the non real spectrum of a class of 2 2 block operator matrices with self adjoint operators a and d on the diagonal and operators b and b as off diagonal entries one of our main results resembles gershgorin s circle theorem the enclosures are applied to j frame operators

polynomial operator matrices as semigroup generators the 2 2 case on considere des systemes d equations d evolution non lineaires ecrits sous la forme u t au t ou u est une fonction a valeurs dans un espace produit e n et a a ij n m est une matrice dont les a ij sont des operateurs lineaires sur e on etudie le cas ou les a ij sont des polynomes p ij a par rapport a un seul operateur a sur e et on se restreint au cas des matrices 2 2

the spectrum of unbounded operator matrices with non diagonal domain abstract systems of linear evolution equations involving non diagonal boundary conditions yield operator matrices having non diagonal domains in products of banach spaces we show how to compute the spectrum of these matrices by using virtual matrix elements and characteristic operator functions

global existence for semilinear parabolic systems on etudie des problemes aux valeurs limites et initiales paraboliques semilineaires de la forme u t a t u f t x u du d 2m 1 u dans t 0 b t u 0 sur t 0 u t 0 u 0 sur ou est un domaine de r n

on the spectrum of evolution operators generated by hyperbolic systems abstract we prove that the asymptotic behavior of semigroups generated by mixed initial value problems for hyperbolic systems in one space variable is determined by the zeroes of the characteristic equation the proof is based on the following reduction principle we construct a reduced system which is much simpler than the given one such that the difference of the semigroups is a compact operator the construction of the reduced system is presented in the non autonomous case because it has implifications in the study of systems which are time periodic

matrices of operators and regularized semigroups where p is a matr ix of polynomials in n variables and ia1 ia is a family of c o m m u t i n g generators of bounded linear strongly cont inuous groups of operators intuitively one wants to take the exponent ia l of the matr ix of opera to r s p a since the spec t rum of ak is real for all k this means we want the complex matr ix pi j x to be contained in a left half plane in some sense for all x in r the strongest sense is to have the numerical range of the complex matr ix conta ined in a half plane r e z 0 xer a sense that is easier to calculate or at least estimate is to have the spectrum of p d x conta ined in a left half plane for all x r the system 1 1 is then said to be petrowsky correct see 9 the intuit ion we just described is not quite true in general wi thout some