polynomial bound on the number of scattering poles on montre que dans la diffusion par un potentiel infiniment differentiable a support compact les poles de l operateur de diffusion sont a distribution polynomiale

c α preserving operators on separable banach spaces abstract let t be a bounded linear operator from a separable banach space x to a banach space y a necessary and sufficient condition on t for the existence of a subspace z of x such that z is isomorphic to c and the restriction of t to z is an isomorphism is given the special case where x is the disc algebra is then considered and results similar to those previously obtained by the author for c k spaces are obtained for the disc algebra finally some additional results of the same type are proved for subspaces of c k with small annihilator

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

self controlled case series method with smooth age effect the self controlled case series method commonly used to investigate potential associations between vaccines and adverse events requires information on cases only and automatically controls all age independent multiplicative confounders while allowing for an age dependent baseline incidence in the parametric version of the method we modelled the age specific relative incidence by using a piecewise constant function whereas in the semiparametric version we left it unspecified however mis specification of age groups in the parametric version can lead to biassed estimates of exposure effect and the semiparametric approach runs into computational problems when the number of cases in the study is moderately large we thus propose to use a penalized likelihood approach where the age effect is modelled using splines we use a linear combination of cubic m splines to approximate the age specific relative incidence and integrated splines for the cumulative relative incidence we conducted a simulation study to evaluate the performance of the new approach and its efficiency relative to the parametric and semiparametric approaches results show that the new approach performs equivalently to the existing methods when the sample size is small and works well for large data sets we applied the new spline based approach to data on febrile convulsions and paediatric vaccines copyright 2013 john wiley sons ltd

stability for the multifrequency inverse medium problem abstract the solution of a multi frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies in this paper rigorous stability estimates are derived when the frequency takes value in a bounded interval it is showed that the ill posedness of the inverse medium problem decreases as the width of the frequency interval becomes larger more precisely under certain regularity assumptions on the refractive index the estimates indicate that the power in holder stability is an increasing function of the largest value in the frequency band finally a lipschitz stability estimate is obtained for the observable part of the medium function defined through a truncated trace formula

preserving operators on spaces let a c k x be a bounded linear operator where if is a compact hausdorff space and x is a separable banach space sufficient conditions are given for a to be an isomorphism into when restricted to a subspace y of c k such that y is isometrically isomorphic to a space c a of continuous functions on the space of ordinal numbers less than or equal to the countable ordinal a 1 for a compact hausdorff space k c k will denote the banach space of continuous real valued functions on k with the supremum norm the greek letters a s and y will be reserved for countable ordinal numbers we consider the set 0 a y 0 x 0 for each countable ordinal a we will define a family pa x b of open subsets g and associated measures ju g g b let p0 x b g jttg g is an open set in k ixg g b and g g x if a s 1 then pa x b g nc g jiig g p0 x b and there is a disjoint sequence g of open subsets of g and associated measures xg such that g ftg g ps x b ju gn jug and ung c g if a is a limit ordinal then x b g xg g p0 x b there is a disjoint sequence of open subsets gn of g with associated measures xg such that fic nc ung c g and g jug g pa x b where an a the notation a a means that a is an increasing sequence of ordinals with a sup an a simple example illustrating the sets pa x b is contained in 4 received by the editors march 20 1979 and in revised form july 30 1981 1980 mathematics subject classification primary 46e15 research on this paper was partially supported by the national science foundation grant number mcs 77 01690 1982 american mathematical society o0o2 9939 82 oo0o o726 so5 oo

pseudospectra of semiclassical pseudo differential operators the pseudo spectra or spectral instability of non selfadjoint operators is a topic of current interest in applied mathematics for example in computational fluid dynamics it affects the study of the stability of laminar flows in fact even for the most basic flows the computations entirely fails to predict what is observed in the experiments the explanation is that for non normal operators the resolvent could be very large far away from the spectrum which makes computation of the eigenvalues impossible the occurence of false eigenvalues is due to the existence of quasi modes i e approximate local solutions to the eigenvalue problem the quasi modes appear since the nirenberg treves condition psi is not satisfied for topological reasons less

distribution of poles for scattering on the real line abstract the density of scattering poles is shown to be proportional to the length of the convex hull of the support of the potential in the case of a potential with finite singularities at the endpoints of the support asymptotic formulae for the poles are given while in the c 0 case an example of a potential with infinitely many scattering poles on i r is constructed the scattering amplitude of a compactly supported potential is also characterized

spline based self controlled case series method the self controlled case series sccs method is an alternative to study designs such as cohort and case control methods and is used to investigate potential associations between the timing of vaccine or other drug exposures and adverse events it requires information only on cases individuals who have experienced the adverse event at least once and automatically controls all fixed confounding variables that could modify the true association between exposure and adverse event time varying confounders such as age on the other hand are not automatically controlled and must be allowed for explicitly the original sccs method used step functions to represent risk periods windows of exposed time and age effects hence exposure risk periods and or age groups have to be prespecified a priori but a poor choice of group boundaries may lead to biased estimates in this paper we propose a nonparametric sccs method in which both age and exposure effects are represented by spline functions at the same time to avoid a numerical integration of the product of these two spline functions in the likelihood function of the sccs method we defined the first second and third integrals of i splines based on the definition of integrals of m splines simulation studies showed that the new method performs well this new method is applied to data on pediatric vaccines copyright 2017 john wiley sons ltd

reconstruction of a potential on the line that is a priori known on the half line in this paper the authors study the inverse schrodinger scattering on the real line a method is given that allows unique reconstruction of a potential that is a priori known on the half line from the knowledge of the reflection coefficient and the bound state energies in particular no information on the forming constants is required the method is based on an appropriate trace formula and on the solution of the nonlinear ordinary differential equation that is obtained when the potential is replaced by its trace formula in the schrodinger equation the deift trubowitz approach to inverse scattering is followed the main new point is the way in which bound states are treated in addition to its mathematical interest the case when the potential is a priori known on the half line is particularly interesting in many applications one can consider for example a potential that has compact support or that it is zero on a half line

operators on c k spaces preserving copies of schreier spaces it is proved that an operator t c k x k compact metrizable x a separable banach space for which the e szlenk index of t bx is greater than or equal to 1 is an isomorphism on a subspace of c k isomorphic to x the schreier space of order as a corollary one obtains that a complemented subspace of c k with szlenk index equal to 1 contains a subspace isomorphic to x

a penalized likelihood approach for arbitrarily censored and truncated data application to age specific incidence of dementia the cos model is the model of choice when analyzing survival data presenting only right censoring and left truncation there is a need for methods that can accommodate more complex observation schemes involving general censoring and truncation in addition it is important in many epidemiological applications to have a smooth estimate of the hazard function we show that the penalized likelihood approach gives a solution to these problems the solution of the maximum of the penalized likelihood is approximated on a basis of splines the smoothing parameter is estimated using approximate cross validation confidence bands can be given a simulation study shows that this approach gives better results than the smoothed nelson aalen estimator we apply this method to the analysis of data from a large cohort study on cerebral aging the age specific incidence of dementia is estimated and risk factors of dementia studied

inverse schro dinger scattering on the line with partial knowledge of the potential the one dimensional schrodinger equation is considered when the potential and its first moment are absolutely integrable the potential is uniquely constructed in terms of the scattering data consisting of the reflection coefficient from the right left and the knowledge of the potential on the right left half line of the real axis hence neither the bound state energies nor the bound state norming constants are needed to determine the potential and in fact these are uniquely determined by the scattering data an explicit example is provided also considered are two inverse scattering problems for a generalized schrodinger equation with two potentials when the potential to be recovered is partially known

sum rules for jacobi matrices and their applications to spectral theory we discuss the proof of and systematic application of case s sum rules for jacobi matrices of special interest is a linear combination of two of his sum rules which has strictly positive terms among our results are a complete classification of the spectral measures of all jacobi matrices j for which j j 0 is hilbert schmidt and a proof of nevai s conjecture that the szego condition holds if j j 0 is trace class

on the resonances and eigenvalues for a 1d half crystal with localised impurity we consider the schrdinger operator h on the half line with a periodic potential p plus a compactly supported potential q for generic p its essential spectrum has an infinite sequence of open gaps we determine the asymptotics of the resonance counting function and show that for sufficiently high energy each non degenerate gap contains exactly one eigenvalue or antibound state giving asymptotics for their positions conversely for any potential q and for any sequences n 0 1 and xn 0 there exists a potential p such that xn is the length of the n th gap n and h has exactly n eigenvalues and 1 n antibound state in each high energy gap moreover we show that between any two eigenvalues in a gap there is an odd number of antibound states and hence deduce an asymptotic lower bound on the number of antibound states in an adiabatic limit

distribution of scattering resonances for generic schrodinger operators abstract let v be the schrodinger operator acting on l 2 r d c with d 3 odd here v is a bounded real or complex valued function vanishing outside the closed ball of center 0 and radius a if v belongs to the class m a of potentials introduced by christiansen we show that when r the resonances of v scaled down by the factor r are asymptotically distributed with respect to an explicit probability distribution on the lower unit half disc of the complex plane the rate of convergence is also considered for subclasses of potentials

painleve formulas of the limiting distributions for nonnull complex sample covariance matrices in a recent study of large non null sample covariance matrices a new sequence of functions gener alizing the gue tracy widom distribution of random matrix theory was obtained this paper derives painleve formulas of these functions and use them to prove that they are indeed distribution functions applications of these new distribution functions to last passage percolation queues in tandem and to tally asymmetric simple exclusion process are also discussed as a part of the proof a representation of orthogonal polynomials on the unit circle in terms of an operator on a discrete set is presented

inverse problems for selfadjoint schrodinger operators on the half line with compactly supported potentials for a selfadjoint schrodinger operator on the half line with a real valued integrable and compactly supported potential it is investigated whether the boundary parameter at the origin and the potential can uniquely be determined by the scattering matrix or by the absolute value of the jost function known at positive energies without having the bound state information it is proved that except in one special case where the scattering matrix has no bound states and its value is 1 at zero energy the determination by the scattering matrix is unique in the special case it is shown that there are exactly two distinct sets consisting of a potential and a boundary parameter yielding the same scattering matrix and a characterization of the nonuniqueness is provided a reconstruction from the scattering matrix is outlined yielding all the corresponding potentials and boundary parameters the concept of eligible resonances is introduced and such resonances correspond to real energy resonances that can b

asymptotic number of scattering resonances for generic schrodinger operators let v be the schrodinger operator acting on l 2 mathbb r d mathbb c with d geq 3 odd here v is a bounded real or complex function vanishing outside the closed ball of center 0 and of radius a let n v r denote the number of resonances of v with modulus r we show that if the potential v is generic in a sense of pluripotential theory then n v r c d a dr d o r d 3 over 16 epsilon quad mbox as r to infty for any e 0 where c d is a dimensional constant

bound states and inverse scattering for the schrodinger equation in one dimension the one dimensional schrodinger equation is considered when the potential and its first moment are absolutely integrable when the potential has support contained on the left right half line it is uniquely constructed by using only the reflection coefficient from the right left the bound state norming constants determine whether the potential has support contained on a half line or on the full line the bound state energies and the unique set of norming constants yielding the potential with support contained on the left right half line are completely determined by the reflection coefficient from the right left an explicit example is provided

self controlled case series analysis with event dependent observation periods the self controlled case series method may be used to study the association between a time varying exposure and a health event it is based only on cases and it controls for fixed confounders exposure and event histories are collected for each case over a predefined observation period the method requires that observation periods should be independent of event times this requirement is violated when events increase the mortality rate since censoring of the observation periods is then event dependent in this article the case series method for rare nonrecurrent events is extended to remove this independence assumption thus introducing an additional term in the likelihood that depends on the censoring process in order to remain within the case series framework in which only cases are sampled the model is reparameterized so that this additional term becomes estimable from the distribution of intervals from event to end of observation the exposure effect of primary interest may be estimated unbiasedl

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

the hurwitz theorem for bessel functions and antibound states in spectral theory an 1889 result of hurwitz is that the bessel function j v c v 0 c 0 has no zeros for 2 n v n 1 with integer n a new application of this result is given which describes the behaviour of jost functions and antibound states for one dimensional schrodinger equations with exponentially decaying potential a new hurwitz type theorem with similar applications is developed for hypergeometric functions extensions are obtained where the power series are terminated after 2 n 1 terms and larger zero free intervals 2 n v are found